TSTP Solution File: GRP568-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:28:16 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 56
% Syntax : Number of formulae : 307 ( 256 unt; 6 typ; 0 def)
% Number of atoms : 354 ( 349 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 89 ( 40 ~; 36 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 149 ( 142 !; 0 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(double_divide_type,type,
double_divide: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
^ [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/sandbox/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(b,a) = double_divide(double_divide(a,b),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(b,a) = double_divide(double_divide(a,b),identity),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
double_divide(double_divide(a,b),identity) = multiply(b,a),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
<=> ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(b,a),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(b,a),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(b,a),
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/sandbox/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(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
identity = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = identity,
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
^ [A: $i] :
refl(
( ( inverse(A) = double_divide(A,identity) )
<=> ( inverse(A) = double_divide(A,identity) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
tff(34,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),identity),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),identity) = inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(b,a),inverse(double_divide(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
identity = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(unit_resolution,[status(thm)],[40,26]) ).
tff(42,plain,
double_divide(double_divide(b,a),inverse(double_divide(b,a))) = identity,
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),identity) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),identity),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[42]) ).
tff(46,plain,
double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(transitivity,[status(thm)],[45,44,39]) ).
tff(47,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(b,a)) = double_divide(double_divide(b,a),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
inverse(double_divide(b,a)) = double_divide(double_divide(b,a),identity),
inference(unit_resolution,[status(thm)],[47,36]) ).
tff(49,plain,
double_divide(double_divide(b,a),identity) = inverse(double_divide(b,a)),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(b,a),identity),
inference(monotonicity,[status(thm)],[42]) ).
tff(51,plain,
double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = inverse(double_divide(b,a)),
inference(transitivity,[status(thm)],[50,49]) ).
tff(52,plain,
double_divide(double_divide(b,a),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
double_divide(double_divide(double_divide(b,a),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(monotonicity,[status(thm)],[52,46]) ).
tff(54,plain,
double_divide(double_divide(double_divide(b,a),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = identity,
inference(transitivity,[status(thm)],[53,29]) ).
tff(55,plain,
double_divide(double_divide(b,a),double_divide(double_divide(double_divide(b,a),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(b,a),identity),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
double_divide(double_divide(b,a),identity) = double_divide(double_divide(b,a),double_divide(double_divide(double_divide(b,a),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(b,inverse(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
identity = double_divide(b,inverse(b)),
inference(unit_resolution,[status(thm)],[57,26]) ).
tff(59,plain,
double_divide(b,inverse(b)) = identity,
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(b) = double_divide(b,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
inverse(b) = double_divide(b,identity),
inference(unit_resolution,[status(thm)],[60,36]) ).
tff(62,plain,
double_divide(b,identity) = inverse(b),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(b,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(b,identity),
inference(unit_resolution,[status(thm)],[63,17]) ).
tff(65,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),inverse(double_divide(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(unit_resolution,[status(thm)],[65,17]) ).
tff(67,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[42,42]) ).
tff(68,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(transitivity,[status(thm)],[67,44,39]) ).
tff(69,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(transitivity,[status(thm)],[69,29,41]) ).
tff(71,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(monotonicity,[status(thm)],[70,46]) ).
tff(72,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = identity,
inference(transitivity,[status(thm)],[71,29]) ).
tff(73,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[42,72]) ).
tff(74,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
double_divide(identity,identity) = double_divide(double_divide(b,inverse(b)),identity),
inference(monotonicity,[status(thm)],[58]) ).
tff(76,plain,
double_divide(double_divide(b,inverse(b)),identity) = double_divide(identity,identity),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
double_divide(double_divide(b,inverse(b)),identity) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(transitivity,[status(thm)],[76,74]) ).
tff(78,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[77,67]) ).
tff(79,plain,
double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(transitivity,[status(thm)],[78,66]) ).
tff(80,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(monotonicity,[status(thm)],[79,46]) ).
tff(81,plain,
double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = identity,
inference(transitivity,[status(thm)],[80,29]) ).
tff(82,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[42,81]) ).
tff(83,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(transitivity,[status(thm)],[82,74]) ).
tff(84,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(b,inverse(b)),identity),
inference(unit_resolution,[status(thm)],[85,17]) ).
tff(87,plain,
double_divide(double_divide(b,inverse(b)),identity) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = identity,
inference(transitivity,[status(thm)],[45,75,87,84,66,42]) ).
tff(89,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)) = b,
inference(unit_resolution,[status(thm)],[89,17]) ).
tff(91,plain,
double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[67]) ).
tff(92,plain,
double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = b,
inference(transitivity,[status(thm)],[91,90]) ).
tff(93,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(b,identity),
inference(monotonicity,[status(thm)],[92,88]) ).
tff(94,plain,
double_divide(b,identity) = double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = b,
inference(unit_resolution,[status(thm)],[95,17]) ).
tff(97,plain,
double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(b,identity),
inference(monotonicity,[status(thm)],[42]) ).
tff(98,plain,
double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = inverse(b),
inference(transitivity,[status(thm)],[97,62]) ).
tff(99,plain,
double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(b,inverse(b)),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(transitivity,[status(thm)],[99,59,41]) ).
tff(101,plain,
double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(monotonicity,[status(thm)],[100,46]) ).
tff(102,plain,
double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = identity,
inference(transitivity,[status(thm)],[101,29]) ).
tff(103,plain,
double_divide(b,double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(b,identity),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
double_divide(b,identity) = double_divide(b,double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[104,67]) ).
tff(106,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = b,
inference(transitivity,[status(thm)],[105,96]) ).
tff(107,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(b,identity),
inference(monotonicity,[status(thm)],[106,88]) ).
tff(108,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(transitivity,[status(thm)],[107,94]) ).
tff(109,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = b,
inference(unit_resolution,[status(thm)],[112,17]) ).
tff(114,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),
inference(unit_resolution,[status(thm)],[114,17]) ).
tff(116,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[67]) ).
tff(117,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),
inference(transitivity,[status(thm)],[116,115]) ).
tff(118,plain,
double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[117,45]) ).
tff(119,plain,
double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(identity,identity)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(identity,identity)) = b,
inference(unit_resolution,[status(thm)],[120,17]) ).
tff(122,plain,
b = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = identity,
inference(transitivity,[status(thm)],[67,75,87,84,66,42]) ).
tff(124,plain,
double_divide(b,double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(b,identity),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
double_divide(b,double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(b,double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(transitivity,[status(thm)],[124,104]) ).
tff(126,plain,
double_divide(double_divide(b,double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[125,45]) ).
tff(127,plain,
double_divide(double_divide(b,double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(transitivity,[status(thm)],[126,96,122,119]) ).
tff(128,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[67]) ).
tff(132,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = b,
inference(transitivity,[status(thm)],[131,130,113]) ).
tff(133,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(b,identity),
inference(monotonicity,[status(thm)],[132,88]) ).
tff(134,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(transitivity,[status(thm)],[133,94]) ).
tff(135,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(unit_resolution,[status(thm)],[137,17]) ).
tff(139,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
b = double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(transitivity,[status(thm)],[122,119]) ).
tff(141,plain,
double_divide(identity,b) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(monotonicity,[status(thm)],[41,140]) ).
tff(142,plain,
double_divide(identity,b) = inverse(b),
inference(transitivity,[status(thm)],[141,139,136,111,64,62]) ).
tff(143,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(unit_resolution,[status(thm)],[143,17]) ).
tff(145,plain,
double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
double_divide(double_divide(b,inverse(b)),identity) = inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a)))),
inference(transitivity,[status(thm)],[76,44,39]) ).
tff(147,plain,
double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(monotonicity,[status(thm)],[41,146]) ).
tff(148,plain,
double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)) = identity,
inference(transitivity,[status(thm)],[147,29]) ).
tff(149,plain,
double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[76]) ).
tff(150,plain,
double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity)) = b,
inference(transitivity,[status(thm)],[149,121]) ).
tff(151,plain,
double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(a,b),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(a,b),identity),
inference(monotonicity,[status(thm)],[151,148]) ).
tff(153,plain,
double_divide(double_divide(a,b),identity) = double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(a,b),identity),
inference(monotonicity,[status(thm)],[42]) ).
tff(155,plain,
double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[154,153]) ).
tff(156,plain,
double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[156,45]) ).
tff(158,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[104,76]) ).
tff(160,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity)) = b,
inference(transitivity,[status(thm)],[159,96]) ).
tff(161,plain,
double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(a,b),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
double_divide(double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(a,b),identity),
inference(monotonicity,[status(thm)],[161,148]) ).
tff(163,plain,
double_divide(double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[162,153]) ).
tff(164,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)) = a,
inference(unit_resolution,[status(thm)],[164,17]) ).
tff(166,plain,
a = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)) = a,
inference(unit_resolution,[status(thm)],[167,17]) ).
tff(169,plain,
double_divide(double_divide(a,b),identity) = double_divide(double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))),
inference(symmetry,[status(thm)],[162]) ).
tff(170,plain,
double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[154,169]) ).
tff(171,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,identity),double_divide(double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[171,45]) ).
tff(173,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(transitivity,[status(thm)],[172,168,166,158]) ).
tff(174,plain,
double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(b,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(179,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(b,identity),
inference(unit_resolution,[status(thm)],[178,17]) ).
tff(180,plain,
double_divide(b,identity) = double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
double_divide(b,identity) = double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),
inference(transitivity,[status(thm)],[180,177,115]) ).
tff(182,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[181,163]) ).
tff(183,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(a,b),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(a,b),identity),
inference(unit_resolution,[status(thm)],[183,17]) ).
tff(185,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(a,b),
inference(unit_resolution,[status(thm)],[185,17]) ).
tff(187,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(a,b),inverse(double_divide(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
identity = double_divide(double_divide(a,b),inverse(double_divide(a,b))),
inference(unit_resolution,[status(thm)],[187,26]) ).
tff(189,plain,
double_divide(double_divide(a,b),inverse(double_divide(a,b))) = identity,
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(a,b)) = double_divide(double_divide(a,b),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
inverse(double_divide(a,b)) = double_divide(double_divide(a,b),identity),
inference(unit_resolution,[status(thm)],[190,36]) ).
tff(192,plain,
double_divide(double_divide(a,b),identity) = inverse(double_divide(a,b)),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = inverse(double_divide(a,b)),
inference(transitivity,[status(thm)],[154,192]) ).
tff(194,plain,
double_divide(double_divide(a,b),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(a,b),inverse(double_divide(a,b))),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
double_divide(double_divide(a,b),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,a),inverse(double_divide(b,a))),
inference(transitivity,[status(thm)],[194,189,41]) ).
tff(196,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),inverse(double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(monotonicity,[status(thm)],[195,46]) ).
tff(197,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = identity,
inference(transitivity,[status(thm)],[196,29]) ).
tff(198,plain,
double_divide(double_divide(a,b),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(a,b),identity),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
double_divide(double_divide(a,b),identity) = double_divide(double_divide(a,b),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
double_divide(double_divide(double_divide(a,b),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[199,67]) ).
tff(201,plain,
double_divide(double_divide(double_divide(a,b),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(a,b),
inference(transitivity,[status(thm)],[200,186]) ).
tff(202,plain,
double_divide(double_divide(double_divide(double_divide(a,b),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(a,b),identity),
inference(monotonicity,[status(thm)],[201,88]) ).
tff(203,plain,
double_divide(double_divide(a,b),identity) = double_divide(double_divide(double_divide(double_divide(a,b),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(a,b),
inference(unit_resolution,[status(thm)],[204,17]) ).
tff(206,plain,
double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[67]) ).
tff(207,plain,
double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(a,b),
inference(transitivity,[status(thm)],[206,205]) ).
tff(208,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(a,b),identity),
inference(monotonicity,[status(thm)],[207,88]) ).
tff(209,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(double_divide(a,b),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(transitivity,[status(thm)],[208,203]) ).
tff(210,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(a,b),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(213,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(unit_resolution,[status(thm)],[212,17]) ).
tff(214,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,inverse(b)),identity),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[84]) ).
tff(216,plain,
double_divide(double_divide(b,a),inverse(double_divide(b,a))) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[66]) ).
tff(217,plain,
double_divide(double_divide(b,a),inverse(double_divide(b,a))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[216,215,86,76]) ).
tff(218,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(transitivity,[status(thm)],[218,158]) ).
tff(220,plain,
double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[220,45]) ).
tff(222,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(symmetry,[status(thm)],[221]) ).
tff(223,plain,
double_divide(identity,b) = double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(transitivity,[status(thm)],[141,139,136,111,64,180,177,222]) ).
tff(224,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(225,plain,
double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),
inference(unit_resolution,[status(thm)],[224,17]) ).
tff(226,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(b,identity),inverse(double_divide(b,identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(227,plain,
identity = double_divide(double_divide(b,identity),inverse(double_divide(b,identity))),
inference(unit_resolution,[status(thm)],[226,26]) ).
tff(228,plain,
double_divide(double_divide(b,identity),inverse(double_divide(b,identity))) = identity,
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(b,identity)) = double_divide(double_divide(b,identity),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(230,plain,
inverse(double_divide(b,identity)) = double_divide(double_divide(b,identity),identity),
inference(unit_resolution,[status(thm)],[229,36]) ).
tff(231,plain,
double_divide(double_divide(b,identity),identity) = inverse(double_divide(b,identity)),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
identity = double_divide(identity,identity),
inference(transitivity,[status(thm)],[41,216,215,86,76]) ).
tff(233,plain,
double_divide(double_divide(b,identity),identity) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[104,232]) ).
tff(234,plain,
double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(b,identity),identity),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
b = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[96]) ).
tff(236,plain,
b = inverse(double_divide(b,identity)),
inference(transitivity,[status(thm)],[235,234,231]) ).
tff(237,plain,
double_divide(double_divide(b,identity),b) = double_divide(double_divide(b,identity),inverse(double_divide(b,identity))),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
double_divide(double_divide(b,identity),b) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[237,228,41,216,215,86,76]) ).
tff(239,plain,
double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(b,identity),b)) = double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(b,identity),b)) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[239,225]) ).
tff(241,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(b,identity),b)),double_divide(identity,b)) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(monotonicity,[status(thm)],[240,223]) ).
tff(242,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(b,identity),b)),double_divide(identity,b)) = double_divide(double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[241,214,211,184,169]) ).
tff(243,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(b,identity),b)),double_divide(identity,b))) = double_divide(double_divide(b,identity),double_divide(double_divide(a,double_divide(double_divide(b,identity),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(b,identity),b)),double_divide(identity,b))) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[243,182]) ).
tff(245,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(b,identity),b)),double_divide(identity,b))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(b,identity),b)),double_divide(identity,b))),double_divide(identity,identity)) = double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(247,plain,
double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(b,identity),b)),double_divide(identity,b))),double_divide(identity,identity)) = double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(unit_resolution,[status(thm)],[246,17]) ).
tff(248,plain,
double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(b,identity),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(b,identity),b)),double_divide(identity,b))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(250,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(unit_resolution,[status(thm)],[249,17]) ).
tff(251,plain,
double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[67]) ).
tff(252,plain,
double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[251,225]) ).
tff(253,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[252,45]) ).
tff(254,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = a,
inference(transitivity,[status(thm)],[253,165]) ).
tff(255,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(identity,a),
inference(monotonicity,[status(thm)],[42,254]) ).
tff(256,plain,
double_divide(identity,a) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(258,plain,
double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),
inference(unit_resolution,[status(thm)],[257,17]) ).
tff(259,plain,
double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[67]) ).
tff(260,plain,
double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),
inference(transitivity,[status(thm)],[259,258]) ).
tff(261,plain,
double_divide(double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[260,45]) ).
tff(262,plain,
double_divide(double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = a,
inference(transitivity,[status(thm)],[261,165]) ).
tff(263,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(identity,a),
inference(monotonicity,[status(thm)],[42,262]) ).
tff(264,plain,
double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(transitivity,[status(thm)],[263,256]) ).
tff(265,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(b,double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(b,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(267,plain,
double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)) = double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(unit_resolution,[status(thm)],[266,17]) ).
tff(268,plain,
double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))) = double_divide(double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(double_divide(double_divide(b,a),inverse(double_divide(b,a))),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity)) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[76]) ).
tff(270,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity)) = a,
inference(transitivity,[status(thm)],[269,165]) ).
tff(271,plain,
double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))) = double_divide(b,a),
inference(monotonicity,[status(thm)],[270]) ).
tff(272,plain,
double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))) = double_divide(double_divide(b,a),identity),
inference(monotonicity,[status(thm)],[271,148]) ).
tff(273,plain,
double_divide(double_divide(b,a),identity) = double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))),
inference(symmetry,[status(thm)],[272]) ).
tff(274,plain,
double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a)))) = double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity))),
inference(transitivity,[status(thm)],[50,273]) ).
tff(275,plain,
double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),
inference(monotonicity,[status(thm)],[274]) ).
tff(276,plain,
double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))) = double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[275,45]) ).
tff(277,plain,
double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
b = double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[90]) ).
tff(279,plain,
b = double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(transitivity,[status(thm)],[278,277]) ).
tff(280,plain,
double_divide(double_divide(b,a),b) = double_divide(double_divide(b,a),double_divide(double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(b,inverse(b)),identity))),double_divide(identity,double_divide(double_divide(b,inverse(b)),identity)))),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
double_divide(double_divide(b,a),b) = double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a))))),
inference(transitivity,[status(thm)],[280,268,265,250,248,245,158]) ).
tff(282,plain,
double_divide(double_divide(a,b),double_divide(double_divide(b,a),b)) = double_divide(double_divide(a,b),double_divide(double_divide(double_divide(b,double_divide(double_divide(b,double_divide(b,a)),double_divide(identity,a))),double_divide(double_divide(a,b),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(monotonicity,[status(thm)],[281]) ).
tff(283,plain,
double_divide(double_divide(a,b),double_divide(double_divide(b,a),b)) = b,
inference(transitivity,[status(thm)],[282,145,130,113]) ).
tff(284,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(b,a),b)),double_divide(identity,b)) = double_divide(b,inverse(b)),
inference(monotonicity,[status(thm)],[283,142]) ).
tff(285,plain,
double_divide(double_divide(double_divide(a,b),double_divide(double_divide(b,a),b)),double_divide(identity,b)) = identity,
inference(transitivity,[status(thm)],[284,59]) ).
tff(286,plain,
double_divide(double_divide(b,a),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(b,a),b)),double_divide(identity,b))) = double_divide(double_divide(b,a),identity),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
double_divide(double_divide(b,a),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(b,a),b)),double_divide(identity,b))) = double_divide(double_divide(b,a),double_divide(double_divide(double_divide(b,a),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),
inference(transitivity,[status(thm)],[286,56]) ).
tff(288,plain,
double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(b,a),b)),double_divide(identity,b))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(b,a),double_divide(double_divide(b,a),double_divide(double_divide(b,a),inverse(double_divide(b,a))))),double_divide(identity,double_divide(double_divide(b,a),inverse(double_divide(b,a)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(b,a),b)),double_divide(identity,b))),double_divide(identity,identity)) = double_divide(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(290,plain,
double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(b,a),b)),double_divide(identity,b))),double_divide(identity,identity)) = double_divide(a,b),
inference(unit_resolution,[status(thm)],[289,17]) ).
tff(291,plain,
double_divide(a,b) = double_divide(double_divide(double_divide(b,a),double_divide(double_divide(double_divide(a,b),double_divide(double_divide(b,a),b)),double_divide(identity,b))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
double_divide(a,b) = double_divide(b,a),
inference(transitivity,[status(thm)],[291,288,19]) ).
tff(293,plain,
double_divide(double_divide(a,b),identity) = double_divide(double_divide(b,a),identity),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
double_divide(double_divide(b,a),identity) = double_divide(double_divide(a,b),identity),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(a,b) = double_divide(double_divide(b,a),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(296,plain,
multiply(a,b) = double_divide(double_divide(b,a),identity),
inference(unit_resolution,[status(thm)],[295,7]) ).
tff(297,plain,
multiply(a,b) = multiply(b,a),
inference(transitivity,[status(thm)],[296,294,10]) ).
tff(298,plain,
( ( multiply(a,b) != multiply(b,a) )
<=> ( multiply(a,b) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(299,axiom,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
tff(300,plain,
multiply(a,b) != multiply(b,a),
inference(modus_ponens,[status(thm)],[299,298]) ).
tff(301,plain,
$false,
inference(unit_resolution,[status(thm)],[300,297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 17:53:45 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------