%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP495-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:56 AM UTC 2025
% Result : Unsatisfiable 2.61s 2.81s
% Output : Proof 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 93
% Syntax : Number of formulae : 547 ( 459 unt; 0 typ; 0 def)
% Number of atoms : 643 ( 638 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 175 ( 83 ~; 79 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 259 ( 252 !; 0 ?; 259 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(c3_type,type,
c3: $i ).
tff(b3_type,type,
b3: $i ).
tff(a3_type,type,
a3: $i ).
tff(double_divide_type,type,
double_divide: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
^ [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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(5,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(a3,multiply(b3,c3)) = double_divide(double_divide(multiply(b3,c3),a3),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(a3,multiply(b3,c3)) = double_divide(double_divide(multiply(b3,c3),a3),identity),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
double_divide(double_divide(multiply(b3,c3),a3),identity) = multiply(a3,multiply(b3,c3)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
<=> ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))) = identity,
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [A: $i] :
refl(( ( identity = double_divide(A,inverse(A)) )
<=> ( identity = double_divide(A,inverse(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
tff(24,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
identity = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = identity,
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
identity = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(unit_resolution,[status(thm)],[30,26]) ).
tff(32,plain,
double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) = identity,
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = inverse(identity),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
inverse(identity) = inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
^ [A: $i] :
refl(( ( inverse(A) = double_divide(A,identity) )
<=> ( inverse(A) = double_divide(A,identity) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
tff(39,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(identity) = double_divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
inverse(identity) = double_divide(identity,identity),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
double_divide(identity,identity) = inverse(identity),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
double_divide(identity,identity) = inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[44,34]) ).
tff(46,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[31,45]) ).
tff(47,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[19]) ).
tff(48,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[47,46,29]) ).
tff(49,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[48,19]) ).
tff(50,plain,
identity = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
inference(symmetry,[status(thm)],[19]) ).
tff(51,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(multiply(b3,c3),a3),inverse(double_divide(multiply(b3,c3),a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
identity = double_divide(double_divide(multiply(b3,c3),a3),inverse(double_divide(multiply(b3,c3),a3))),
inference(unit_resolution,[status(thm)],[51,26]) ).
tff(53,plain,
double_divide(double_divide(multiply(b3,c3),a3),inverse(double_divide(multiply(b3,c3),a3))) = identity,
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(multiply(b3,c3),a3),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
inverse(double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(multiply(b3,c3),a3),identity),
inference(unit_resolution,[status(thm)],[54,41]) ).
tff(56,plain,
double_divide(double_divide(multiply(b3,c3),a3),identity) = inverse(double_divide(multiply(b3,c3),a3)),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)) = double_divide(double_divide(multiply(b3,c3),a3),inverse(double_divide(multiply(b3,c3),a3))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
inference(transitivity,[status(thm)],[57,53,50]) ).
tff(59,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[47]) ).
tff(60,plain,
double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)) = identity,
inference(transitivity,[status(thm)],[57,53]) ).
tff(61,plain,
double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[61,59]) ).
tff(63,plain,
double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),
inference(monotonicity,[status(thm)],[62,58]) ).
tff(64,plain,
double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[63,49]) ).
tff(65,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)))) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)))) = double_divide(multiply(b3,c3),a3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)))) = double_divide(multiply(b3,c3),a3),
inference(unit_resolution,[status(thm)],[66,17]) ).
tff(68,plain,
double_divide(multiply(b3,c3),a3) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
double_divide(multiply(b3,c3),a3) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[68,65]) ).
tff(70,plain,
double_divide(double_divide(multiply(b3,c3),a3),identity) = double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),identity),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),identity) = double_divide(double_divide(multiply(b3,c3),a3),identity),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(identity,identity),double_divide(identity,double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
multiply(double_divide(identity,identity),double_divide(identity,double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),identity),
inference(unit_resolution,[status(thm)],[72,7]) ).
tff(74,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))) = identity,
inference(unit_resolution,[status(thm)],[74,17]) ).
tff(76,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
inference(transitivity,[status(thm)],[75,50]) ).
tff(77,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[75]) ).
tff(78,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[77,59]) ).
tff(79,plain,
double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),
inference(monotonicity,[status(thm)],[78,76]) ).
tff(80,plain,
double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3))))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[79,49]) ).
tff(81,plain,
double_divide(identity,double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[46,29]) ).
tff(82,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))))) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[81,80]) ).
tff(83,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))))) = double_divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))))) = double_divide(identity,identity),
inference(unit_resolution,[status(thm)],[83,17]) ).
tff(85,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
double_divide(identity,identity) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(transitivity,[status(thm)],[85,82,46,29,31]) ).
tff(87,plain,
multiply(double_divide(identity,identity),double_divide(identity,double_divide(multiply(b3,c3),a3))) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))) = multiply(double_divide(identity,identity),double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))) = double_divide(double_divide(multiply(b3,c3),a3),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
double_divide(double_divide(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))) = double_divide(double_divide(multiply(b3,c3),a3),identity),
inference(unit_resolution,[status(thm)],[89,17]) ).
tff(91,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),
inference(unit_resolution,[status(thm)],[91,17]) ).
tff(93,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),
inference(monotonicity,[status(thm)],[93,92]) ).
tff(95,plain,
double_divide(identity,identity) = identity,
inference(transitivity,[status(thm)],[85,82,46,29]) ).
tff(96,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(identity,identity) = double_divide(double_divide(identity,identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
multiply(identity,identity) = double_divide(double_divide(identity,identity),identity),
inference(unit_resolution,[status(thm)],[97,7]) ).
tff(99,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(unit_resolution,[status(thm)],[99,17]) ).
tff(101,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(102,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),identity) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),identity),
inference(monotonicity,[status(thm)],[32]) ).
tff(104,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[103,102]) ).
tff(105,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[95,95]) ).
tff(106,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[32,32]) ).
tff(107,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[107,105,85,82,46,29]) ).
tff(109,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity))),
inference(monotonicity,[status(thm)],[108,104]) ).
tff(110,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),double_divide(identity,double_divide(b3,a3)))))),
inference(symmetry,[status(thm)],[82]) ).
tff(112,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(identity,identity)),
inference(symmetry,[status(thm)],[46]) ).
tff(113,plain,
identity = double_divide(identity,identity),
inference(transitivity,[status(thm)],[28,112,111,84]) ).
tff(114,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity))),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(c3,b3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(c3,b3),
inference(unit_resolution,[status(thm)],[116,17]) ).
tff(118,plain,
double_divide(c3,b3) = double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
double_divide(c3,b3) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(transitivity,[status(thm)],[118,115,110]) ).
tff(120,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = identity,
inference(transitivity,[status(thm)],[106,85,82,46,29]) ).
tff(121,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))) = double_divide(c3,b3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))) = double_divide(c3,b3),
inference(unit_resolution,[status(thm)],[121,17]) ).
tff(123,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
identity = double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))),
inference(unit_resolution,[status(thm)],[123,26]) ).
tff(125,plain,
double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))) = identity,
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(c3,b3)) = double_divide(double_divide(c3,b3),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
inverse(double_divide(c3,b3)) = double_divide(double_divide(c3,b3),identity),
inference(unit_resolution,[status(thm)],[126,41]) ).
tff(128,plain,
double_divide(double_divide(c3,b3),identity) = inverse(double_divide(c3,b3)),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
inference(transitivity,[status(thm)],[129,125,50]) ).
tff(131,plain,
double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)) = identity,
inference(transitivity,[status(thm)],[129,125]) ).
tff(132,plain,
double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[132,59]) ).
tff(134,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),
inference(monotonicity,[status(thm)],[133,130]) ).
tff(135,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[134,49]) ).
tff(136,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)) = double_divide(c3,b3),
inference(transitivity,[status(thm)],[137,122]) ).
tff(139,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),identity) = double_divide(double_divide(c3,b3),identity),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(identity,identity),double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
multiply(double_divide(identity,identity),double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),identity),
inference(unit_resolution,[status(thm)],[140,7]) ).
tff(142,plain,
double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[32,28,112,111,84]) ).
tff(143,plain,
multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))) = multiply(double_divide(identity,identity),double_divide(identity,double_divide(c3,b3))),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
inference(unit_resolution,[status(thm)],[144,7]) ).
tff(146,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(148,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(c3,b3),identity),
inference(transitivity,[status(thm)],[147,146,143,141,139]) ).
tff(149,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
inference(monotonicity,[status(thm)],[148,120]) ).
tff(150,plain,
double_divide(double_divide(double_divide(c3,b3),identity),identity) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
double_divide(double_divide(double_divide(c3,b3),identity),identity) = double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[113]) ).
tff(152,plain,
double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(transitivity,[status(thm)],[152,150]) ).
tff(154,plain,
double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[32]) ).
tff(155,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
identity = double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[28,112,111,84,155]) ).
tff(157,plain,
double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
inference(monotonicity,[status(thm)],[156,153]) ).
tff(158,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(c3,b3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(c3,b3)),
inference(unit_resolution,[status(thm)],[159,17]) ).
tff(161,plain,
double_divide(identity,double_divide(c3,b3)) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))))) = double_divide(identity,double_divide(c3,b3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))))) = double_divide(identity,double_divide(c3,b3)),
inference(unit_resolution,[status(thm)],[162,17]) ).
tff(164,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(b3,c3) = double_divide(double_divide(c3,b3),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
multiply(b3,c3) = double_divide(double_divide(c3,b3),identity),
inference(unit_resolution,[status(thm)],[164,7]) ).
tff(166,plain,
double_divide(double_divide(c3,b3),identity) = multiply(b3,c3),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
double_divide(double_divide(double_divide(c3,b3),identity),a3) = double_divide(multiply(b3,c3),a3),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
double_divide(multiply(b3,c3),a3) = double_divide(double_divide(double_divide(c3,b3),identity),a3),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))) = double_divide(multiply(b3,c3),a3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))) = double_divide(multiply(b3,c3),a3),
inference(unit_resolution,[status(thm)],[169,17]) ).
tff(171,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(c3,b3),identity),a3),
inference(transitivity,[status(thm)],[170,168]) ).
tff(172,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[171]) ).
tff(173,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)),
inference(monotonicity,[status(thm)],[172,171]) ).
tff(174,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(unit_resolution,[status(thm)],[174,17]) ).
tff(176,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))) = identity,
inference(unit_resolution,[status(thm)],[176,17]) ).
tff(178,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
inference(transitivity,[status(thm)],[177,50]) ).
tff(179,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[177]) ).
tff(180,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[179,59]) ).
tff(181,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity)))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),
inference(monotonicity,[status(thm)],[180,178]) ).
tff(182,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),
inference(symmetry,[status(thm)],[49]) ).
tff(184,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),
inference(transitivity,[status(thm)],[183,182]) ).
tff(185,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),
inference(monotonicity,[status(thm)],[32]) ).
tff(186,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),identity))))),
inference(monotonicity,[status(thm)],[185,184]) ).
tff(187,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[113]) ).
tff(188,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = double_divide(double_divide(c3,b3),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = double_divide(double_divide(c3,b3),identity),
inference(unit_resolution,[status(thm)],[188,17]) ).
tff(190,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = inverse(double_divide(c3,b3)),
inference(transitivity,[status(thm)],[189,128]) ).
tff(191,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)))),
inference(symmetry,[status(thm)],[173]) ).
tff(192,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))))),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = double_divide(identity,double_divide(c3,b3)),
inference(transitivity,[status(thm)],[192,163]) ).
tff(194,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)) = double_divide(c3,b3),
inference(transitivity,[status(thm)],[194,137,122]) ).
tff(196,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)))) = double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))),
inference(monotonicity,[status(thm)],[195,190]) ).
tff(197,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)))) = identity,
inference(transitivity,[status(thm)],[196,125]) ).
tff(198,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),
inference(symmetry,[status(thm)],[185]) ).
tff(199,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),identity),
inference(monotonicity,[status(thm)],[198,197]) ).
tff(200,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))) = double_divide(identity,double_divide(identity,double_divide(c3,b3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))) = double_divide(identity,double_divide(identity,double_divide(c3,b3))),
inference(unit_resolution,[status(thm)],[200,17]) ).
tff(202,plain,
double_divide(identity,double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
double_divide(identity,double_divide(identity,double_divide(c3,b3))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(transitivity,[status(thm)],[202,199,187,186,175]) ).
tff(204,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),
inference(monotonicity,[status(thm)],[203,173]) ).
tff(205,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))))),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
double_divide(double_divide(c3,b3),identity) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),
inference(symmetry,[status(thm)],[189]) ).
tff(207,plain,
double_divide(double_divide(c3,b3),double_divide(identity,identity)) = double_divide(double_divide(c3,b3),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(208,plain,
double_divide(double_divide(c3,b3),double_divide(identity,identity)) = double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))),
inference(transitivity,[status(thm)],[207,206,205,163,161,158]) ).
tff(209,plain,
double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
inference(monotonicity,[status(thm)],[208,119]) ).
tff(210,plain,
double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)) = identity,
inference(transitivity,[status(thm)],[209,100,32]) ).
tff(211,plain,
multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = multiply(identity,identity),
inference(monotonicity,[status(thm)],[32,210]) ).
tff(212,plain,
multiply(double_divide(identity,identity),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),
inference(monotonicity,[status(thm)],[86]) ).
tff(213,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(identity,identity),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
multiply(double_divide(identity,identity),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),identity),
inference(unit_resolution,[status(thm)],[213,7]) ).
tff(215,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),identity) = multiply(double_divide(identity,identity),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),identity),
inference(monotonicity,[status(thm)],[210]) ).
tff(217,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = identity,
inference(transitivity,[status(thm)],[216,215,212,211,98,96,85,82,46,29]) ).
tff(218,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)))),
inference(symmetry,[status(thm)],[65]) ).
tff(219,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity))))) = double_divide(identity,double_divide(multiply(b3,c3),a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(220,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity))))) = double_divide(identity,double_divide(multiply(b3,c3),a3)),
inference(unit_resolution,[status(thm)],[219,17]) ).
tff(221,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity))) = double_divide(c3,b3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity))) = double_divide(c3,b3),
inference(unit_resolution,[status(thm)],[221,17]) ).
tff(223,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity))),double_divide(identity,identity)) = double_divide(double_divide(c3,b3),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity)))) = double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),
inference(monotonicity,[status(thm)],[223,222]) ).
tff(225,plain,
double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity)))),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),identity))))),
inference(monotonicity,[status(thm)],[225]) ).
tff(227,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = double_divide(identity,double_divide(multiply(b3,c3),a3)),
inference(transitivity,[status(thm)],[226,220]) ).
tff(228,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)) = double_divide(multiply(b3,c3),a3),
inference(transitivity,[status(thm)],[228,218,67]) ).
tff(230,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)))) = double_divide(double_divide(multiply(b3,c3),a3),identity),
inference(monotonicity,[status(thm)],[229,217]) ).
tff(231,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(232,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)))) = identity,
inference(unit_resolution,[status(thm)],[231,17]) ).
tff(233,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)))),identity) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(235,plain,
multiply(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)))),identity),
inference(unit_resolution,[status(thm)],[234,7]) ).
tff(236,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(c3,b3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(237,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(c3,b3)),
inference(unit_resolution,[status(thm)],[236,17]) ).
tff(238,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(double_divide(c3,b3),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
inverse(double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
inference(unit_resolution,[status(thm)],[238,41]) ).
tff(240,plain,
double_divide(double_divide(double_divide(c3,b3),identity),identity) = inverse(double_divide(double_divide(c3,b3),identity)),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
inference(monotonicity,[status(thm)],[32]) ).
tff(242,plain,
double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = inverse(double_divide(double_divide(c3,b3),identity)),
inference(transitivity,[status(thm)],[241,240]) ).
tff(243,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(c3,b3),identity),inverse(double_divide(double_divide(c3,b3),identity))),
inference(monotonicity,[status(thm)],[148,242]) ).
tff(244,plain,
double_divide(double_divide(double_divide(c3,b3),identity),inverse(double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(c3,b3),identity),inverse(double_divide(double_divide(c3,b3),identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(246,plain,
identity = double_divide(double_divide(double_divide(c3,b3),identity),inverse(double_divide(double_divide(c3,b3),identity))),
inference(unit_resolution,[status(thm)],[245,26]) ).
tff(247,plain,
identity = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(transitivity,[status(thm)],[246,244]) ).
tff(248,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
inference(monotonicity,[status(thm)],[247]) ).
tff(249,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(250,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)) = double_divide(identity,double_divide(c3,b3)),
inference(transitivity,[status(thm)],[249,248,237]) ).
tff(251,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))) = double_divide(c3,b3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))) = double_divide(c3,b3),
inference(unit_resolution,[status(thm)],[253,17]) ).
tff(255,plain,
double_divide(c3,b3) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
double_divide(c3,b3) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),
inference(transitivity,[status(thm)],[255,252]) ).
tff(257,plain,
multiply(double_divide(c3,b3),double_divide(double_divide(c3,b3),double_divide(identity,identity))) = multiply(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[256,208]) ).
tff(258,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(c3,b3),double_divide(double_divide(c3,b3),double_divide(identity,identity))) = double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(259,plain,
multiply(double_divide(c3,b3),double_divide(double_divide(c3,b3),double_divide(identity,identity))) = double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),identity),
inference(unit_resolution,[status(thm)],[258,7]) ).
tff(260,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),identity) = multiply(double_divide(c3,b3),double_divide(double_divide(c3,b3),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(262,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[261,260,257,235,233,85,82,46,29]) ).
tff(263,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[262]) ).
tff(264,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity))) = identity,
inference(transitivity,[status(thm)],[263,85,82,46,29]) ).
tff(265,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))))) = double_divide(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)),
inference(monotonicity,[status(thm)],[264,230]) ).
tff(266,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))))) = double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))))) = double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(unit_resolution,[status(thm)],[266,17]) ).
tff(268,plain,
double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))))),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(multiply(b3,c3),a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(270,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(multiply(b3,c3),a3)),
inference(unit_resolution,[status(thm)],[269,17]) ).
tff(271,plain,
double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(272,plain,
double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity) = double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(274,plain,
multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
inference(unit_resolution,[status(thm)],[273,7]) ).
tff(275,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(277,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(multiply(b3,c3),a3),identity),
inference(transitivity,[status(thm)],[276,275,88,73,71]) ).
tff(278,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),
inference(monotonicity,[status(thm)],[277,120]) ).
tff(279,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[278,272]) ).
tff(280,plain,
double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = identity,
inference(transitivity,[status(thm)],[154,85,82,46,29]) ).
tff(281,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),
inference(monotonicity,[status(thm)],[280,279]) ).
tff(282,plain,
double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))) = double_divide(identity,double_divide(multiply(b3,c3),a3)),
inference(transitivity,[status(thm)],[282,270]) ).
tff(284,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))) = double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(monotonicity,[status(thm)],[283]) ).
tff(285,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))) = double_divide(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)),
inference(transitivity,[status(thm)],[284,268,265]) ).
tff(286,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[285,94]) ).
tff(287,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(288,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),
inference(unit_resolution,[status(thm)],[287,17]) ).
tff(289,plain,
double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))))),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
double_divide(identity,double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
inference(symmetry,[status(thm)],[270]) ).
tff(291,plain,
double_divide(identity,double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(multiply(b3,c3),a3),identity),
inference(transitivity,[status(thm)],[290,281,289,286,90]) ).
tff(292,plain,
multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))) = multiply(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)),
inference(monotonicity,[status(thm)],[32,291]) ).
tff(293,plain,
multiply(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
multiply(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)) = multiply(double_divide(identity,identity),double_divide(double_divide(multiply(b3,c3),a3),identity)),
inference(monotonicity,[status(thm)],[113]) ).
tff(295,plain,
multiply(double_divide(identity,identity),double_divide(double_divide(multiply(b3,c3),a3),identity)) = multiply(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)),
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(identity,identity),double_divide(double_divide(multiply(b3,c3),a3),identity)) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(297,plain,
multiply(double_divide(identity,identity),double_divide(double_divide(multiply(b3,c3),a3),identity)) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),identity),
inference(unit_resolution,[status(thm)],[296,7]) ).
tff(298,plain,
double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),identity) = multiply(double_divide(identity,identity),double_divide(double_divide(multiply(b3,c3),a3),identity)),
inference(symmetry,[status(thm)],[297]) ).
tff(299,plain,
double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),identity) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[60]) ).
tff(300,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(301,plain,
multiply(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),identity),
inference(unit_resolution,[status(thm)],[300,7]) ).
tff(302,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)) = double_divide(multiply(b3,c3),a3),
inference(transitivity,[status(thm)],[218,67]) ).
tff(303,plain,
multiply(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))) = multiply(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(multiply(b3,c3),a3)),
inference(monotonicity,[status(thm)],[291,302]) ).
tff(304,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(305,plain,
multiply(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),identity),
inference(unit_resolution,[status(thm)],[304,7]) ).
tff(306,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),identity) = multiply(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[305]) ).
tff(307,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(308,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[307,306,303,301,299]) ).
tff(309,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3)))) = double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3)))),
inference(monotonicity,[status(thm)],[308]) ).
tff(310,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3)))) = double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3)))),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3)))) = double_divide(double_divide(b3,a3),double_divide(identity,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(312,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3)))) = double_divide(double_divide(b3,a3),double_divide(identity,identity)),
inference(unit_resolution,[status(thm)],[311,17]) ).
tff(313,plain,
double_divide(double_divide(b3,a3),double_divide(identity,identity)) = double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3)))),
inference(symmetry,[status(thm)],[312]) ).
tff(314,plain,
double_divide(double_divide(b3,a3),double_divide(identity,identity)) = double_divide(double_divide(b3,a3),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(315,plain,
double_divide(double_divide(b3,a3),identity) = double_divide(double_divide(b3,a3),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[314]) ).
tff(316,plain,
double_divide(double_divide(b3,a3),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3)))),
inference(transitivity,[status(thm)],[315,313,310]) ).
tff(317,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))))),
inference(monotonicity,[status(thm)],[316]) ).
tff(318,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),
inference(symmetry,[status(thm)],[317]) ).
tff(319,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))))) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(320,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))))) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),
inference(unit_resolution,[status(thm)],[319,17]) ).
tff(321,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(identity,double_divide(multiply(b3,c3),a3))))),
inference(symmetry,[status(thm)],[320]) ).
tff(322,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),identity) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[113]) ).
tff(323,plain,
double_divide(double_divide(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))))),
inference(symmetry,[status(thm)],[286]) ).
tff(324,plain,
double_divide(double_divide(multiply(b3,c3),a3),identity) = double_divide(double_divide(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)))),
inference(symmetry,[status(thm)],[90]) ).
tff(325,plain,
double_divide(double_divide(multiply(b3,c3),a3),identity) = double_divide(identity,double_divide(multiply(b3,c3),a3)),
inference(transitivity,[status(thm)],[324,323,288,282,270]) ).
tff(326,plain,
double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),identity),
inference(monotonicity,[status(thm)],[325]) ).
tff(327,plain,
double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),
inference(transitivity,[status(thm)],[271,326,322,321,318]) ).
tff(328,plain,
double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[327,113]) ).
tff(329,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),identity),
inference(symmetry,[status(thm)],[328]) ).
tff(330,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(331,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(b3,a3),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
multiply(double_divide(double_divide(b3,a3),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),identity),
inference(unit_resolution,[status(thm)],[332,7]) ).
tff(334,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),b3))) = c3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(335,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),b3))) = c3,
inference(unit_resolution,[status(thm)],[334,17]) ).
tff(336,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))) = b3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(337,plain,
double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))) = b3,
inference(unit_resolution,[status(thm)],[336,17]) ).
tff(338,plain,
b3 = double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = b3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(340,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = b3,
inference(unit_resolution,[status(thm)],[339,17]) ).
tff(341,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),
inference(transitivity,[status(thm)],[340,338]) ).
tff(342,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[341]) ).
tff(343,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)))) = double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3)))),
inference(monotonicity,[status(thm)],[342,341]) ).
tff(344,plain,
double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),
inference(symmetry,[status(thm)],[343]) ).
tff(345,plain,
double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),b3) = double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3)))),
inference(monotonicity,[status(thm)],[338]) ).
tff(346,plain,
double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),b3) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),
inference(transitivity,[status(thm)],[345,344]) ).
tff(347,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(348,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),
inference(unit_resolution,[status(thm)],[347,17]) ).
tff(349,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(350,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))) = identity,
inference(unit_resolution,[status(thm)],[349,17]) ).
tff(351,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[105,85,82,46,29]) ).
tff(352,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(monotonicity,[status(thm)],[351]) ).
tff(353,plain,
double_divide(identity,double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)),
inference(symmetry,[status(thm)],[352]) ).
tff(354,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),
inference(monotonicity,[status(thm)],[250,353]) ).
tff(355,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(356,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(unit_resolution,[status(thm)],[355,17]) ).
tff(357,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[189]) ).
tff(358,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)))) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)),
inference(monotonicity,[status(thm)],[357,189]) ).
tff(359,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))),
inference(monotonicity,[status(thm)],[359]) ).
tff(361,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(transitivity,[status(thm)],[360,356]) ).
tff(362,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(c3,b3),identity))),
inference(monotonicity,[status(thm)],[362,361]) ).
tff(364,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity)))) = identity,
inference(transitivity,[status(thm)],[363,354,350]) ).
tff(365,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),identity) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
inference(monotonicity,[status(thm)],[189]) ).
tff(366,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)),double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(367,plain,
multiply(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)),double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),identity),
inference(unit_resolution,[status(thm)],[366,7]) ).
tff(368,plain,
multiply(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)),double_divide(identity,double_divide(identity,double_divide(c3,b3)))) = multiply(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)),double_divide(identity,double_divide(double_divide(c3,b3),identity))),
inference(monotonicity,[status(thm)],[203]) ).
tff(369,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)),double_divide(identity,double_divide(identity,double_divide(c3,b3)))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(370,plain,
multiply(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)),double_divide(identity,double_divide(identity,double_divide(c3,b3)))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),identity),
inference(unit_resolution,[status(thm)],[369,7]) ).
tff(371,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),identity) = multiply(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)),double_divide(identity,double_divide(identity,double_divide(c3,b3)))),
inference(symmetry,[status(thm)],[370]) ).
tff(372,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),
inference(symmetry,[status(thm)],[192]) ).
tff(373,plain,
double_divide(identity,double_divide(c3,b3)) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))))),
inference(symmetry,[status(thm)],[163]) ).
tff(374,plain,
double_divide(identity,double_divide(c3,b3)) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),
inference(transitivity,[status(thm)],[373,372]) ).
tff(375,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),identity) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),identity),
inference(monotonicity,[status(thm)],[374]) ).
tff(376,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(c3,b3)),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(377,plain,
double_divide(c3,b3) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))),
inference(symmetry,[status(thm)],[122]) ).
tff(378,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(c3,b3),identity)))) = double_divide(c3,b3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(379,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(c3,b3),identity)))) = double_divide(c3,b3),
inference(unit_resolution,[status(thm)],[378,17]) ).
tff(380,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(c3,b3),identity)) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(monotonicity,[status(thm)],[32]) ).
tff(381,plain,
double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[132,46,29]) ).
tff(382,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(c3,b3),identity))) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),
inference(monotonicity,[status(thm)],[381,380]) ).
tff(383,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(c3,b3),identity))),
inference(symmetry,[status(thm)],[382]) ).
tff(384,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(c3,b3),identity)))),
inference(monotonicity,[status(thm)],[156,383]) ).
tff(385,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[384,379,377,136,376,375,371,368,367,365,151]) ).
tff(386,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))))) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),identity),
inference(monotonicity,[status(thm)],[385,364]) ).
tff(387,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(c3,b3),identity))))),
inference(symmetry,[status(thm)],[386]) ).
tff(388,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(389,plain,
multiply(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),identity),
inference(unit_resolution,[status(thm)],[388,7]) ).
tff(390,plain,
multiply(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity)) = multiply(identity,double_divide(double_divide(c3,b3),identity)),
inference(monotonicity,[status(thm)],[95]) ).
tff(391,plain,
multiply(identity,double_divide(double_divide(c3,b3),identity)) = multiply(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity)),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
double_divide(double_divide(c3,b3),identity) = double_divide(identity,double_divide(c3,b3)),
inference(transitivity,[status(thm)],[206,205,163]) ).
tff(393,plain,
multiply(identity,double_divide(double_divide(c3,b3),identity)) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))),
inference(monotonicity,[status(thm)],[31,392]) ).
tff(394,plain,
multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))) = multiply(identity,double_divide(double_divide(c3,b3),identity)),
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
multiply(double_divide(identity,identity),double_divide(identity,double_divide(c3,b3))) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))),
inference(symmetry,[status(thm)],[143]) ).
tff(396,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),identity) = multiply(double_divide(identity,identity),double_divide(identity,double_divide(c3,b3))),
inference(symmetry,[status(thm)],[141]) ).
tff(397,plain,
double_divide(double_divide(c3,b3),identity) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),identity),
inference(symmetry,[status(thm)],[139]) ).
tff(398,plain,
double_divide(double_divide(c3,b3),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),
inference(transitivity,[status(thm)],[207,397,396,395,394,391,389,387,348]) ).
tff(399,plain,
double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),b3)) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))),
inference(monotonicity,[status(thm)],[398,346]) ).
tff(400,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))) = double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),b3)),
inference(symmetry,[status(thm)],[399]) ).
tff(401,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(402,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(unit_resolution,[status(thm)],[401,17]) ).
tff(403,plain,
double_divide(identity,double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))),
inference(symmetry,[status(thm)],[402]) ).
tff(404,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(405,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(unit_resolution,[status(thm)],[404,17]) ).
tff(406,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))) = double_divide(b3,a3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(407,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))) = double_divide(b3,a3),
inference(unit_resolution,[status(thm)],[406,17]) ).
tff(408,plain,
double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)) = double_divide(double_divide(b3,a3),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[407]) ).
tff(409,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3)),
inference(monotonicity,[status(thm)],[408,407]) ).
tff(410,plain,
double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),
inference(symmetry,[status(thm)],[409]) ).
tff(411,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))))),
inference(monotonicity,[status(thm)],[410]) ).
tff(412,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),
inference(symmetry,[status(thm)],[411]) ).
tff(413,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))))) = double_divide(identity,double_divide(b3,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(414,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))))) = double_divide(identity,double_divide(b3,a3)),
inference(unit_resolution,[status(thm)],[413,17]) ).
tff(415,plain,
double_divide(identity,double_divide(b3,a3)) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))))),
inference(symmetry,[status(thm)],[414]) ).
tff(416,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(b3,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(417,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(b3,a3)),
inference(unit_resolution,[status(thm)],[416,17]) ).
tff(418,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),identity),
inference(monotonicity,[status(thm)],[32]) ).
tff(419,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(c3,b3),identity),a3),
inference(transitivity,[status(thm)],[418,322,218,67,168]) ).
tff(420,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))) = double_divide(b3,a3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(421,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))) = double_divide(b3,a3),
inference(unit_resolution,[status(thm)],[420,17]) ).
tff(422,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(b3,a3)) = double_divide(double_divide(b3,a3),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(423,plain,
inverse(double_divide(b3,a3)) = double_divide(double_divide(b3,a3),identity),
inference(unit_resolution,[status(thm)],[422,41]) ).
tff(424,plain,
double_divide(double_divide(b3,a3),identity) = inverse(double_divide(b3,a3)),
inference(symmetry,[status(thm)],[423]) ).
tff(425,plain,
double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(monotonicity,[status(thm)],[424]) ).
tff(426,plain,
double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
inference(transitivity,[status(thm)],[425,32,50]) ).
tff(427,plain,
double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)) = identity,
inference(transitivity,[status(thm)],[425,32]) ).
tff(428,plain,
double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[427]) ).
tff(429,plain,
double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[428,59]) ).
tff(430,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),
inference(monotonicity,[status(thm)],[429,426]) ).
tff(431,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[430,49]) ).
tff(432,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[431]) ).
tff(433,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),
inference(symmetry,[status(thm)],[432]) ).
tff(434,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)) = double_divide(b3,a3),
inference(transitivity,[status(thm)],[433,421]) ).
tff(435,plain,
double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),identity) = double_divide(double_divide(b3,a3),identity),
inference(monotonicity,[status(thm)],[434]) ).
tff(436,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(identity,identity),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(437,plain,
multiply(double_divide(identity,identity),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),identity),
inference(unit_resolution,[status(thm)],[436,7]) ).
tff(438,plain,
multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))) = multiply(double_divide(identity,identity),double_divide(identity,double_divide(b3,a3))),
inference(monotonicity,[status(thm)],[142]) ).
tff(439,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(440,plain,
multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
inference(unit_resolution,[status(thm)],[439,7]) ).
tff(441,plain,
double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),
inference(symmetry,[status(thm)],[440]) ).
tff(442,plain,
double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(443,plain,
double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(b3,a3),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[442,441,438,437,435,315]) ).
tff(444,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)),
inference(monotonicity,[status(thm)],[443,419]) ).
tff(445,plain,
double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(symmetry,[status(thm)],[444]) ).
tff(446,plain,
double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)),
inference(monotonicity,[status(thm)],[168]) ).
tff(447,plain,
double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(transitivity,[status(thm)],[446,445]) ).
tff(448,plain,
double_divide(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))))),
inference(symmetry,[status(thm)],[265]) ).
tff(449,plain,
double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(450,plain,
double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),identity) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[449]) ).
tff(451,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(452,plain,
multiply(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),identity),
inference(unit_resolution,[status(thm)],[451,7]) ).
tff(453,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),identity) = multiply(double_divide(identity,identity),double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(symmetry,[status(thm)],[73]) ).
tff(454,plain,
double_divide(double_divide(multiply(b3,c3),a3),identity) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[70,453,87,292,452,450]) ).
tff(455,plain,
double_divide(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),double_divide(identity,identity))),
inference(monotonicity,[status(thm)],[454]) ).
tff(456,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),double_divide(identity,identity))) = double_divide(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)),
inference(symmetry,[status(thm)],[455]) ).
tff(457,plain,
double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(458,plain,
double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),identity) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[457]) ).
tff(459,plain,
double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),identity) = multiply(identity,double_divide(double_divide(multiply(b3,c3),a3),identity)),
inference(symmetry,[status(thm)],[452]) ).
tff(460,plain,
double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[449,459,294,297,458]) ).
tff(461,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),double_divide(identity,identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity))),
inference(monotonicity,[status(thm)],[460]) ).
tff(462,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),identity),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[461]) ).
tff(463,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity))),
inference(monotonicity,[status(thm)],[113]) ).
tff(464,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[463]) ).
tff(465,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(multiply(b3,c3),a3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(466,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(multiply(b3,c3),a3),
inference(unit_resolution,[status(thm)],[465,17]) ).
tff(467,plain,
double_divide(multiply(b3,c3),a3) = double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(identity,identity)),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[466]) ).
tff(468,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(transitivity,[status(thm)],[218,67,467,464,462,456,448,267]) ).
tff(469,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
inference(monotonicity,[status(thm)],[468,447]) ).
tff(470,plain,
double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)) = double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),
inference(symmetry,[status(thm)],[446]) ).
tff(471,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3))),
inference(monotonicity,[status(thm)],[470]) ).
tff(472,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),
inference(transitivity,[status(thm)],[471,469,417,415,412]) ).
tff(473,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)))) = double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3)))),
inference(monotonicity,[status(thm)],[342,472]) ).
tff(474,plain,
double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),
inference(symmetry,[status(thm)],[473]) ).
tff(475,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(b3,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(476,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(b3,a3)),
inference(unit_resolution,[status(thm)],[475,17]) ).
tff(477,plain,
double_divide(double_divide(double_divide(b3,a3),identity),identity) = double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[113]) ).
tff(478,plain,
double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(b3,a3),identity),
inference(transitivity,[status(thm)],[442,441,438,437,435]) ).
tff(479,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
inference(monotonicity,[status(thm)],[478,120]) ).
tff(480,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[479,477]) ).
tff(481,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),
inference(monotonicity,[status(thm)],[280,480]) ).
tff(482,plain,
double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
inference(symmetry,[status(thm)],[481]) ).
tff(483,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(484,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),
inference(unit_resolution,[status(thm)],[483,17]) ).
tff(485,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(486,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),
inference(unit_resolution,[status(thm)],[485,17]) ).
tff(487,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[486]) ).
tff(488,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),
inference(monotonicity,[status(thm)],[487,486]) ).
tff(489,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))))) = double_divide(identity,double_divide(b3,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(490,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))))) = double_divide(identity,double_divide(b3,a3)),
inference(unit_resolution,[status(thm)],[489,17]) ).
tff(491,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))) = double_divide(c3,b3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(492,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))) = double_divide(c3,b3),
inference(unit_resolution,[status(thm)],[491,17]) ).
tff(493,plain,
double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)) = double_divide(double_divide(c3,b3),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[492]) ).
tff(494,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),
inference(monotonicity,[status(thm)],[493,492]) ).
tff(495,plain,
double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),
inference(symmetry,[status(thm)],[494]) ).
tff(496,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity))))),
inference(monotonicity,[status(thm)],[495]) ).
tff(497,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = double_divide(identity,double_divide(b3,a3)),
inference(transitivity,[status(thm)],[496,490]) ).
tff(498,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[497]) ).
tff(499,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)) = double_divide(b3,a3),
inference(transitivity,[status(thm)],[498,433,421]) ).
tff(500,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)))) = double_divide(double_divide(b3,a3),identity),
inference(monotonicity,[status(thm)],[499,217]) ).
tff(501,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))))) = double_divide(identity,double_divide(double_divide(b3,a3),identity)),
inference(monotonicity,[status(thm)],[264,500]) ).
tff(502,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))))) = double_divide(identity,double_divide(identity,double_divide(b3,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(503,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))))) = double_divide(identity,double_divide(identity,double_divide(b3,a3))),
inference(unit_resolution,[status(thm)],[502,17]) ).
tff(504,plain,
double_divide(identity,double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))))),
inference(symmetry,[status(thm)],[503]) ).
tff(505,plain,
double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))) = double_divide(identity,double_divide(b3,a3)),
inference(transitivity,[status(thm)],[482,476]) ).
tff(506,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)))) = double_divide(identity,double_divide(identity,double_divide(b3,a3))),
inference(monotonicity,[status(thm)],[505]) ).
tff(507,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)))) = double_divide(identity,double_divide(double_divide(b3,a3),identity)),
inference(transitivity,[status(thm)],[506,504,501]) ).
tff(508,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[507,488]) ).
tff(509,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(double_divide(b3,a3),identity)))))),
inference(symmetry,[status(thm)],[508]) ).
tff(510,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(511,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),identity),
inference(unit_resolution,[status(thm)],[510,17]) ).
tff(512,plain,
double_divide(double_divide(b3,a3),identity) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(identity,identity)))),
inference(symmetry,[status(thm)],[511]) ).
tff(513,plain,
double_divide(double_divide(b3,a3),identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),
inference(transitivity,[status(thm)],[512,509,484,482,476,415,412]) ).
tff(514,plain,
double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(515,plain,
double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity) = double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[514]) ).
tff(516,plain,
double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity),double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3)))),
inference(monotonicity,[status(thm)],[515,513]) ).
tff(517,plain,
double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity),double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),
inference(transitivity,[status(thm)],[516,474]) ).
tff(518,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))) = double_divide(identity,double_divide(multiply(b3,c3),a3)),
inference(monotonicity,[status(thm)],[302]) ).
tff(519,plain,
double_divide(identity,double_divide(multiply(b3,c3),a3)) = double_divide(identity,double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[518]) ).
tff(520,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)) = double_divide(identity,double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),
inference(transitivity,[status(thm)],[329,298,295,293,88,73,71,324,323,288,282,270,519]) ).
tff(521,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))))),
inference(monotonicity,[status(thm)],[520,517]) ).
tff(522,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),b3)),
inference(transitivity,[status(thm)],[521,405,403,400]) ).
tff(523,plain,
double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity),
inference(monotonicity,[status(thm)],[338,32]) ).
tff(524,plain,
double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity) = double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(symmetry,[status(thm)],[523]) ).
tff(525,plain,
double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)) = double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[514,524]) ).
tff(526,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[107]) ).
tff(527,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[105]) ).
tff(528,plain,
identity = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[28,112,111,84,527,526]) ).
tff(529,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[528,525]) ).
tff(530,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[529]) ).
tff(531,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[528,524]) ).
tff(532,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity)) = double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity))),
inference(transitivity,[status(thm)],[531,530]) ).
tff(533,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity))),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),double_divide(identity,identity)),b3))),
inference(monotonicity,[status(thm)],[532,522]) ).
tff(534,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(535,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),
inference(unit_resolution,[status(thm)],[534,17]) ).
tff(536,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(b3,a3))),identity),double_divide(double_divide(b3,a3),identity)))),
inference(symmetry,[status(thm)],[535]) ).
tff(537,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))) = c3,
inference(transitivity,[status(thm)],[536,533,335]) ).
tff(538,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(a3,b3) = double_divide(double_divide(b3,a3),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(539,plain,
multiply(a3,b3) = double_divide(double_divide(b3,a3),identity),
inference(unit_resolution,[status(thm)],[538,7]) ).
tff(540,plain,
double_divide(double_divide(b3,a3),identity) = multiply(a3,b3),
inference(symmetry,[status(thm)],[539]) ).
tff(541,plain,
multiply(double_divide(double_divide(b3,a3),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)))) = multiply(multiply(a3,b3),c3),
inference(monotonicity,[status(thm)],[540,537]) ).
tff(542,plain,
multiply(multiply(a3,b3),c3) = multiply(double_divide(double_divide(b3,a3),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)))),
inference(symmetry,[status(thm)],[541]) ).
tff(543,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(transitivity,[status(thm)],[542,333,331,329,298,295,293,88,73,71,10]) ).
tff(544,plain,
( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
<=> ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(545,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
tff(546,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(modus_ponens,[status(thm)],[545,544]) ).
tff(547,plain,
$false,
inference(unit_resolution,[status(thm)],[546,543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP495-1 : TPTP v9.0.0. Released v2.6.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 16:16:03 EDT 2025
% 0.13/0.35 % CPUTime :
% 2.61/2.81 % SZS status Unsatisfiable
% 2.61/2.81 % SZS output start Proof
% See solution above
% 2.75/2.92 % E exiting
%------------------------------------------------------------------------------