%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP582-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:07 AM UTC 2025
% Result : Unsatisfiable 0.74s 0.91s
% Output : Proof 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 69
% Syntax : Number of formulae : 419 ( 355 unt; 0 typ; 0 def)
% Number of atoms : 491 ( 486 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 127 ( 59 ~; 55 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 19 ( 3 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 173 ( 166 !; 0 ?; 173 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(double_divide_type,type,
double_divide: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( double_divide(double_divide(A,double_divide(double_divide(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(2,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)],[1]) ).
tff(3,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(4,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/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(5,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)],[4,3]) ).
tff(6,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)],[5]) ).
tff(7,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)],[6,2]) ).
tff(8,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(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(( ( identity = double_divide(A,inverse(A)) )
<=> ( identity = double_divide(A,inverse(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
tff(14,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [A: $i] :
refl(( ( inverse(A) = double_divide(A,identity) )
<=> ( inverse(A) = double_divide(A,identity) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
tff(24,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity),
inference(unit_resolution,[status(thm)],[30,26]) ).
tff(32,plain,
double_divide(double_divide(a2,identity),identity) = inverse(double_divide(a2,identity)),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(unit_resolution,[status(thm)],[37,16]) ).
tff(39,plain,
identity = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
inference(transitivity,[status(thm)],[38,34]) ).
tff(40,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
double_divide(identity,identity) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(transitivity,[status(thm)],[40,36,29]) ).
tff(42,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),inverse(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
identity = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),inverse(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(unit_resolution,[status(thm)],[42,16]) ).
tff(44,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),inverse(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) = identity,
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
inverse(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),identity),
inference(unit_resolution,[status(thm)],[45,26]) ).
tff(47,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),identity) = inverse(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = identity,
inference(symmetry,[status(thm)],[38]) ).
tff(49,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[34,48]) ).
tff(50,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),identity),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[50,48]) ).
tff(54,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),
inference(transitivity,[status(thm)],[53,52,47]) ).
tff(55,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),inverse(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(transitivity,[status(thm)],[55,44]) ).
tff(57,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(transitivity,[status(thm)],[36,29]) ).
tff(58,plain,
double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[38,57]) ).
tff(59,plain,
double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
inference(transitivity,[status(thm)],[58,19,38,34]) ).
tff(60,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[59,56]) ).
tff(61,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(transitivity,[status(thm)],[60,36,29]) ).
tff(62,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(transitivity,[status(thm)],[62,19,38]) ).
tff(64,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[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(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(unit_resolution,[status(thm)],[65,7]) ).
tff(67,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
double_divide(identity,identity) = identity,
inference(transitivity,[status(thm)],[40,67,64,19]) ).
tff(69,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),identity),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(identity,identity),
inference(symmetry,[status(thm)],[40]) ).
tff(72,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[64]) ).
tff(73,plain,
identity = double_divide(identity,identity),
inference(transitivity,[status(thm)],[18,72,66,71]) ).
tff(74,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[57]) ).
tff(75,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = identity,
inference(transitivity,[status(thm)],[74,19]) ).
tff(76,plain,
double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) = double_divide(a2,identity),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
double_divide(a2,identity) = double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(symmetry,[status(thm)],[76]) ).
tff(78,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(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(a2,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(a2,identity),
inference(unit_resolution,[status(thm)],[78,7]) ).
tff(80,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[49,71]) ).
tff(81,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(transitivity,[status(thm)],[81,79,77]) ).
tff(83,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(transitivity,[status(thm)],[67,64,19,38]) ).
tff(86,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),
inference(monotonicity,[status(thm)],[85,84]) ).
tff(87,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[86,73]) ).
tff(88,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),identity),
inference(symmetry,[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(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(unit_resolution,[status(thm)],[89,7]) ).
tff(91,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) = double_divide(double_divide(a2,identity),identity),
inference(monotonicity,[status(thm)],[75]) ).
tff(93,plain,
double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(symmetry,[status(thm)],[92]) ).
tff(94,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(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),identity),
inference(unit_resolution,[status(thm)],[94,7]) ).
tff(96,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[80]) ).
tff(97,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(transitivity,[status(thm)],[96,95,93]) ).
tff(98,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),
inference(monotonicity,[status(thm)],[85,99]) ).
tff(101,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = inverse(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),
inference(transitivity,[status(thm)],[52,47]) ).
tff(103,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),inverse(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = identity,
inference(transitivity,[status(thm)],[103,44]) ).
tff(105,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
inference(monotonicity,[status(thm)],[48]) ).
tff(106,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[106,104]) ).
tff(108,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,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(110,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)],[109]) ).
tff(111,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(112,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(113,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),identity),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),identity),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(unit_resolution,[status(thm)],[116,115]) ).
tff(118,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
identity = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))),
inference(unit_resolution,[status(thm)],[118,16]) ).
tff(120,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))) = identity,
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity),
inference(unit_resolution,[status(thm)],[121,26]) ).
tff(123,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) = inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[39,48]) ).
tff(125,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[125,93]) ).
tff(127,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),identity)),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
identity = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))),
inference(unit_resolution,[status(thm)],[130,16]) ).
tff(132,plain,
double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))) = identity,
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
inverse(double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
inference(unit_resolution,[status(thm)],[133,26]) ).
tff(135,plain,
double_divide(double_divide(double_divide(a2,identity),identity),identity) = inverse(double_divide(double_divide(a2,identity),identity)),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)) = identity,
inference(transitivity,[status(thm)],[136,132]) ).
tff(138,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[127,137]) ).
tff(139,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))) = inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(transitivity,[status(thm)],[138,129,123]) ).
tff(140,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(a2,identity),identity),
inference(monotonicity,[status(thm)],[104]) ).
tff(141,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(transitivity,[status(thm)],[140,93]) ).
tff(142,plain,
double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(transitivity,[status(thm)],[58,72,66,125]) ).
tff(143,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[142,141]) ).
tff(144,plain,
double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))),
inference(symmetry,[status(thm)],[140]) ).
tff(145,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),
inference(symmetry,[status(thm)],[58]) ).
tff(146,plain,
identity = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),
inference(transitivity,[status(thm)],[18,145]) ).
tff(147,plain,
double_divide(identity,double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(monotonicity,[status(thm)],[146,144]) ).
tff(148,plain,
double_divide(identity,double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(transitivity,[status(thm)],[147,143]) ).
tff(149,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))),
inference(monotonicity,[status(thm)],[148,139]) ).
tff(150,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(transitivity,[status(thm)],[149,120,38]) ).
tff(151,plain,
multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),identity)) = multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),identity),identity)),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))))),identity),
inference(unit_resolution,[status(thm)],[152,115]) ).
tff(154,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))))),identity) = multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),identity)),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))))),identity),
inference(monotonicity,[status(thm)],[68]) ).
tff(156,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(a2,identity),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(unit_resolution,[status(thm)],[156,7]) ).
tff(158,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))),
inference(transitivity,[status(thm)],[98,158,155,154,151,117,108]) ).
tff(160,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),
inference(transitivity,[status(thm)],[48,18,145]) ).
tff(161,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(monotonicity,[status(thm)],[160,159]) ).
tff(162,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[106,75]) ).
tff(164,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(transitivity,[status(thm)],[107,164]) ).
tff(166,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[142,165]) ).
tff(167,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(symmetry,[status(thm)],[166]) ).
tff(168,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(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(unit_resolution,[status(thm)],[168,7]) ).
tff(170,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[73]) ).
tff(171,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
multiply(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),identity),
inference(unit_resolution,[status(thm)],[171,115]) ).
tff(173,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity),
inference(unit_resolution,[status(thm)],[173,26]) ).
tff(175,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) = inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[125,164]) ).
tff(177,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),identity),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),inverse(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
identity = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),inverse(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))),
inference(unit_resolution,[status(thm)],[180,16]) ).
tff(182,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),inverse(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = identity,
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
inverse(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),identity),
inference(unit_resolution,[status(thm)],[183,26]) ).
tff(185,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),identity) = inverse(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[106,48]) ).
tff(187,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),identity),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = inverse(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(transitivity,[status(thm)],[189,185]) ).
tff(191,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),inverse(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = identity,
inference(transitivity,[status(thm)],[191,182]) ).
tff(193,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),identity),
inference(monotonicity,[status(thm)],[177,192]) ).
tff(194,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(transitivity,[status(thm)],[193,179,175]) ).
tff(195,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(monotonicity,[status(thm)],[146,108]) ).
tff(196,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(transitivity,[status(thm)],[195,166]) ).
tff(197,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))),
inference(monotonicity,[status(thm)],[196,194]) ).
tff(198,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(200,plain,
identity = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))),
inference(unit_resolution,[status(thm)],[199,16]) ).
tff(201,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(transitivity,[status(thm)],[48,200,198]) ).
tff(202,plain,
multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = multiply(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,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(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(unit_resolution,[status(thm)],[203,7]) ).
tff(205,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),inverse(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(206,plain,
identity = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),inverse(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))),
inference(unit_resolution,[status(thm)],[205,16]) ).
tff(207,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),inverse(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = identity,
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
inverse(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),identity),
inference(unit_resolution,[status(thm)],[208,26]) ).
tff(210,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),identity) = inverse(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[187,48]) ).
tff(212,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),identity),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = inverse(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(transitivity,[status(thm)],[214,210]) ).
tff(216,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),inverse(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[216,207,18,72,66,71]) ).
tff(218,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = identity,
inference(transitivity,[status(thm)],[218,204,67,64,19]) ).
tff(220,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[187,75]) ).
tff(221,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[125,221]) ).
tff(223,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[187,104]) ).
tff(225,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(transitivity,[status(thm)],[224,221]) ).
tff(226,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[142,225]) ).
tff(227,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))),
inference(symmetry,[status(thm)],[224]) ).
tff(228,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(monotonicity,[status(thm)],[146,227]) ).
tff(229,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(transitivity,[status(thm)],[228,226,223]) ).
tff(230,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),identity),
inference(monotonicity,[status(thm)],[229,219]) ).
tff(231,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),inverse(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(233,plain,
identity = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),inverse(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),
inference(unit_resolution,[status(thm)],[232,16]) ).
tff(234,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),inverse(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))) = identity,
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(236,plain,
inverse(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),identity),
inference(unit_resolution,[status(thm)],[235,26]) ).
tff(237,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),identity) = inverse(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[106]) ).
tff(239,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),identity),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = inverse(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),
inference(transitivity,[status(thm)],[239,237]) ).
tff(241,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),inverse(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = identity,
inference(transitivity,[status(thm)],[241,234]) ).
tff(243,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),identity),
inference(monotonicity,[status(thm)],[223,242]) ).
tff(244,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(transitivity,[status(thm)],[243,231]) ).
tff(245,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(246,plain,
multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(unit_resolution,[status(thm)],[245,115]) ).
tff(247,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity),
inference(unit_resolution,[status(thm)],[247,26]) ).
tff(249,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) = inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
inference(monotonicity,[status(thm)],[75]) ).
tff(251,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[125,251]) ).
tff(253,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),identity),
inference(monotonicity,[status(thm)],[253]) ).
tff(255,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),identity),
inference(monotonicity,[status(thm)],[253,242]) ).
tff(257,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(transitivity,[status(thm)],[256,255,249]) ).
tff(258,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
inference(monotonicity,[status(thm)],[104]) ).
tff(259,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(transitivity,[status(thm)],[258,251]) ).
tff(260,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[142,259]) ).
tff(261,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))),
inference(symmetry,[status(thm)],[258]) ).
tff(262,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(monotonicity,[status(thm)],[146,261]) ).
tff(263,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(transitivity,[status(thm)],[262,260]) ).
tff(264,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))),
inference(monotonicity,[status(thm)],[263,257]) ).
tff(265,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
identity = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))),
inference(unit_resolution,[status(thm)],[266,16]) ).
tff(268,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(transitivity,[status(thm)],[48,267,265]) ).
tff(269,plain,
multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = multiply(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(monotonicity,[status(thm)],[268]) ).
tff(270,plain,
multiply(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(symmetry,[status(thm)],[269]) ).
tff(271,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(272,plain,
multiply(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),identity),
inference(unit_resolution,[status(thm)],[271,115]) ).
tff(273,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),identity) = multiply(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(symmetry,[status(thm)],[272]) ).
tff(274,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[73]) ).
tff(275,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),identity),
inference(symmetry,[status(thm)],[274]) ).
tff(276,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(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(277,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(unit_resolution,[status(thm)],[276,7]) ).
tff(278,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(transitivity,[status(thm)],[262,260,278,275,273,270,246]) ).
tff(280,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),
inference(monotonicity,[status(thm)],[279,244]) ).
tff(281,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(symmetry,[status(thm)],[280]) ).
tff(282,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(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(283,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),
inference(unit_resolution,[status(thm)],[282,7]) ).
tff(284,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[80]) ).
tff(285,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(transitivity,[status(thm)],[284,204,67,64,19]) ).
tff(286,plain,
double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
inference(transitivity,[status(thm)],[124,67,64,19,38,34]) ).
tff(287,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[286,285]) ).
tff(288,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = identity,
inference(transitivity,[status(thm)],[287,67,64,19]) ).
tff(289,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[34,288]) ).
tff(290,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
inference(transitivity,[status(thm)],[289,67,64,19,38,34]) ).
tff(291,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[290,68]) ).
tff(292,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(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(293,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),
inference(unit_resolution,[status(thm)],[292,7]) ).
tff(294,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[293]) ).
tff(295,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(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(296,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),
inference(unit_resolution,[status(thm)],[295,7]) ).
tff(297,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[80]) ).
tff(298,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(transitivity,[status(thm)],[297,296,294,291,67,64,19]) ).
tff(299,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[286,298]) ).
tff(300,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = identity,
inference(transitivity,[status(thm)],[299,67,64,19]) ).
tff(301,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[34,300]) ).
tff(302,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
inference(transitivity,[status(thm)],[301,67,64,19,38,34]) ).
tff(303,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[302,68]) ).
tff(304,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
identity = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(transitivity,[status(thm)],[18,72,66,304,283,281]) ).
tff(306,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),
inference(monotonicity,[status(thm)],[186,305]) ).
tff(307,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(symmetry,[status(thm)],[306]) ).
tff(308,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(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(309,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),
inference(unit_resolution,[status(thm)],[308,7]) ).
tff(310,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(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(311,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
inference(unit_resolution,[status(thm)],[310,7]) ).
tff(312,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[73]) ).
tff(313,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(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(314,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(unit_resolution,[status(thm)],[313,7]) ).
tff(315,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[80]) ).
tff(316,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(transitivity,[status(thm)],[315,314,164]) ).
tff(317,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[316]) ).
tff(318,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(transitivity,[status(thm)],[48,18,72,66]) ).
tff(319,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(monotonicity,[status(thm)],[318,317]) ).
tff(320,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),identity),
inference(monotonicity,[status(thm)],[319,68]) ).
tff(321,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(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(unit_resolution,[status(thm)],[321,7]) ).
tff(323,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[322]) ).
tff(324,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(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(325,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(unit_resolution,[status(thm)],[324,7]) ).
tff(326,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[80]) ).
tff(327,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(transitivity,[status(thm)],[326,325,221]) ).
tff(328,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[327]) ).
tff(329,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(monotonicity,[status(thm)],[318,328]) ).
tff(330,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(symmetry,[status(thm)],[328]) ).
tff(331,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(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(332,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(unit_resolution,[status(thm)],[331,7]) ).
tff(333,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[80]) ).
tff(334,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(transitivity,[status(thm)],[333,332,330]) ).
tff(335,plain,
double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(transitivity,[status(thm)],[124,67,64,19,38]) ).
tff(336,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),
inference(monotonicity,[status(thm)],[335,334]) ).
tff(337,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))),
inference(transitivity,[status(thm)],[336,329,323,320,312,311,261]) ).
tff(338,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(monotonicity,[status(thm)],[160,337]) ).
tff(339,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),
inference(transitivity,[status(thm)],[338,260,253]) ).
tff(340,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),identity),
inference(monotonicity,[status(thm)],[339,68]) ).
tff(341,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[340]) ).
tff(342,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(343,plain,
multiply(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)),identity),
inference(unit_resolution,[status(thm)],[342,115]) ).
tff(344,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(a2,identity),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(345,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(unit_resolution,[status(thm)],[344,7]) ).
tff(346,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity),
inference(monotonicity,[status(thm)],[68]) ).
tff(347,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(349,plain,
multiply(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity),
inference(unit_resolution,[status(thm)],[348,115]) ).
tff(350,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(351,plain,
identity = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))),
inference(unit_resolution,[status(thm)],[350,16]) ).
tff(352,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))) = identity,
inference(symmetry,[status(thm)],[351]) ).
tff(353,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(354,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity),
inference(unit_resolution,[status(thm)],[353,26]) ).
tff(355,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) = inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(symmetry,[status(thm)],[354]) ).
tff(356,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(a2,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[125,77]) ).
tff(357,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(a2,identity)),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(a2,identity)),identity),
inference(monotonicity,[status(thm)],[357]) ).
tff(359,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(a2,identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),identity),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = identity,
inference(transitivity,[status(thm)],[33,48]) ).
tff(361,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(a2,identity)),identity),
inference(monotonicity,[status(thm)],[357,360]) ).
tff(362,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(transitivity,[status(thm)],[361,359,355]) ).
tff(363,plain,
double_divide(a2,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(a2,identity),
inference(monotonicity,[status(thm)],[104]) ).
tff(364,plain,
double_divide(a2,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(transitivity,[status(thm)],[363,77]) ).
tff(365,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(a2,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[142,364]) ).
tff(366,plain,
double_divide(a2,identity) = double_divide(a2,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))),
inference(symmetry,[status(thm)],[363]) ).
tff(367,plain,
double_divide(identity,double_divide(a2,identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),double_divide(a2,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
inference(monotonicity,[status(thm)],[146,366]) ).
tff(368,plain,
double_divide(identity,double_divide(a2,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(transitivity,[status(thm)],[367,365]) ).
tff(369,plain,
double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),inverse(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))),
inference(monotonicity,[status(thm)],[368,362]) ).
tff(370,plain,
double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = identity,
inference(transitivity,[status(thm)],[369,352]) ).
tff(371,plain,
multiply(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),identity)) = multiply(identity,double_divide(double_divide(a2,identity),identity)),
inference(monotonicity,[status(thm)],[370]) ).
tff(372,plain,
multiply(identity,double_divide(double_divide(a2,identity),identity)) = multiply(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),identity)),
inference(symmetry,[status(thm)],[371]) ).
tff(373,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(identity,double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(374,plain,
multiply(identity,double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
inference(unit_resolution,[status(thm)],[373,115]) ).
tff(375,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) = multiply(identity,double_divide(double_divide(a2,identity),identity)),
inference(symmetry,[status(thm)],[374]) ).
tff(376,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(transitivity,[status(thm)],[375,372,349,347,345]) ).
tff(377,plain,
multiply(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),
inference(monotonicity,[status(thm)],[376]) ).
tff(378,plain,
multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = multiply(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),
inference(symmetry,[status(thm)],[377]) ).
tff(379,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(380,plain,
multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),identity),
inference(unit_resolution,[status(thm)],[379,115]) ).
tff(381,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),identity) = multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(transitivity,[status(thm)],[167,162,101,91,88,381,378,343,341,309,307]) ).
tff(383,plain,
multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
inference(monotonicity,[status(thm)],[382]) ).
tff(384,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(385,plain,
multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(unit_resolution,[status(thm)],[384,115]) ).
tff(386,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(symmetry,[status(thm)],[385]) ).
tff(387,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),identity),
inference(monotonicity,[status(thm)],[177,48]) ).
tff(388,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[387]) ).
tff(389,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(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(390,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
inference(unit_resolution,[status(thm)],[389,7]) ).
tff(391,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[73]) ).
tff(392,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[80]) ).
tff(393,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(transitivity,[status(thm)],[392,311,251]) ).
tff(394,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[393]) ).
tff(395,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(monotonicity,[status(thm)],[318,394]) ).
tff(396,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),identity),
inference(monotonicity,[status(thm)],[395,68]) ).
tff(397,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(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(398,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),
inference(unit_resolution,[status(thm)],[397,7]) ).
tff(399,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[398]) ).
tff(400,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(symmetry,[status(thm)],[317]) ).
tff(401,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),
inference(monotonicity,[status(thm)],[400]) ).
tff(402,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))) = inverse(double_divide(double_divide(a2,identity),identity)),
inference(transitivity,[status(thm)],[401,319,399,396,391,390,135]) ).
tff(403,plain,
double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))) = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))),
inference(monotonicity,[status(thm)],[402]) ).
tff(404,plain,
double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))) = identity,
inference(transitivity,[status(thm)],[403,132]) ).
tff(405,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[286,404]) ).
tff(406,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))))))) = identity,
inference(transitivity,[status(thm)],[405,67,64,19]) ).
tff(407,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),identity),
inference(monotonicity,[status(thm)],[177,406]) ).
tff(408,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(transitivity,[status(thm)],[407,388]) ).
tff(409,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[408,68]) ).
tff(410,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(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(411,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),identity),
inference(unit_resolution,[status(thm)],[410,7]) ).
tff(412,plain,
double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[411]) ).
tff(413,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(identity,a2) = double_divide(double_divide(a2,identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(414,plain,
multiply(identity,a2) = double_divide(double_divide(a2,identity),identity),
inference(unit_resolution,[status(thm)],[413,115]) ).
tff(415,plain,
multiply(identity,a2) = a2,
inference(transitivity,[status(thm)],[414,412,409,386,383,202,172,170,169,167,162,101,91,88,70,9]) ).
tff(416,plain,
( ( multiply(identity,a2) != a2 )
<=> ( multiply(identity,a2) != a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(417,axiom,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(418,plain,
multiply(identity,a2) != a2,
inference(modus_ponens,[status(thm)],[417,416]) ).
tff(419,plain,
$false,
inference(unit_resolution,[status(thm)],[418,415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP582-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:19:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.74/0.91 % SZS status Unsatisfiable
% 0.74/0.91 % SZS output start Proof
% See solution above
% 0.85/1.08 % E exiting
%------------------------------------------------------------------------------