Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : GRP455-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:07:47 AM UTC 2025

% Result   : Unsatisfiable 0.20s 0.41s
% Output   : Proof 0.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   42
%            Number of leaves      :   34
% Syntax   : Number of formulae    :  242 ( 212 unt;   0 typ;   0 def)
%            Number of atoms       :  278 ( 274 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   60 (  27   ~;  23   |;   0   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :   20 (   2 avg)
%            Number of FOOLs       :    3 (   3 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    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  118 ( 112   !;   0   ?; 118   :)

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

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

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

tff(divide_type,type,
    divide: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(22,plain,
    ( ~ ! [A: $i] : ( identity = divide(A,A) )
    | ( identity = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(23,plain,
    identity = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),
    inference(unit_resolution,[status(thm)],[22,16]) ).

tff(24,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))) = identity,
    inference(symmetry,[status(thm)],[23]) ).

tff(25,plain,
    divide(identity,identity) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),
    inference(monotonicity,[status(thm)],[18,18]) ).

tff(26,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[24,19]) ).

tff(27,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))) = identity,
    inference(transitivity,[status(thm)],[26,25,24]) ).

tff(28,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))) = divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))),
    inference(monotonicity,[status(thm)],[27]) ).

tff(29,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))),
    inference(monotonicity,[status(thm)],[28]) ).

tff(30,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))) = identity,
    inference(transitivity,[status(thm)],[29,21,19]) ).

tff(31,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,30]) ).

tff(32,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))) = identity,
    inference(transitivity,[status(thm)],[31,25,24]) ).

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

tff(34,plain,
    divide(identity,identity) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),
    inference(symmetry,[status(thm)],[33]) ).

tff(35,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))) = divide(identity,identity),
    inference(symmetry,[status(thm)],[25]) ).

tff(36,plain,
    identity = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),
    inference(transitivity,[status(thm)],[23,35,34]) ).

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

tff(38,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))) = divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))),
    inference(symmetry,[status(thm)],[37]) ).

tff(39,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(40,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),
    inference(unit_resolution,[status(thm)],[39,7]) ).

tff(41,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))),
    inference(symmetry,[status(thm)],[40]) ).

tff(42,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))) = divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))),
    inference(transitivity,[status(thm)],[41,38]) ).

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

tff(44,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))) = divide(divide(identity,a2),divide(identity,a2)),
    inference(unit_resolution,[status(thm)],[43,7]) ).

tff(45,plain,
    divide(identity,identity) = identity,
    inference(transitivity,[status(thm)],[25,24]) ).

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

tff(47,plain,
    divide(divide(identity,identity),identity) = identity,
    inference(transitivity,[status(thm)],[46,25,24]) ).

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

tff(49,plain,
    divide(a2,divide(divide(divide(identity,identity),identity),a2)) = divide(a2,divide(identity,a2)),
    inference(monotonicity,[status(thm)],[48]) ).

tff(50,plain,
    divide(a2,divide(identity,a2)) = divide(a2,divide(divide(divide(identity,identity),identity),a2)),
    inference(symmetry,[status(thm)],[49]) ).

tff(51,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2))) = divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))),
    inference(monotonicity,[status(thm)],[27,50]) ).

tff(52,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(divide(divide(identity,identity),identity),a2))) = divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))),
    inference(monotonicity,[status(thm)],[27]) ).

tff(53,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(divide(divide(identity,identity),identity),a2)))) = divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))),
    inference(monotonicity,[status(thm)],[19,52]) ).

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

tff(55,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))) = divide(divide(identity,a2),divide(identity,a2)),
    inference(transitivity,[status(thm)],[26,25,24,18]) ).

tff(56,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(divide(divide(identity,identity),identity),a2))))),
    inference(monotonicity,[status(thm)],[55,54]) ).

tff(57,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(divide(divide(identity,identity),identity),a2)))))),
    inference(monotonicity,[status(thm)],[19,56]) ).

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

tff(59,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(divide(divide(identity,identity),identity),a2)))),
    inference(transitivity,[status(thm)],[28,54]) ).

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

tff(61,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(divide(divide(identity,identity),identity),a2)))))),
    inference(monotonicity,[status(thm)],[19,60]) ).

tff(62,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))),
    inference(transitivity,[status(thm)],[61,58]) ).

tff(63,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),
    inference(monotonicity,[status(thm)],[18,62]) ).

tff(64,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),
    inference(symmetry,[status(thm)],[63]) ).

tff(65,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2)))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))),
    inference(monotonicity,[status(thm)],[64,51]) ).

tff(66,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2)))) = identity,
    inference(transitivity,[status(thm)],[65,44,19]) ).

tff(67,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2))))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,66]) ).

tff(68,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2))))) = identity,
    inference(transitivity,[status(thm)],[67,25,24]) ).

tff(69,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2)))))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[68]) ).

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

tff(71,plain,
    identity = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2)))))),
    inference(transitivity,[status(thm)],[23,35,70]) ).

tff(72,plain,
    divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2)))))),divide(a2,divide(identity,a2))),
    inference(monotonicity,[status(thm)],[71,49]) ).

tff(73,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2)))))),divide(a2,divide(identity,a2))) = divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))),
    inference(symmetry,[status(thm)],[72]) ).

tff(74,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2)))))),divide(a2,divide(identity,a2))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(75,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2)))))),divide(a2,divide(identity,a2))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),
    inference(unit_resolution,[status(thm)],[74,7]) ).

tff(76,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(a2,divide(identity,a2)))))),divide(a2,divide(identity,a2))),
    inference(symmetry,[status(thm)],[75]) ).

tff(77,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))) = divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))),
    inference(transitivity,[status(thm)],[76,73]) ).

tff(78,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))),
    inference(monotonicity,[status(thm)],[64,77]) ).

tff(79,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))) = identity,
    inference(transitivity,[status(thm)],[78,44,19]) ).

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

tff(81,plain,
    divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))),
    inference(monotonicity,[status(thm)],[80,42]) ).

tff(82,plain,
    divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))))) = identity,
    inference(transitivity,[status(thm)],[81,21,19]) ).

tff(83,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,82]) ).

tff(84,plain,
    divide(identity,identity) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))),
    inference(symmetry,[status(thm)],[83]) ).

tff(85,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),a2) = divide(divide(identity,a2),divide(identity,a2)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(86,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),a2) = divide(divide(identity,a2),divide(identity,a2)),
    inference(unit_resolution,[status(thm)],[85,7]) ).

tff(87,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))) = divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))),
    inference(transitivity,[status(thm)],[80,41,38]) ).

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

tff(89,plain,
    divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),a2) = a2,
    inference(transitivity,[status(thm)],[88,9]) ).

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

tff(91,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),a2)) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))),
    inference(transitivity,[status(thm)],[90,86,19,23,35,84]) ).

tff(92,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),a2))) = divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))))))),
    inference(monotonicity,[status(thm)],[91]) ).

tff(93,plain,
    divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),a2)))) = divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))),
    inference(monotonicity,[status(thm)],[92]) ).

tff(94,plain,
    divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))) = divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),a2)))),
    inference(symmetry,[status(thm)],[93]) ).

tff(95,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))) = divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(96,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))) = divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))),
    inference(unit_resolution,[status(thm)],[95,7]) ).

tff(97,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))))) = divide(divide(identity,a2),divide(identity,a2)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(98,plain,
    divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))))) = divide(divide(identity,a2),divide(identity,a2)),
    inference(unit_resolution,[status(thm)],[97,7]) ).

tff(99,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),
    inference(monotonicity,[status(thm)],[27]) ).

tff(100,plain,
    divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))))) = divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))))),
    inference(monotonicity,[status(thm)],[99]) ).

tff(101,plain,
    divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))))) = identity,
    inference(transitivity,[status(thm)],[100,98,19]) ).

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

tff(103,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))) = identity,
    inference(transitivity,[status(thm)],[102,25,24]) ).

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

tff(105,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))))))) = identity,
    inference(transitivity,[status(thm)],[104,25,24]) ).

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

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

tff(108,plain,
    divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))) = divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),a2)))),
    inference(transitivity,[status(thm)],[37,40,107,96,94]) ).

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

tff(110,plain,
    divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),a2)))),a2) = divide(divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))),a2),
    inference(symmetry,[status(thm)],[109]) ).

tff(111,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),a2)))),a2) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(112,plain,
    divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),a2)))),a2) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),
    inference(unit_resolution,[status(thm)],[111,7]) ).

tff(113,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,divide(a2,divide(divide(divide(identity,identity),identity),a2)))))))),a2)))),a2),
    inference(symmetry,[status(thm)],[112]) ).

tff(114,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2)))))),divide(divide(identity,a2),divide(identity,a2))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(115,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2)))))),divide(divide(identity,a2),divide(identity,a2))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),
    inference(unit_resolution,[status(thm)],[114,7]) ).

tff(116,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(identity,a2))) = divide(divide(identity,a2),divide(identity,a2)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(117,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(identity,a2))) = divide(divide(identity,a2),divide(identity,a2)),
    inference(unit_resolution,[status(thm)],[116,7]) ).

tff(118,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2)) = divide(identity,divide(identity,a2)),
    inference(monotonicity,[status(thm)],[27]) ).

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

tff(120,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2))) = identity,
    inference(transitivity,[status(thm)],[119,117,19]) ).

tff(121,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2)))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,120]) ).

tff(122,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2)))) = identity,
    inference(transitivity,[status(thm)],[121,25,24]) ).

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

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

tff(125,plain,
    identity = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2))))),
    inference(transitivity,[status(thm)],[23,35,124]) ).

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

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

tff(128,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2))))),divide(identity,a2)) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(129,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2))))),divide(identity,a2)) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),
    inference(unit_resolution,[status(thm)],[128,7]) ).

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

tff(131,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))) = divide(identity,divide(identity,a2)),
    inference(transitivity,[status(thm)],[130,127]) ).

tff(132,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2))))),divide(identity,a2)) = divide(divide(identity,a2),divide(identity,a2)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(133,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2))))),divide(identity,a2)) = divide(divide(identity,a2),divide(identity,a2)),
    inference(unit_resolution,[status(thm)],[132,7]) ).

tff(134,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2) = divide(identity,a2),
    inference(monotonicity,[status(thm)],[27]) ).

tff(135,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)) = divide(identity,divide(identity,a2)),
    inference(monotonicity,[status(thm)],[19,134]) ).

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

tff(137,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),
    inference(monotonicity,[status(thm)],[55,136]) ).

tff(138,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),
    inference(monotonicity,[status(thm)],[19,137]) ).

tff(139,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))),
    inference(symmetry,[status(thm)],[138]) ).

tff(140,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2)) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)),
    inference(transitivity,[status(thm)],[118,136]) ).

tff(141,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),
    inference(monotonicity,[status(thm)],[140]) ).

tff(142,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2)))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),
    inference(monotonicity,[status(thm)],[19,141]) ).

tff(143,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2)))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))),
    inference(transitivity,[status(thm)],[142,139]) ).

tff(144,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),
    inference(monotonicity,[status(thm)],[18,143]) ).

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

tff(146,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,a2))))),divide(identity,a2)),
    inference(monotonicity,[status(thm)],[145,134]) ).

tff(147,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)) = identity,
    inference(transitivity,[status(thm)],[146,133,19]) ).

tff(148,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,147]) ).

tff(149,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))) = identity,
    inference(transitivity,[status(thm)],[148,25,24]) ).

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

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

tff(152,plain,
    identity = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),
    inference(transitivity,[status(thm)],[23,35,151]) ).

tff(153,plain,
    divide(identity,a2) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),a2),
    inference(monotonicity,[status(thm)],[152]) ).

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

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

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

tff(157,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),a2),
    inference(symmetry,[status(thm)],[156]) ).

tff(158,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))) = divide(identity,a2),
    inference(transitivity,[status(thm)],[157,154]) ).

tff(159,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))) = divide(divide(identity,a2),divide(identity,a2)),
    inference(monotonicity,[status(thm)],[158,158]) ).

tff(160,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))) = identity,
    inference(transitivity,[status(thm)],[159,19]) ).

tff(161,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),
    inference(monotonicity,[status(thm)],[160]) ).

tff(162,plain,
    divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(identity,a2))),
    inference(monotonicity,[status(thm)],[161,131]) ).

tff(163,plain,
    divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))) = identity,
    inference(transitivity,[status(thm)],[162,117,19]) ).

tff(164,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,163]) ).

tff(165,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))) = divide(divide(identity,a2),divide(identity,a2)),
    inference(transitivity,[status(thm)],[164,25,24,18]) ).

tff(166,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))) = divide(divide(identity,a2),divide(identity,a2)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(167,plain,
    divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))) = divide(divide(identity,a2),divide(identity,a2)),
    inference(unit_resolution,[status(thm)],[166,7]) ).

tff(168,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),
    inference(monotonicity,[status(thm)],[27]) ).

tff(169,plain,
    divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))) = divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))),
    inference(monotonicity,[status(thm)],[168]) ).

tff(170,plain,
    divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))) = identity,
    inference(transitivity,[status(thm)],[169,167,19]) ).

tff(171,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,170]) ).

tff(172,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))) = identity,
    inference(transitivity,[status(thm)],[171,25,24]) ).

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

tff(174,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))) = identity,
    inference(transitivity,[status(thm)],[173,25,24]) ).

tff(175,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),
    inference(monotonicity,[status(thm)],[174]) ).

tff(176,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(177,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),
    inference(unit_resolution,[status(thm)],[176,7]) ).

tff(178,plain,
    divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),
    inference(symmetry,[status(thm)],[177]) ).

tff(179,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))) = divide(divide(identity,a2),divide(identity,a2)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(180,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))) = divide(divide(identity,a2),divide(identity,a2)),
    inference(unit_resolution,[status(thm)],[179,7]) ).

tff(181,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),
    inference(monotonicity,[status(thm)],[55,139]) ).

tff(182,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),
    inference(monotonicity,[status(thm)],[19,181]) ).

tff(183,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)),
    inference(transitivity,[status(thm)],[182,130,127,136]) ).

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

tff(185,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),
    inference(monotonicity,[status(thm)],[184]) ).

tff(186,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),
    inference(symmetry,[status(thm)],[185]) ).

tff(187,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(divide(identity,a2),divide(identity,a2)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(188,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(divide(identity,a2),divide(identity,a2)),
    inference(unit_resolution,[status(thm)],[187,7]) ).

tff(189,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))),
    inference(symmetry,[status(thm)],[182]) ).

tff(190,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))),
    inference(transitivity,[status(thm)],[168,139]) ).

tff(191,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),
    inference(monotonicity,[status(thm)],[190]) ).

tff(192,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),
    inference(monotonicity,[status(thm)],[19,191]) ).

tff(193,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))),
    inference(transitivity,[status(thm)],[192,189]) ).

tff(194,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))),
    inference(monotonicity,[status(thm)],[18,193]) ).

tff(195,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))),
    inference(symmetry,[status(thm)],[194]) ).

tff(196,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))),
    inference(symmetry,[status(thm)],[184]) ).

tff(197,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))))),
    inference(transitivity,[status(thm)],[196,195]) ).

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

tff(199,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = identity,
    inference(transitivity,[status(thm)],[198,188,19]) ).

tff(200,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),
    inference(monotonicity,[status(thm)],[199]) ).

tff(201,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),
    inference(transitivity,[status(thm)],[200,186]) ).

tff(202,plain,
    divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))),
    inference(monotonicity,[status(thm)],[201]) ).

tff(203,plain,
    divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))))) = identity,
    inference(transitivity,[status(thm)],[202,180,19]) ).

tff(204,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,203]) ).

tff(205,plain,
    divide(identity,identity) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))),
    inference(symmetry,[status(thm)],[204]) ).

tff(206,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[27,19]) ).

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

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

tff(209,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))))) = divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2)))))))),
    inference(monotonicity,[status(thm)],[19,208]) ).

tff(210,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))),
    inference(transitivity,[status(thm)],[209,178,175,139]) ).

tff(211,plain,
    divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2)))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),
    inference(monotonicity,[status(thm)],[18,210]) ).

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

tff(213,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))))) = divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2)))))),divide(divide(identity,a2),divide(identity,a2))),
    inference(monotonicity,[status(thm)],[212,165]) ).

tff(214,plain,
    divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))))) = divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),a2))),
    inference(transitivity,[status(thm)],[213,115]) ).

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

tff(216,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))) = divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(217,plain,
    divide(divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))) = divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),
    inference(unit_resolution,[status(thm)],[216,7]) ).

tff(218,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B )
    | ( divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))) = divide(divide(identity,a2),divide(identity,a2)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(219,plain,
    divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))) = divide(divide(identity,a2),divide(identity,a2)),
    inference(unit_resolution,[status(thm)],[218,7]) ).

tff(220,plain,
    divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),
    inference(monotonicity,[status(thm)],[27]) ).

tff(221,plain,
    divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))) = divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))),
    inference(monotonicity,[status(thm)],[220]) ).

tff(222,plain,
    divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))) = identity,
    inference(transitivity,[status(thm)],[221,219,19]) ).

tff(223,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))) = divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,222]) ).

tff(224,plain,
    divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))) = identity,
    inference(transitivity,[status(thm)],[223,25,24]) ).

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

tff(226,plain,
    divide(identity,identity) = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))))),
    inference(symmetry,[status(thm)],[225]) ).

tff(227,plain,
    identity = divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))),divide(identity,divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2)))))))))),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(identity,a2))),divide(divide(identity,a2),divide(identity,a2))),divide(identity,divide(identity,a2))))))))),
    inference(transitivity,[status(thm)],[23,35,226]) ).

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

tff(229,plain,
    ^ [B: $i,A: $i] :
      refl(( ( multiply(A,B) = divide(A,divide(identity,B)) )
      <=> ( multiply(A,B) = divide(A,divide(identity,B)) ) )),
    inference(bind,[status(th)],[]) ).

tff(230,plain,
    ( ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
  <=> ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ) ),
    inference(quant_intro,[status(thm)],[229]) ).

tff(231,plain,
    ( ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
  <=> ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(232,axiom,
    ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).

tff(233,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
    inference(modus_ponens,[status(thm)],[232,231]) ).

tff(234,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
    inference(skolemize,[status(sab)],[233]) ).

tff(235,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
    inference(modus_ponens,[status(thm)],[234,230]) ).

tff(236,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
    | ( multiply(identity,a2) = divide(identity,divide(identity,a2)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(237,plain,
    multiply(identity,a2) = divide(identity,divide(identity,a2)),
    inference(unit_resolution,[status(thm)],[236,235]) ).

tff(238,plain,
    multiply(identity,a2) = a2,
    inference(transitivity,[status(thm)],[237,126,129,228,217,215,113,110,9]) ).

tff(239,plain,
    ( ( multiply(identity,a2) != a2 )
  <=> ( multiply(identity,a2) != a2 ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(240,axiom,
    multiply(identity,a2) != a2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).

tff(241,plain,
    multiply(identity,a2) != a2,
    inference(modus_ponens,[status(thm)],[240,239]) ).

tff(242,plain,
    $false,
    inference(unit_resolution,[status(thm)],[241,238]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11  % Problem    : GRP455-1 : TPTP v9.0.0. Released v2.6.0.
% 0.08/0.11  % Command    : run_E %s %d THM
% 0.13/0.32  % Computer : n006.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit   : 300
% 0.13/0.32  % WCLimit    : 300
% 0.13/0.32  % DateTime   : Thu Jun 19 16:07:35 EDT 2025
% 0.13/0.32  % CPUTime    : 
% 0.20/0.41  % SZS status Unsatisfiable
% 0.20/0.41  % SZS output start Proof
% See solution above
% 0.48/0.63  % E exiting
%------------------------------------------------------------------------------