Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : GRP115-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n003.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 05:07:01 AM UTC 2025

% Result   : Unsatisfiable 0.50s 0.70s
% Output   : Proof 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   55
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  371 ( 324 unt;   0 typ;   0 def)
%            Number of atoms       :  420 ( 418 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   96 (  48   ~;  44   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :   25 (   3 avg)
%            Number of FOOLs       :    1 (   1 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    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :  159 ( 156   !;   0   ?; 159   :)

% Comments : 
%------------------------------------------------------------------------------
tff(identity_type,type,
    identity: $i ).

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

tff(a_type,type,
    a: $i ).

tff(1,plain,
    ^ [Z: $i,Y: $i,X: $i] :
      refl(( ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
      <=> ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y ) )),
    inference(bind,[status(th)],[]) ).

tff(2,plain,
    ( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
  <=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
  <=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(4,axiom,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

tff(5,plain,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = identity ) ),
    inference(quant_inst,[status(thm)],[]) ).

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

tff(10,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))) = multiply(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(11,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))) = multiply(identity,identity),
    inference(unit_resolution,[status(thm)],[10,7]) ).

tff(12,plain,
    multiply(identity,identity) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),
    inference(symmetry,[status(thm)],[11]) ).

tff(13,plain,
    multiply(multiply(identity,identity),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(monotonicity,[status(thm)],[12]) ).

tff(14,plain,
    multiply(identity,multiply(multiply(identity,identity),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(monotonicity,[status(thm)],[13]) ).

tff(15,plain,
    multiply(multiply(identity,multiply(multiply(identity,identity),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[14]) ).

tff(16,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[15]) ).

tff(17,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(symmetry,[status(thm)],[16]) ).

tff(18,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(19,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(unit_resolution,[status(thm)],[18,7]) ).

tff(20,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

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

tff(22,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(a,a) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(23,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(a,a),
    inference(unit_resolution,[status(thm)],[22,7]) ).

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

tff(25,plain,
    multiply(multiply(a,a),multiply(a,a)) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[24,24]) ).

tff(26,plain,
    multiply(identity,multiply(multiply(a,a),multiply(a,a))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[25]) ).

tff(27,plain,
    multiply(identity,multiply(multiply(a,a),multiply(a,a))) = multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),
    inference(transitivity,[status(thm)],[26,21]) ).

tff(28,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(29,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),
    inference(unit_resolution,[status(thm)],[28,7]) ).

tff(30,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(symmetry,[status(thm)],[29]) ).

tff(31,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))) = identity,
    inference(transitivity,[status(thm)],[30,17,9]) ).

tff(32,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(monotonicity,[status(thm)],[31]) ).

tff(33,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a)) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[32,24]) ).

tff(34,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[31,33]) ).

tff(35,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))) = identity,
    inference(transitivity,[status(thm)],[34,17,9]) ).

tff(36,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a)))) = multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),
    inference(monotonicity,[status(thm)],[35,27]) ).

tff(37,plain,
    multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a)))),
    inference(symmetry,[status(thm)],[36]) ).

tff(38,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

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

tff(40,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))),
    inference(monotonicity,[status(thm)],[39,37]) ).

tff(41,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(transitivity,[status(thm)],[40,19]) ).

tff(42,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(monotonicity,[status(thm)],[31,41]) ).

tff(43,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[42]) ).

tff(44,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(symmetry,[status(thm)],[43]) ).

tff(45,plain,
    identity = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(symmetry,[status(thm)],[9]) ).

tff(46,plain,
    identity = multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),
    inference(transitivity,[status(thm)],[45,16,29]) ).

tff(47,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[46,44]) ).

tff(48,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(symmetry,[status(thm)],[47]) ).

tff(49,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(50,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))),
    inference(unit_resolution,[status(thm)],[49,7]) ).

tff(51,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(symmetry,[status(thm)],[50]) ).

tff(52,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(53,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))),
    inference(unit_resolution,[status(thm)],[52,7]) ).

tff(54,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(55,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(identity,identity),
    inference(unit_resolution,[status(thm)],[54,7]) ).

tff(56,plain,
    multiply(identity,identity) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),
    inference(symmetry,[status(thm)],[55]) ).

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

tff(58,plain,
    multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))),
    inference(monotonicity,[status(thm)],[57]) ).

tff(59,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))),
    inference(symmetry,[status(thm)],[58]) ).

tff(60,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(61,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),
    inference(unit_resolution,[status(thm)],[60,7]) ).

tff(62,plain,
    multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))),
    inference(symmetry,[status(thm)],[61]) ).

tff(63,plain,
    multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))) = multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))),
    inference(transitivity,[status(thm)],[62,59]) ).

tff(64,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))) = multiply(identity,identity),
    inference(monotonicity,[status(thm)],[31,31]) ).

tff(65,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),
    inference(transitivity,[status(thm)],[64,56]) ).

tff(66,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity)) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))),
    inference(monotonicity,[status(thm)],[65,56]) ).

tff(67,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))),
    inference(monotonicity,[status(thm)],[31,66]) ).

tff(68,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),
    inference(symmetry,[status(thm)],[67]) ).

tff(69,plain,
    multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),
    inference(transitivity,[status(thm)],[62,68]) ).

tff(70,plain,
    multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))),
    inference(monotonicity,[status(thm)],[69,63]) ).

tff(71,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[46,70]) ).

tff(72,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = identity,
    inference(transitivity,[status(thm)],[71,39,30,17,9]) ).

tff(73,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(74,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(unit_resolution,[status(thm)],[73,7]) ).

tff(75,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))) = multiply(identity,multiply(identity,identity)),
    inference(monotonicity,[status(thm)],[64]) ).

tff(76,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[31]) ).

tff(77,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = identity,
    inference(transitivity,[status(thm)],[76,17,9]) ).

tff(78,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))) = multiply(identity,identity),
    inference(monotonicity,[status(thm)],[77,31]) ).

tff(79,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))) = multiply(identity,multiply(identity,identity)),
    inference(monotonicity,[status(thm)],[31,78]) ).

tff(80,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))))) = multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),
    inference(monotonicity,[status(thm)],[79,75]) ).

tff(81,plain,
    multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))))),
    inference(symmetry,[status(thm)],[80]) ).

tff(82,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[46,81]) ).

tff(83,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))) = identity,
    inference(transitivity,[status(thm)],[39,30,17,9]) ).

tff(84,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))) = multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),
    inference(monotonicity,[status(thm)],[83]) ).

tff(85,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(transitivity,[status(thm)],[84,82,74]) ).

tff(86,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[31,85]) ).

tff(87,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = identity,
    inference(transitivity,[status(thm)],[86,17,9]) ).

tff(88,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(identity,identity),
    inference(monotonicity,[status(thm)],[87,72]) ).

tff(89,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(identity,multiply(identity,identity)),
    inference(monotonicity,[status(thm)],[31,88]) ).

tff(90,plain,
    multiply(identity,multiply(identity,identity)) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))),
    inference(symmetry,[status(thm)],[89]) ).

tff(91,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))) = multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),
    inference(monotonicity,[status(thm)],[77]) ).

tff(92,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(transitivity,[status(thm)],[91,82,74]) ).

tff(93,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[31,92]) ).

tff(94,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = identity,
    inference(transitivity,[status(thm)],[93,17,9]) ).

tff(95,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(identity,identity),
    inference(monotonicity,[status(thm)],[94,72]) ).

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

tff(97,plain,
    multiply(identity,multiply(identity,identity)) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))),
    inference(monotonicity,[status(thm)],[46,96]) ).

tff(98,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(identity,multiply(identity,identity)),
    inference(symmetry,[status(thm)],[97]) ).

tff(99,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(100,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(unit_resolution,[status(thm)],[99,7]) ).

tff(101,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))),
    inference(symmetry,[status(thm)],[100]) ).

tff(102,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(103,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(unit_resolution,[status(thm)],[102,7]) ).

tff(104,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))))) = multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),
    inference(symmetry,[status(thm)],[82]) ).

tff(105,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))))))),
    inference(symmetry,[status(thm)],[74]) ).

tff(106,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))),
    inference(symmetry,[status(thm)],[53]) ).

tff(107,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),
    inference(transitivity,[status(thm)],[55,12]) ).

tff(108,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(monotonicity,[status(thm)],[107]) ).

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

tff(110,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[109]) ).

tff(111,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[110]) ).

tff(112,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(113,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(unit_resolution,[status(thm)],[112,7]) ).

tff(114,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(symmetry,[status(thm)],[113]) ).

tff(115,plain,
    identity = multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),
    inference(transitivity,[status(thm)],[45,16,47,50,106,89,97,100,105,104]) ).

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

tff(117,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),
    inference(transitivity,[status(thm)],[105,104]) ).

tff(118,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[117,117]) ).

tff(119,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = identity,
    inference(transitivity,[status(thm)],[118,114,111,17,9]) ).

tff(120,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(identity,identity),
    inference(monotonicity,[status(thm)],[119]) ).

tff(121,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),
    inference(transitivity,[status(thm)],[120,116,114,111,47,50,106,89,97,100,105,104]) ).

tff(122,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(identity,multiply(identity,identity)),
    inference(transitivity,[status(thm)],[71,39,30,47,50,106,89]) ).

tff(123,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(124,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(unit_resolution,[status(thm)],[123,7]) ).

tff(125,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),
    inference(transitivity,[status(thm)],[120,56]) ).

tff(126,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[77]) ).

tff(127,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = identity,
    inference(transitivity,[status(thm)],[126,17,9]) ).

tff(128,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(identity,identity),
    inference(monotonicity,[status(thm)],[31,127]) ).

tff(129,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),
    inference(transitivity,[status(thm)],[128,56]) ).

tff(130,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))),
    inference(monotonicity,[status(thm)],[129,125]) ).

tff(131,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))))),
    inference(symmetry,[status(thm)],[130]) ).

tff(132,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))),
    inference(monotonicity,[status(thm)],[46,131]) ).

tff(133,plain,
    multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))) = identity,
    inference(transitivity,[status(thm)],[58,132,124,101,98,90,53,51,48,17,9]) ).

tff(134,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))) = multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(135,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))) = multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))),
    inference(unit_resolution,[status(thm)],[134,7]) ).

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

tff(137,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(138,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))),
    inference(unit_resolution,[status(thm)],[137,7]) ).

tff(139,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity)) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))),
    inference(monotonicity,[status(thm)],[56]) ).

tff(140,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))),
    inference(monotonicity,[status(thm)],[139]) ).

tff(141,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),
    inference(transitivity,[status(thm)],[140,138,136]) ).

tff(142,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity),
    inference(monotonicity,[status(thm)],[141,133]) ).

tff(143,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))),
    inference(symmetry,[status(thm)],[142]) ).

tff(144,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[143]) ).

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

tff(146,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),
    inference(symmetry,[status(thm)],[140]) ).

tff(147,plain,
    multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))),
    inference(symmetry,[status(thm)],[138]) ).

tff(148,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))) = multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(149,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))) = multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))),
    inference(unit_resolution,[status(thm)],[148,7]) ).

tff(150,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),
    inference(transitivity,[status(thm)],[149,147,146]) ).

tff(151,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))),
    inference(monotonicity,[status(thm)],[150,63]) ).

tff(152,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[151]) ).

tff(153,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),
    inference(transitivity,[status(thm)],[152,145]) ).

tff(154,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))),
    inference(monotonicity,[status(thm)],[153,122]) ).

tff(155,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(symmetry,[status(thm)],[71]) ).

tff(156,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),
    inference(symmetry,[status(thm)],[39]) ).

tff(157,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(transitivity,[status(thm)],[101,98,90,53,51,48,29,156,155]) ).

tff(158,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(symmetry,[status(thm)],[152]) ).

tff(159,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(160,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(unit_resolution,[status(thm)],[159,7]) ).

tff(161,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),
    inference(symmetry,[status(thm)],[160]) ).

tff(162,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))) = a ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(163,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))) = a,
    inference(unit_resolution,[status(thm)],[162,7]) ).

tff(164,plain,
    a = multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),
    inference(symmetry,[status(thm)],[163]) ).

tff(165,plain,
    multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[164,117]) ).

tff(166,plain,
    multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(transitivity,[status(thm)],[165,161,158]) ).

tff(167,plain,
    multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),
    inference(monotonicity,[status(thm)],[166,157]) ).

tff(168,plain,
    multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))),
    inference(transitivity,[status(thm)],[167,154]) ).

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

tff(170,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[169,121]) ).

tff(171,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))))),
    inference(symmetry,[status(thm)],[170]) ).

tff(172,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))),
    inference(monotonicity,[status(thm)],[171]) ).

tff(173,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(174,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity),
    inference(unit_resolution,[status(thm)],[173,7]) ).

tff(175,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),
    inference(symmetry,[status(thm)],[174]) ).

tff(176,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))),
    inference(symmetry,[status(thm)],[132]) ).

tff(177,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))),
    inference(symmetry,[status(thm)],[124]) ).

tff(178,plain,
    multiply(identity,multiply(identity,identity)) = multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))),
    inference(transitivity,[status(thm)],[97,100,177,176,59]) ).

tff(179,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

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

tff(181,plain,
    multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),
    inference(symmetry,[status(thm)],[149]) ).

tff(182,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),
    inference(transitivity,[status(thm)],[135,181]) ).

tff(183,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),a) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a),
    inference(monotonicity,[status(thm)],[182]) ).

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

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

tff(186,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),a)),multiply(identity,multiply(a,a)))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),
    inference(monotonicity,[status(thm)],[185]) ).

tff(187,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),a)),multiply(identity,multiply(a,a)))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity)))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

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

tff(189,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity)))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),a)),multiply(identity,multiply(a,a)))),
    inference(symmetry,[status(thm)],[188]) ).

tff(190,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity)))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(191,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity)))))),
    inference(unit_resolution,[status(thm)],[190,7]) ).

tff(192,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(193,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))),
    inference(unit_resolution,[status(thm)],[192,7]) ).

tff(194,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity)))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),
    inference(symmetry,[status(thm)],[191]) ).

tff(195,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),a)),multiply(identity,multiply(a,a)))),
    inference(symmetry,[status(thm)],[186]) ).

tff(196,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),
    inference(transitivity,[status(thm)],[195,188,194]) ).

tff(197,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[196]) ).

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

tff(199,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))),
    inference(monotonicity,[status(thm)],[198]) ).

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

tff(201,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(202,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a))),
    inference(unit_resolution,[status(thm)],[201,7]) ).

tff(203,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))),
    inference(symmetry,[status(thm)],[202]) ).

tff(204,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(205,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a))),
    inference(unit_resolution,[status(thm)],[204,7]) ).

tff(206,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(207,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(unit_resolution,[status(thm)],[206,7]) ).

tff(208,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(transitivity,[status(thm)],[120,116,114,111,29,156,155]) ).

tff(209,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity)) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))),
    inference(monotonicity,[status(thm)],[56]) ).

tff(210,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))),
    inference(monotonicity,[status(thm)],[209]) ).

tff(211,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),
    inference(symmetry,[status(thm)],[210]) ).

tff(212,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),
    inference(transitivity,[status(thm)],[205,203,200,211]) ).

tff(213,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))),
    inference(monotonicity,[status(thm)],[212,63]) ).

tff(214,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[213]) ).

tff(215,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(symmetry,[status(thm)],[214]) ).

tff(216,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))),
    inference(transitivity,[status(thm)],[177,176,59]) ).

tff(217,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))),
    inference(symmetry,[status(thm)],[193]) ).

tff(218,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

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

tff(220,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),
    inference(transitivity,[status(thm)],[219,217,211]) ).

tff(221,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))),
    inference(monotonicity,[status(thm)],[220,216]) ).

tff(222,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[221]) ).

tff(223,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(transitivity,[status(thm)],[222,215]) ).

tff(224,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),
    inference(monotonicity,[status(thm)],[223,208]) ).

tff(225,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))))),
    inference(symmetry,[status(thm)],[224]) ).

tff(226,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))),
    inference(monotonicity,[status(thm)],[225]) ).

tff(227,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))),
    inference(symmetry,[status(thm)],[226]) ).

tff(228,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(229,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(unit_resolution,[status(thm)],[228,7]) ).

tff(230,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))))),
    inference(symmetry,[status(thm)],[229]) ).

tff(231,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))) = multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),
    inference(monotonicity,[status(thm)],[77]) ).

tff(232,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a)))),
    inference(transitivity,[status(thm)],[231,37]) ).

tff(233,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))),
    inference(monotonicity,[status(thm)],[232]) ).

tff(234,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(symmetry,[status(thm)],[233]) ).

tff(235,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(multiply(identity,multiply(identity,identity)),a) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(236,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(multiply(identity,multiply(identity,identity)),a),
    inference(unit_resolution,[status(thm)],[235,7]) ).

tff(237,plain,
    multiply(multiply(identity,multiply(identity,identity)),a) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(symmetry,[status(thm)],[236]) ).

tff(238,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(identity,multiply(identity,identity)),
    inference(transitivity,[status(thm)],[101,98]) ).

tff(239,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a) = multiply(multiply(identity,multiply(identity,identity)),a),
    inference(monotonicity,[status(thm)],[238]) ).

tff(240,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(transitivity,[status(thm)],[239,237]) ).

tff(241,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a)) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[240,24]) ).

tff(242,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a)) = multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),
    inference(transitivity,[status(thm)],[241,105,104]) ).

tff(243,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a))) = multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[117,242]) ).

tff(244,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a))) = identity,
    inference(transitivity,[status(thm)],[243,114,111,17,9]) ).

tff(245,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a)))) = multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),
    inference(monotonicity,[status(thm)],[244,27]) ).

tff(246,plain,
    multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a)))),
    inference(symmetry,[status(thm)],[245]) ).

tff(247,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a)))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a)))),
    inference(transitivity,[status(thm)],[36,246]) ).

tff(248,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(transitivity,[status(thm)],[30,47,50,106,89,97,100]) ).

tff(249,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))),
    inference(monotonicity,[status(thm)],[248,247]) ).

tff(250,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))),
    inference(symmetry,[status(thm)],[249]) ).

tff(251,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = a ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(252,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = a,
    inference(unit_resolution,[status(thm)],[251,7]) ).

tff(253,plain,
    a = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))),
    inference(symmetry,[status(thm)],[252]) ).

tff(254,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = a ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(255,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = a,
    inference(unit_resolution,[status(thm)],[254,7]) ).

tff(256,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(identity,multiply(multiply(a,a),multiply(a,a))),
    inference(symmetry,[status(thm)],[26]) ).

tff(257,plain,
    multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(symmetry,[status(thm)],[21]) ).

tff(258,plain,
    multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))) = multiply(identity,multiply(multiply(a,a),multiply(a,a))),
    inference(transitivity,[status(thm)],[257,256]) ).

tff(259,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(a,a) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(260,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(a,a),
    inference(unit_resolution,[status(thm)],[259,7]) ).

tff(261,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a) = multiply(a,a),
    inference(monotonicity,[status(thm)],[163]) ).

tff(262,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)) = multiply(a,multiply(a,a)),
    inference(monotonicity,[status(thm)],[261]) ).

tff(263,plain,
    multiply(a,multiply(a,a)) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),
    inference(symmetry,[status(thm)],[262]) ).

tff(264,plain,
    multiply(multiply(a,multiply(a,a)),multiply(identity,multiply(a,a))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a))),
    inference(monotonicity,[status(thm)],[263]) ).

tff(265,plain,
    multiply(a,multiply(multiply(a,multiply(a,a)),multiply(identity,multiply(a,a)))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),
    inference(monotonicity,[status(thm)],[264]) ).

tff(266,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))) = multiply(a,multiply(multiply(a,multiply(a,a)),multiply(identity,multiply(a,a)))),
    inference(symmetry,[status(thm)],[265]) ).

tff(267,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(monotonicity,[status(thm)],[266]) ).

tff(268,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(monotonicity,[status(thm)],[267]) ).

tff(269,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(transitivity,[status(thm)],[268,260,24]) ).

tff(270,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[269]) ).

tff(271,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(symmetry,[status(thm)],[270]) ).

tff(272,plain,
    multiply(multiply(a,a),multiply(a,a)) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(transitivity,[status(thm)],[25,271]) ).

tff(273,plain,
    multiply(a,multiply(multiply(a,a),multiply(a,a))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[272]) ).

tff(274,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(a,multiply(multiply(a,a),multiply(a,a))),
    inference(symmetry,[status(thm)],[273]) ).

tff(275,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(276,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a))),
    inference(unit_resolution,[status(thm)],[275,7]) ).

tff(277,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(symmetry,[status(thm)],[276]) ).

tff(278,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))) = multiply(a,multiply(multiply(a,a),multiply(a,a))),
    inference(transitivity,[status(thm)],[191,189,186,180,277,274]) ).

tff(279,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))) = multiply(multiply(a,multiply(multiply(a,a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a)))),
    inference(monotonicity,[status(thm)],[278,258]) ).

tff(280,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))),
    inference(monotonicity,[status(thm)],[279]) ).

tff(281,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(transitivity,[status(thm)],[280,255,253,250,234]) ).

tff(282,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(monotonicity,[status(thm)],[281]) ).

tff(283,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(symmetry,[status(thm)],[282]) ).

tff(284,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(285,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(unit_resolution,[status(thm)],[284,7]) ).

tff(286,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(monotonicity,[status(thm)],[119]) ).

tff(287,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(a,a),
    inference(transitivity,[status(thm)],[286,23]) ).

tff(288,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = identity,
    inference(transitivity,[status(thm)],[101,98,90,53,51,48,17,9]) ).

tff(289,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(identity,multiply(a,a)),
    inference(monotonicity,[status(thm)],[288,287]) ).

tff(290,plain,
    multiply(identity,multiply(a,a)) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(symmetry,[status(thm)],[289]) ).

tff(291,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(292,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(unit_resolution,[status(thm)],[291,7]) ).

tff(293,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),
    inference(transitivity,[status(thm)],[101,98,90,53,51,48,29]) ).

tff(294,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[293]) ).

tff(295,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = identity,
    inference(transitivity,[status(thm)],[294,292,101,98,90,53,51,48,17,9]) ).

tff(296,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(monotonicity,[status(thm)],[295]) ).

tff(297,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(a,a),
    inference(transitivity,[status(thm)],[296,23]) ).

tff(298,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(identity,multiply(a,a)),
    inference(monotonicity,[status(thm)],[288,297]) ).

tff(299,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(transitivity,[status(thm)],[298,290]) ).

tff(300,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[299]) ).

tff(301,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),
    inference(monotonicity,[status(thm)],[300]) ).

tff(302,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),
    inference(symmetry,[status(thm)],[301]) ).

tff(303,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(304,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(unit_resolution,[status(thm)],[303,7]) ).

tff(305,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),
    inference(symmetry,[status(thm)],[304]) ).

tff(306,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(transitivity,[status(thm)],[82,74,305,302,285,283,230,227,207]) ).

tff(307,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[163,306]) ).

tff(308,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))),
    inference(transitivity,[status(thm)],[307,205,203,200,193]) ).

tff(309,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),
    inference(monotonicity,[status(thm)],[308]) ).

tff(310,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(multiply(a,a),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(311,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(multiply(a,a),identity),
    inference(unit_resolution,[status(thm)],[310,7]) ).

tff(312,plain,
    multiply(multiply(a,a),identity) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),
    inference(symmetry,[status(thm)],[311]) ).

tff(313,plain,
    multiply(multiply(a,a),identity) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a))),
    inference(transitivity,[status(thm)],[312,309,191,189,186,180]) ).

tff(314,plain,
    multiply(a,multiply(multiply(a,a),identity)) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),
    inference(monotonicity,[status(thm)],[313]) ).

tff(315,plain,
    multiply(a,multiply(multiply(a,a),identity)) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),
    inference(transitivity,[status(thm)],[314,149,147,146]) ).

tff(316,plain,
    multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))),
    inference(monotonicity,[status(thm)],[315,178]) ).

tff(317,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(318,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))) = multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))),
    inference(unit_resolution,[status(thm)],[317,7]) ).

tff(319,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(monotonicity,[status(thm)],[31]) ).

tff(320,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a)) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[319,24]) ).

tff(321,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[31,320]) ).

tff(322,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),
    inference(symmetry,[status(thm)],[321]) ).

tff(323,plain,
    multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),
    inference(transitivity,[status(thm)],[257,322]) ).

tff(324,plain,
    multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a)))),
    inference(monotonicity,[status(thm)],[323,258]) ).

tff(325,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))),
    inference(monotonicity,[status(thm)],[46,324]) ).

tff(326,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(symmetry,[status(thm)],[325]) ).

tff(327,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(328,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(unit_resolution,[status(thm)],[327,7]) ).

tff(329,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))),
    inference(symmetry,[status(thm)],[328]) ).

tff(330,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(transitivity,[status(thm)],[329,326]) ).

tff(331,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(332,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(unit_resolution,[status(thm)],[331,7]) ).

tff(333,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),a)),multiply(identity,multiply(a,a)))),
    inference(symmetry,[status(thm)],[180]) ).

tff(334,plain,
    multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[271]) ).

tff(335,plain,
    multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),
    inference(transitivity,[status(thm)],[334,276,333,195,188,194]) ).

tff(336,plain,
    multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[335]) ).

tff(337,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),
    inference(monotonicity,[status(thm)],[336]) ).

tff(338,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))))),
    inference(monotonicity,[status(thm)],[337]) ).

tff(339,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))),
    inference(monotonicity,[status(thm)],[338]) ).

tff(340,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))))),
    inference(symmetry,[status(thm)],[339]) ).

tff(341,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))) = multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(transitivity,[status(thm)],[217,340,332]) ).

tff(342,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[31,341]) ).

tff(343,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),
    inference(transitivity,[status(thm)],[342,322]) ).

tff(344,plain,
    multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a)))),
    inference(monotonicity,[status(thm)],[343,258]) ).

tff(345,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))),
    inference(monotonicity,[status(thm)],[344]) ).

tff(346,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(symmetry,[status(thm)],[345]) ).

tff(347,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(transitivity,[status(thm)],[329,346]) ).

tff(348,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(monotonicity,[status(thm)],[347,330]) ).

tff(349,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[46,348]) ).

tff(350,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(symmetry,[status(thm)],[349]) ).

tff(351,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y )
    | ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(352,plain,
    multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))),
    inference(unit_resolution,[status(thm)],[351,7]) ).

tff(353,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),a)),multiply(identity,multiply(a,a))),multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(symmetry,[status(thm)],[352]) ).

tff(354,plain,
    multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity))) = multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))),
    inference(transitivity,[status(thm)],[316,142,175,172,103,105,104]) ).

tff(355,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity))))),
    inference(monotonicity,[status(thm)],[164,354]) ).

tff(356,plain,
    a = multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(transitivity,[status(thm)],[164,355,307,205,203,200,193,353,350]) ).

tff(357,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(symmetry,[status(thm)],[280]) ).

tff(358,plain,
    a = multiply(a,multiply(multiply(a,multiply(multiply(a,a),multiply(a,a))),multiply(identity,multiply(multiply(a,a),multiply(a,a))))),
    inference(symmetry,[status(thm)],[255]) ).

tff(359,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),
    inference(transitivity,[status(thm)],[163,358,357]) ).

tff(360,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))),
    inference(monotonicity,[status(thm)],[359,330]) ).

tff(361,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(monotonicity,[status(thm)],[360]) ).

tff(362,plain,
    multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(symmetry,[status(thm)],[361]) ).

tff(363,plain,
    multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity))) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))),multiply(identity,multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))),multiply(multiply(a,multiply(multiply(a,multiply(a,multiply(multiply(a,multiply(a,a)),a))),identity)),multiply(identity,multiply(identity,identity))))))),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(identity,multiply(multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))),multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(symmetry,[status(thm)],[219]) ).

tff(364,plain,
    a = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),
    inference(transitivity,[status(thm)],[164,355,307,205,203,200,193,363,362]) ).

tff(365,plain,
    multiply(a,a) = multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))))))),
    inference(monotonicity,[status(thm)],[364,356]) ).

tff(366,plain,
    multiply(a,multiply(a,a)) = multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,multiply(multiply(a,a),identity)),multiply(identity,multiply(identity,identity)))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))),multiply(multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a)))),multiply(identity,multiply(multiply(identity,multiply(a,a)),multiply(identity,multiply(a,a))))))))),
    inference(monotonicity,[status(thm)],[365]) ).

tff(367,plain,
    multiply(a,multiply(a,a)) = identity,
    inference(transitivity,[status(thm)],[366,318,316,142,175,172,103,101,98,90,53,51,48,17,9]) ).

tff(368,plain,
    ( ( multiply(a,multiply(a,a)) != identity )
  <=> ( multiply(a,multiply(a,a)) != identity ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(369,axiom,
    multiply(a,multiply(a,a)) != identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_order3) ).

tff(370,plain,
    multiply(a,multiply(a,a)) != identity,
    inference(modus_ponens,[status(thm)],[369,368]) ).

tff(371,plain,
    $false,
    inference(unit_resolution,[status(thm)],[370,367]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GRP115-1 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Thu Jun 19 15:41:09 EDT 2025
% 0.12/0.34  % CPUTime    : 
% 0.50/0.70  % SZS status Unsatisfiable
% 0.50/0.70  % SZS output start Proof
% See solution above
% 0.77/0.95  % E exiting
%------------------------------------------------------------------------------