TSTP Solution File: GRP584-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:28:43 EDT 2022
% Result : Unsatisfiable 0.63s 0.64s
% Output : Proof 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 83
% Number of leaves : 74
% Syntax : Number of formulae : 443 ( 374 unt; 6 typ; 0 def)
% Number of atoms : 508 ( 503 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 125 ( 58 ~; 54 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 20 ( 3 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 185 ( 178 !; 0 ?; 185 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(double_divide_type,type,
double_divide: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
^ [A: $i] :
refl(
( ( identity = double_divide(A,inverse(A)) )
<=> ( identity = double_divide(A,inverse(A)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
tff(5,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
identity = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = identity,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [A: $i] :
refl(
( ( inverse(A) = double_divide(A,identity) )
<=> ( inverse(A) = double_divide(A,identity) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
tff(15,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),identity),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),identity) = inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(b,a),inverse(double_divide(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
identity = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(unit_resolution,[status(thm)],[21,7]) ).
tff(23,plain,
double_divide(double_divide(b,a),inverse(double_divide(b,a))) = identity,
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),identity) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),identity),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(b,inverse(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
identity = double_divide(b,inverse(b)),
inference(unit_resolution,[status(thm)],[26,7]) ).
tff(28,plain,
double_divide(identity,identity) = double_divide(double_divide(b,inverse(b)),identity),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
double_divide(double_divide(b,inverse(b)),identity) = double_divide(identity,identity),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
double_divide(double_divide(b,inverse(b)),identity) = inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(transitivity,[status(thm)],[29,25,20]) ).
tff(31,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)) = identity,
inference(transitivity,[status(thm)],[31,10]) ).
tff(33,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[23,32]) ).
tff(34,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
<=> ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(39,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[23,23]) ).
tff(45,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[44,34]) ).
tff(46,plain,
double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[23]) ).
tff(47,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
double_divide(double_divide(b,inverse(b)),identity) = double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(transitivity,[status(thm)],[29,47]) ).
tff(49,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[48,45]) ).
tff(50,plain,
double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(b,inverse(b)),identity),
inference(transitivity,[status(thm)],[46,28]) ).
tff(51,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[50,49]) ).
tff(52,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
double_divide(double_divide(b,inverse(b)),identity) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[29,34]) ).
tff(54,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[48,53]) ).
tff(55,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(transitivity,[status(thm)],[55,52]) ).
tff(57,plain,
double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(monotonicity,[status(thm)],[22,30]) ).
tff(58,plain,
double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(transitivity,[status(thm)],[57,10,22]) ).
tff(59,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),
inference(monotonicity,[status(thm)],[58,56]) ).
tff(60,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),
inference(unit_resolution,[status(thm)],[61,41]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),inverse(double_divide(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(unit_resolution,[status(thm)],[63,41]) ).
tff(65,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity),
inference(unit_resolution,[status(thm)],[65,41]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),inverse(double_divide(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(unit_resolution,[status(thm)],[67,41]) ).
tff(69,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[29]) ).
tff(70,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity)) = identity,
inference(transitivity,[status(thm)],[69,68,23]) ).
tff(71,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[23,70]) ).
tff(72,plain,
double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),
inference(monotonicity,[status(thm)],[22,52]) ).
tff(73,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[72,71]) ).
tff(74,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[73,66,29,34]) ).
tff(75,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[48,74]) ).
tff(76,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[76,29]) ).
tff(78,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity)) = identity,
inference(transitivity,[status(thm)],[77,64,23]) ).
tff(79,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[23,78]) ).
tff(80,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[44]) ).
tff(81,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[80,66,29,34]) ).
tff(82,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),
inference(monotonicity,[status(thm)],[22,83]) ).
tff(85,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[84,79]) ).
tff(86,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[85,62,60]) ).
tff(87,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),inverse(double_divide(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(unit_resolution,[status(thm)],[89,41]) ).
tff(91,plain,
double_divide(double_divide(b,a),inverse(double_divide(b,a))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),inverse(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
identity = double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),inverse(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))))),
inference(unit_resolution,[status(thm)],[92,7]) ).
tff(94,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),inverse(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))))) = identity,
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity)))))) = double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
inverse(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity)))))) = double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),identity),
inference(unit_resolution,[status(thm)],[95,17]) ).
tff(97,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),identity) = inverse(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity)))))),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
identity = double_divide(identity,identity),
inference(transitivity,[status(thm)],[22,91,88,43,29]) ).
tff(99,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),identity),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),identity),
inference(unit_resolution,[status(thm)],[101,17]) ).
tff(103,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),identity) = inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[98]) ).
tff(105,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),identity),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),
inference(unit_resolution,[status(thm)],[106,41]) ).
tff(108,plain,
double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))) = inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))))),
inference(transitivity,[status(thm)],[108,105,103]) ).
tff(110,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(identity,identity)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(identity,identity)) = b,
inference(unit_resolution,[status(thm)],[110,41]) ).
tff(112,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[88]) ).
tff(113,plain,
double_divide(double_divide(b,inverse(b)),identity) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[43]) ).
tff(114,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))) = identity,
inference(transitivity,[status(thm)],[33,28,113,112,90,23]) ).
tff(115,plain,
double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = identity,
inference(transitivity,[status(thm)],[46,28,113,112,90,23]) ).
tff(116,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[115,114]) ).
tff(117,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[54,116]) ).
tff(118,plain,
double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = b,
inference(transitivity,[status(thm)],[118,111]) ).
tff(120,plain,
double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)) = identity,
inference(transitivity,[status(thm)],[57,10]) ).
tff(121,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(identity,b),
inference(monotonicity,[status(thm)],[120,119]) ).
tff(122,plain,
double_divide(identity,b) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
identity = double_divide(double_divide(b,inverse(b)),identity),
inference(transitivity,[status(thm)],[22,91,88,43]) ).
tff(124,plain,
double_divide(identity,double_divide(identity,b)) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[123,122]) ).
tff(125,plain,
double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))))),
inference(monotonicity,[status(thm)],[124,109]) ).
tff(126,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))))) = double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b))))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
identity = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))))),
inference(unit_resolution,[status(thm)],[127,7]) ).
tff(129,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
identity = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))),
inference(unit_resolution,[status(thm)],[129,7]) ).
tff(131,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))) = identity,
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),identity),
inference(unit_resolution,[status(thm)],[132,17]) ).
tff(134,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),identity) = inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[98]) ).
tff(136,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),identity),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),identity),
inference(unit_resolution,[status(thm)],[137,41]) ).
tff(139,plain,
double_divide(double_divide(b,a),identity) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
double_divide(double_divide(b,a),identity) = inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),
inference(transitivity,[status(thm)],[139,136,134]) ).
tff(141,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity)) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity)) = double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b))))),
inference(transitivity,[status(thm)],[141,131,128,126]) ).
tff(143,plain,
double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))) = double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))) = double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),
inference(unit_resolution,[status(thm)],[145,41]) ).
tff(147,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(identity,identity)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(identity,identity)) = b,
inference(unit_resolution,[status(thm)],[147,41]) ).
tff(149,plain,
double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[117]) ).
tff(150,plain,
double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = b,
inference(transitivity,[status(thm)],[149,148]) ).
tff(151,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(identity,b),
inference(monotonicity,[status(thm)],[120,150]) ).
tff(152,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[151,122]) ).
tff(153,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity)) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[141,131,22,91,88,43,29]) ).
tff(157,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))) = double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))),
inference(transitivity,[status(thm)],[157,155,146,144]) ).
tff(159,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity)))),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))) = double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),
inference(unit_resolution,[status(thm)],[162,41]) ).
tff(164,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[122]) ).
tff(166,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)) = inverse(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity)))))),
inference(transitivity,[status(thm)],[165,164,161,100,97]) ).
tff(167,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))) = double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),inverse(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))))),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[167,94,22,91,88,43,29,34]) ).
tff(169,plain,
double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)) = double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(transitivity,[status(thm)],[57,10,22,91,88,43,29,47]) ).
tff(170,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[169,168]) ).
tff(171,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(symmetry,[status(thm)],[116]) ).
tff(173,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))),
inference(transitivity,[status(thm)],[172,171]) ).
tff(174,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,identity))))),double_divide(identity,identity)) = double_divide(identity,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,identity))))),double_divide(identity,identity)) = double_divide(identity,b),
inference(unit_resolution,[status(thm)],[174,41]) ).
tff(176,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(identity,b),inverse(double_divide(identity,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(177,plain,
identity = double_divide(double_divide(identity,b),inverse(double_divide(identity,b))),
inference(unit_resolution,[status(thm)],[176,7]) ).
tff(178,plain,
double_divide(double_divide(identity,b),inverse(double_divide(identity,b))) = identity,
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(identity,b)) = double_divide(double_divide(identity,b),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(180,plain,
inverse(double_divide(identity,b)) = double_divide(double_divide(identity,b),identity),
inference(unit_resolution,[status(thm)],[179,17]) ).
tff(181,plain,
double_divide(double_divide(identity,b),identity) = inverse(double_divide(identity,b)),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
identity = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))),
inference(transitivity,[status(thm)],[22,91,88,43,29,172,171]) ).
tff(183,plain,
double_divide(double_divide(identity,b),identity) = double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))) = double_divide(double_divide(identity,b),identity),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
double_divide(b,inverse(b)) = identity,
inference(symmetry,[status(thm)],[27]) ).
tff(186,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(b) = double_divide(b,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(187,plain,
inverse(b) = double_divide(b,identity),
inference(unit_resolution,[status(thm)],[186,17]) ).
tff(188,plain,
double_divide(b,identity) = inverse(b),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
double_divide(b,double_divide(b,identity)) = double_divide(b,inverse(b)),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
double_divide(b,double_divide(b,identity)) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))),
inference(transitivity,[status(thm)],[189,185,22,91,88,43,29,172,171]) ).
tff(191,plain,
double_divide(double_divide(identity,b),double_divide(b,double_divide(b,identity))) = double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
double_divide(double_divide(identity,b),double_divide(b,double_divide(b,identity))) = inverse(double_divide(identity,b)),
inference(transitivity,[status(thm)],[191,184,181]) ).
tff(193,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,identity)))) = double_divide(double_divide(identity,b),inverse(double_divide(identity,b))),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,identity)))) = identity,
inference(transitivity,[status(thm)],[193,178]) ).
tff(195,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,identity))))) = double_divide(double_divide(b,identity),identity),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
double_divide(double_divide(b,identity),identity) = double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,identity))))),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(b,identity)) = double_divide(double_divide(b,identity),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(198,plain,
inverse(double_divide(b,identity)) = double_divide(double_divide(b,identity),identity),
inference(unit_resolution,[status(thm)],[197,17]) ).
tff(199,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(identity,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(200,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(identity,b),
inference(unit_resolution,[status(thm)],[199,41]) ).
tff(201,plain,
double_divide(double_divide(b,inverse(b)),identity) = identity,
inference(transitivity,[status(thm)],[113,112,90,23]) ).
tff(202,plain,
double_divide(b,double_divide(double_divide(b,inverse(b)),identity)) = double_divide(b,identity),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
double_divide(b,double_divide(double_divide(b,inverse(b)),identity)) = inverse(b),
inference(transitivity,[status(thm)],[202,188]) ).
tff(204,plain,
double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))) = double_divide(b,inverse(b)),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))),
inference(transitivity,[status(thm)],[204,185,22,91,88,43,29,172,171]) ).
tff(206,plain,
double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))) = double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity)))),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))),
inference(transitivity,[status(thm)],[54,171]) ).
tff(209,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[209,207]) ).
tff(211,plain,
double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(b,inverse(b)),identity),
inference(transitivity,[status(thm)],[57,10,22,91,88,43]) ).
tff(212,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[211,210]) ).
tff(213,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(215,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),
inference(unit_resolution,[status(thm)],[214,41]) ).
tff(216,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b))))),
inference(transitivity,[status(thm)],[28,113,112,90,23,128,126]) ).
tff(217,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)) = double_divide(b,double_divide(b,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(218,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)) = double_divide(b,double_divide(b,b)),
inference(unit_resolution,[status(thm)],[217,41]) ).
tff(219,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(220,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = b,
inference(unit_resolution,[status(thm)],[219,41]) ).
tff(221,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[117]) ).
tff(222,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = b,
inference(transitivity,[status(thm)],[221,220]) ).
tff(223,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(identity,b),
inference(monotonicity,[status(thm)],[120,222]) ).
tff(224,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[223,122]) ).
tff(225,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(b,double_divide(b,b)),
inference(transitivity,[status(thm)],[225,164,161,218]) ).
tff(227,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),
inference(monotonicity,[status(thm)],[226,216]) ).
tff(228,plain,
double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(230,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity),
inference(unit_resolution,[status(thm)],[229,41]) ).
tff(231,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(232,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity),
inference(unit_resolution,[status(thm)],[231,41]) ).
tff(233,plain,
double_divide(b,double_divide(b,identity)) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[189,185,22,91,88,43,29]) ).
tff(234,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[233]) ).
tff(235,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))),
inference(transitivity,[status(thm)],[234,232,29,172,171]) ).
tff(236,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity)))) = double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),
inference(monotonicity,[status(thm)],[235]) ).
tff(237,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))) = double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity)))),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
double_divide(b,double_divide(b,identity)) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[189,185,22,91,88,43,29,34]) ).
tff(239,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,identity))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[48,238]) ).
tff(240,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,identity))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))),
inference(transitivity,[status(thm)],[239,171]) ).
tff(241,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,identity)))) = double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,identity)))) = double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity)))),
inference(transitivity,[status(thm)],[241,237]) ).
tff(243,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,identity))))) = double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))) = double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,identity))))),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[117]) ).
tff(247,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[246,245,230,29,34]) ).
tff(248,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[169,247]) ).
tff(249,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[248,116,34]) ).
tff(250,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[48,249]) ).
tff(251,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(transitivity,[status(thm)],[250,116,47]) ).
tff(252,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[251,34]) ).
tff(253,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(254,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),
inference(unit_resolution,[status(thm)],[253,41]) ).
tff(255,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
double_divide(double_divide(b,inverse(b)),identity) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))),
inference(transitivity,[status(thm)],[29,172,171]) ).
tff(257,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity)))),
inference(transitivity,[status(thm)],[257,237]) ).
tff(259,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),double_divide(b,double_divide(b,identity))))),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b))))),
inference(transitivity,[status(thm)],[259,255,252,116,28,113,112,90,23,128,126]) ).
tff(261,plain,
double_divide(identity,double_divide(identity,b)) = double_divide(b,double_divide(b,b)),
inference(transitivity,[status(thm)],[124,164,161,218]) ).
tff(262,plain,
double_divide(double_divide(identity,double_divide(identity,b)),double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),
inference(monotonicity,[status(thm)],[261,260]) ).
tff(263,plain,
double_divide(double_divide(identity,double_divide(identity,b)),double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[262,228,215,213]) ).
tff(264,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(identity,b),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(b,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(267,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(b,identity),
inference(unit_resolution,[status(thm)],[266,41]) ).
tff(268,plain,
double_divide(b,identity) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
double_divide(b,identity) = double_divide(identity,b),
inference(transitivity,[status(thm)],[268,265,200]) ).
tff(270,plain,
inverse(double_divide(b,identity)) = inverse(double_divide(identity,b)),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
inverse(double_divide(identity,b)) = inverse(double_divide(b,identity)),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))) = double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,identity))))),
inference(transitivity,[status(thm)],[184,181,271,198,196]) ).
tff(273,plain,
double_divide(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(identity,b),double_divide(double_divide(identity,b),double_divide(b,double_divide(b,identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(275,plain,
double_divide(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),
inference(unit_resolution,[status(thm)],[274,41]) ).
tff(276,plain,
double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))) = double_divide(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))) = double_divide(identity,b),
inference(transitivity,[status(thm)],[276,273,175]) ).
tff(278,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),
inference(monotonicity,[status(thm)],[277,173]) ).
tff(279,plain,
double_divide(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[29]) ).
tff(280,plain,
double_divide(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),
inference(transitivity,[status(thm)],[279,275]) ).
tff(281,plain,
double_divide(double_divide(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),double_divide(double_divide(b,inverse(b)),identity)),identity) = double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[280,98]) ).
tff(282,plain,
^ [B: $i,A: $i] :
refl(
( ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) )),
inference(bind,[status(th)],]) ).
tff(283,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
inference(quant_intro,[status(thm)],[282]) ).
tff(284,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(285,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
tff(286,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[285,284]) ).
tff(287,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(skolemize,[status(sab)],[286]) ).
tff(288,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[287,283]) ).
tff(289,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))))) = double_divide(double_divide(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),double_divide(double_divide(b,inverse(b)),identity)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(290,plain,
multiply(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))))) = double_divide(double_divide(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),double_divide(double_divide(b,inverse(b)),identity)),identity),
inference(unit_resolution,[status(thm)],[289,288]) ).
tff(291,plain,
double_divide(b,double_divide(b,b)) = double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[218]) ).
tff(292,plain,
double_divide(b,double_divide(b,b)) = double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),
inference(transitivity,[status(thm)],[291,278]) ).
tff(293,plain,
multiply(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,b))) = multiply(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))))),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,b))) = double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(b,inverse(b)),identity)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(295,plain,
multiply(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,b))) = double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(b,inverse(b)),identity)),identity),
inference(unit_resolution,[status(thm)],[294,288]) ).
tff(296,plain,
double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(b,inverse(b)),identity)),identity) = multiply(double_divide(double_divide(b,inverse(b)),identity),double_divide(b,double_divide(b,b))),
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
double_divide(identity,identity) = identity,
inference(transitivity,[status(thm)],[28,113,112,90,23]) ).
tff(298,plain,
double_divide(double_divide(b,inverse(b)),identity) = double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b))))),
inference(transitivity,[status(thm)],[113,112,90,23,128,126]) ).
tff(299,plain,
double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),
inference(monotonicity,[status(thm)],[298]) ).
tff(300,plain,
double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))) = double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(b,inverse(b)),identity)),
inference(symmetry,[status(thm)],[299]) ).
tff(301,plain,
double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(b,inverse(b)),identity)),identity),
inference(monotonicity,[status(thm)],[300,297]) ).
tff(302,plain,
b = double_divide(double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(identity,double_divide(identity,b)),double_divide(b,double_divide(double_divide(identity,b),double_divide(b,double_divide(b,b)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[148]) ).
tff(303,plain,
b = double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),
inference(transitivity,[status(thm)],[302,301,296,293,290,281,278]) ).
tff(304,plain,
multiply(b,a) = multiply(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),a),
inference(monotonicity,[status(thm)],[303]) ).
tff(305,plain,
multiply(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),a) = multiply(b,a),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),a) = double_divide(double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(307,plain,
multiply(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),a) = double_divide(double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))))),identity),
inference(unit_resolution,[status(thm)],[306,288]) ).
tff(308,plain,
double_divide(double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))))),identity) = multiply(double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),a),
inference(symmetry,[status(thm)],[307]) ).
tff(309,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),inverse(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(310,plain,
identity = double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),inverse(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))))),
inference(unit_resolution,[status(thm)],[309,7]) ).
tff(311,plain,
double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),inverse(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))))) = identity,
inference(symmetry,[status(thm)],[310]) ).
tff(312,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))) = double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(313,plain,
inverse(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))) = double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),identity),
inference(unit_resolution,[status(thm)],[312,17]) ).
tff(314,plain,
double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),identity) = inverse(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),
inference(symmetry,[status(thm)],[313]) ).
tff(315,plain,
double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),identity) = double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[98]) ).
tff(316,plain,
double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(identity,identity)) = double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),identity),
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(318,plain,
identity = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),
inference(unit_resolution,[status(thm)],[317,7]) ).
tff(319,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))) = identity,
inference(symmetry,[status(thm)],[318]) ).
tff(320,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[319,22,91,88,43,29]) ).
tff(321,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[320]) ).
tff(322,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))) = inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),
inference(transitivity,[status(thm)],[321,136,134]) ).
tff(323,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[123]) ).
tff(324,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))),
inference(monotonicity,[status(thm)],[323,322]) ).
tff(325,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))) = double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))),
inference(symmetry,[status(thm)],[324]) ).
tff(326,plain,
double_divide(double_divide(b,a),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))) = double_divide(double_divide(b,a),identity),
inference(monotonicity,[status(thm)],[319]) ).
tff(327,plain,
double_divide(double_divide(b,a),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))) = inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),
inference(transitivity,[status(thm)],[326,139,136,134]) ).
tff(328,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),inverse(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))),
inference(monotonicity,[status(thm)],[323,327]) ).
tff(329,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))) = double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))),
inference(transitivity,[status(thm)],[328,325]) ).
tff(330,plain,
double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))) = double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(identity,identity)) = double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[330]) ).
tff(332,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(identity,identity)) = double_divide(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(333,plain,
double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(identity,identity)) = double_divide(b,a),
inference(unit_resolution,[status(thm)],[332,41]) ).
tff(334,plain,
double_divide(b,a) = double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[333]) ).
tff(335,plain,
double_divide(b,a) = inverse(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),
inference(transitivity,[status(thm)],[334,331,316,314]) ).
tff(336,plain,
double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(b,a)) = double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),inverse(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))))),
inference(monotonicity,[status(thm)],[335]) ).
tff(337,plain,
double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(b,a)) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))),
inference(transitivity,[status(thm)],[336,311,22,91,88,43,29,172,171]) ).
tff(338,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(b,a))) = double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))),
inference(monotonicity,[status(thm)],[337]) ).
tff(339,plain,
double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b))))) = double_divide(double_divide(identity,b),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(b,a))),
inference(symmetry,[status(thm)],[338]) ).
tff(340,plain,
double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))))) = double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(b,a)))),
inference(monotonicity,[status(thm)],[339]) ).
tff(341,plain,
double_divide(double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))))),identity) = double_divide(double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(b,a)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[340,98]) ).
tff(342,plain,
double_divide(double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(b,a)))),double_divide(identity,identity)) = double_divide(double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(b,double_divide(b,b)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,a),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(identity,b)))))),identity),
inference(symmetry,[status(thm)],[341]) ).
tff(343,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(b,a)))),double_divide(identity,identity)) = double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(344,plain,
double_divide(double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(b,a)))),double_divide(identity,identity)) = double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),
inference(unit_resolution,[status(thm)],[343,41]) ).
tff(345,plain,
double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))) = double_divide(double_divide(a,double_divide(double_divide(identity,b),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(b,a)))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[344]) ).
tff(346,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[324,131,22,91,88,43,29]) ).
tff(347,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(348,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(unit_resolution,[status(thm)],[347,41]) ).
tff(349,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(350,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),
inference(unit_resolution,[status(thm)],[349,17]) ).
tff(351,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity) = inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(symmetry,[status(thm)],[350]) ).
tff(352,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),
inference(monotonicity,[status(thm)],[201]) ).
tff(353,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity)) = inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(transitivity,[status(thm)],[352,351]) ).
tff(354,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),
inference(monotonicity,[status(thm)],[353]) ).
tff(355,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[354,319,22,91,88,43,29]) ).
tff(356,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[323,355]) ).
tff(357,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[117]) ).
tff(359,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[358,357]) ).
tff(360,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[211,359]) ).
tff(361,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))),
inference(symmetry,[status(thm)],[360]) ).
tff(362,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(363,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(unit_resolution,[status(thm)],[362,41]) ).
tff(364,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(365,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity),
inference(unit_resolution,[status(thm)],[364,41]) ).
tff(366,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[117]) ).
tff(367,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[366,365,29,34]) ).
tff(368,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[169,367]) ).
tff(369,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[368,116,34]) ).
tff(370,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[48,369]) ).
tff(371,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(transitivity,[status(thm)],[370,116,47]) ).
tff(372,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[371,34]) ).
tff(373,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(374,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),
inference(unit_resolution,[status(thm)],[373,41]) ).
tff(375,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[374]) ).
tff(376,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)),
inference(symmetry,[status(thm)],[31]) ).
tff(377,plain,
identity = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)),
inference(transitivity,[status(thm)],[9,376]) ).
tff(378,plain,
double_divide(double_divide(double_divide(b,a),identity),identity) = double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(monotonicity,[status(thm)],[377]) ).
tff(379,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity)) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[48,378]) ).
tff(380,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[379]) ).
tff(381,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),
inference(monotonicity,[status(thm)],[120,380]) ).
tff(382,plain,
double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity)))),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))) = double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),identity),identity))))),
inference(monotonicity,[status(thm)],[382]) ).
tff(384,plain,
double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))) = identity,
inference(transitivity,[status(thm)],[383,375,372,116,28,113,112,90,23]) ).
tff(385,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),
inference(monotonicity,[status(thm)],[384]) ).
tff(386,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))) = inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(transitivity,[status(thm)],[385,351]) ).
tff(387,plain,
identity = double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(transitivity,[status(thm)],[22,91,88,43,29,47]) ).
tff(388,plain,
double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[387,378]) ).
tff(389,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),
inference(monotonicity,[status(thm)],[388,386]) ).
tff(390,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),
inference(transitivity,[status(thm)],[28,113,112,90,23,318,390]) ).
tff(392,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(393,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(unit_resolution,[status(thm)],[392,41]) ).
tff(394,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[117]) ).
tff(395,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[394,393]) ).
tff(396,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[211,395]) ).
tff(397,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),
inference(monotonicity,[status(thm)],[201,396]) ).
tff(398,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),
inference(monotonicity,[status(thm)],[397,391]) ).
tff(399,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[398]) ).
tff(400,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(401,plain,
double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity),
inference(unit_resolution,[status(thm)],[400,41]) ).
tff(402,plain,
double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[117]) ).
tff(403,plain,
double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[402,401,29,34]) ).
tff(404,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[169,403]) ).
tff(405,plain,
double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[404,116,34]) ).
tff(406,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[48,405]) ).
tff(407,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(transitivity,[status(thm)],[406,116,47]) ).
tff(408,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[407,34]) ).
tff(409,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(410,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),
inference(unit_resolution,[status(thm)],[409,41]) ).
tff(411,plain,
double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[410]) ).
tff(412,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[319,22,91,88,43,29,34]) ).
tff(413,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))) = double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[48,412]) ).
tff(414,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[413,116]) ).
tff(415,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[323,414]) ).
tff(416,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))),
inference(symmetry,[status(thm)],[415]) ).
tff(417,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[29]) ).
tff(418,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))),
inference(transitivity,[status(thm)],[417,416]) ).
tff(419,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),
inference(monotonicity,[status(thm)],[351,418]) ).
tff(420,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),
inference(transitivity,[status(thm)],[419,411,408,116,28,113,112,90,23,318,390]) ).
tff(421,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,a),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(double_divide(b,a),identity),identity),double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))))))),
inference(monotonicity,[status(thm)],[420]) ).
tff(422,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[421,399,363,361]) ).
tff(423,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),
inference(monotonicity,[status(thm)],[422]) ).
tff(424,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[423]) ).
tff(425,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(426,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),
inference(unit_resolution,[status(thm)],[425,41]) ).
tff(427,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),identity),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))) = double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),
inference(transitivity,[status(thm)],[350,427,424,348]) ).
tff(429,plain,
double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))) = double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[428,346]) ).
tff(430,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(identity,identity)) = double_divide(inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))),double_divide(double_divide(double_divide(b,a),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,inverse(b)),identity))))))))),
inference(symmetry,[status(thm)],[429]) ).
tff(431,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(a,b) = double_divide(double_divide(b,a),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(432,plain,
multiply(a,b) = double_divide(double_divide(b,a),identity),
inference(unit_resolution,[status(thm)],[431,288]) ).
tff(433,plain,
multiply(a,b) = multiply(b,a),
inference(transitivity,[status(thm)],[432,139,430,345,342,308,305]) ).
tff(434,plain,
( ( multiply(a,b) != multiply(b,a) )
<=> ( multiply(a,b) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(435,axiom,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
tff(436,plain,
multiply(a,b) != multiply(b,a),
inference(modus_ponens,[status(thm)],[435,434]) ).
tff(437,plain,
$false,
inference(unit_resolution,[status(thm)],[436,433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 17:50:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.63/0.64 % SZS status Unsatisfiable
% 0.63/0.64 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------