TSTP Solution File: GRP495-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP495-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 22:27:49 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 82
% Syntax : Number of formulae : 491 ( 414 unt; 7 typ; 0 def)
% Number of atoms : 562 ( 557 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 139 ( 65 ~; 61 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 202 ( 195 !; 0 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(c3_type,type,
c3: $i ).
tff(b3_type,type,
b3: $i ).
tff(a3_type,type,
a3: $i ).
tff(double_divide_type,type,
double_divide: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(5,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(a3,multiply(b3,c3)) = double_divide(double_divide(multiply(b3,c3),a3),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(a3,multiply(b3,c3)) = double_divide(double_divide(multiply(b3,c3),a3),identity),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
double_divide(double_divide(multiply(b3,c3),a3),identity) = multiply(a3,multiply(b3,c3)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
<=> ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)))) = double_divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)))) = double_divide(identity,identity),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))) = double_divide(b3,a3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))) = double_divide(b3,a3),
inference(unit_resolution,[status(thm)],[20,17]) ).
tff(22,plain,
^ [A: $i] :
refl(
( ( identity = double_divide(A,inverse(A)) )
<=> ( identity = double_divide(A,inverse(A)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
tff(26,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
identity = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) = identity,
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
^ [A: $i] :
refl(
( ( inverse(A) = double_divide(A,identity) )
<=> ( inverse(A) = double_divide(A,identity) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
tff(36,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(b3,a3)) = double_divide(double_divide(b3,a3),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
inverse(double_divide(b3,a3)) = double_divide(double_divide(b3,a3),identity),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
double_divide(double_divide(b3,a3),identity) = inverse(double_divide(b3,a3)),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)) = identity,
inference(transitivity,[status(thm)],[42,31]) ).
tff(44,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
identity = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(unit_resolution,[status(thm)],[44,28]) ).
tff(46,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = identity,
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),identity),
inference(unit_resolution,[status(thm)],[47,38]) ).
tff(49,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),identity) = inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),identity) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[31]) ).
tff(51,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),identity),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
double_divide(identity,identity) = inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[42,52]) ).
tff(54,plain,
double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[53,46]) ).
tff(55,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[54,43]) ).
tff(56,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)) = double_divide(b3,a3),
inference(transitivity,[status(thm)],[57,21]) ).
tff(59,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(unit_resolution,[status(thm)],[59,17]) ).
tff(61,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[52]) ).
tff(62,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[61,46]) ).
tff(63,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(transitivity,[status(thm)],[61,46,30]) ).
tff(64,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[63,52]) ).
tff(65,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[64,46]) ).
tff(66,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[65,62]) ).
tff(67,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[31]) ).
tff(69,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[31,31]) ).
tff(71,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[70,69]) ).
tff(72,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[71,67]) ).
tff(73,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(symmetry,[status(thm)],[70]) ).
tff(74,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(transitivity,[status(thm)],[74,72,60]) ).
tff(76,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[75,52]) ).
tff(77,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[76,46]) ).
tff(78,plain,
double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity))) = double_divide(identity,double_divide(b3,a3)),
inference(monotonicity,[status(thm)],[77,58]) ).
tff(79,plain,
double_divide(identity,double_divide(b3,a3)) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity))) = double_divide(identity,double_divide(b3,a3)),
inference(monotonicity,[status(thm)],[65,58]) ).
tff(81,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity))) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity))),
inference(transitivity,[status(thm)],[80,79]) ).
tff(82,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(unit_resolution,[status(thm)],[83,17]) ).
tff(85,plain,
double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),inverse(double_divide(identity,double_divide(multiply(b3,c3),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
identity = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),inverse(double_divide(identity,double_divide(multiply(b3,c3),a3)))),
inference(unit_resolution,[status(thm)],[86,28]) ).
tff(88,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),inverse(double_divide(identity,double_divide(multiply(b3,c3),a3)))) = identity,
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(identity,double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
inverse(double_divide(identity,double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),identity),
inference(unit_resolution,[status(thm)],[89,38]) ).
tff(91,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),identity) = inverse(double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(multiply(b3,c3),a3),inverse(double_divide(multiply(b3,c3),a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
identity = double_divide(double_divide(multiply(b3,c3),a3),inverse(double_divide(multiply(b3,c3),a3))),
inference(unit_resolution,[status(thm)],[92,28]) ).
tff(94,plain,
double_divide(double_divide(multiply(b3,c3),a3),inverse(double_divide(multiply(b3,c3),a3))) = identity,
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(multiply(b3,c3),a3),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
inverse(double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(multiply(b3,c3),a3),identity),
inference(unit_resolution,[status(thm)],[95,38]) ).
tff(97,plain,
double_divide(double_divide(multiply(b3,c3),a3),identity) = inverse(double_divide(multiply(b3,c3),a3)),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)) = double_divide(double_divide(multiply(b3,c3),a3),inverse(double_divide(multiply(b3,c3),a3))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)) = identity,
inference(transitivity,[status(thm)],[98,94]) ).
tff(100,plain,
double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(transitivity,[status(thm)],[98,94,30]) ).
tff(101,plain,
double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[100,52]) ).
tff(102,plain,
double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[101,46]) ).
tff(103,plain,
double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[102,99]) ).
tff(104,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
identity = double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity))),
inference(transitivity,[status(thm)],[30,85,82,19,104]) ).
tff(106,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),identity) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)))),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)))) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),identity),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)))) = double_divide(multiply(b3,c3),a3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)))) = double_divide(multiply(b3,c3),a3),
inference(unit_resolution,[status(thm)],[108,17]) ).
tff(110,plain,
double_divide(multiply(b3,c3),a3) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)))),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
double_divide(multiply(b3,c3),a3) = inverse(double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(transitivity,[status(thm)],[110,107,91]) ).
tff(112,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),inverse(double_divide(identity,double_divide(multiply(b3,c3),a3)))),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[112,88,30,85,82,19]) ).
tff(114,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[112,88,30,85,82,19,73]) ).
tff(115,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[115,72,60,85,82,19,73]) ).
tff(117,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[116,113]) ).
tff(118,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[72]) ).
tff(120,plain,
double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)))),
inference(symmetry,[status(thm)],[60]) ).
tff(121,plain,
identity = double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3))),
inference(transitivity,[status(thm)],[30,120,119,118]) ).
tff(122,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(identity,double_divide(multiply(b3,c3),a3))))) = double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(identity,double_divide(multiply(b3,c3),a3))))) = double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(unit_resolution,[status(thm)],[122,17]) ).
tff(124,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(identity,a3),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = double_divide(identity,a3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(identity,a3),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))) = double_divide(identity,a3),
inference(unit_resolution,[status(thm)],[124,17]) ).
tff(126,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(b3,c3) = double_divide(double_divide(c3,b3),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
multiply(b3,c3) = double_divide(double_divide(c3,b3),identity),
inference(unit_resolution,[status(thm)],[126,7]) ).
tff(128,plain,
double_divide(double_divide(c3,b3),identity) = multiply(b3,c3),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
double_divide(double_divide(double_divide(c3,b3),identity),a3) = double_divide(multiply(b3,c3),a3),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))) = double_divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))) = double_divide(identity,identity),
inference(unit_resolution,[status(thm)],[130,17]) ).
tff(132,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(a3,inverse(a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
identity = double_divide(a3,inverse(a3)),
inference(unit_resolution,[status(thm)],[132,28]) ).
tff(134,plain,
double_divide(a3,inverse(a3)) = identity,
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(a3) = double_divide(a3,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(136,plain,
inverse(a3) = double_divide(a3,identity),
inference(unit_resolution,[status(thm)],[135,38]) ).
tff(137,plain,
double_divide(a3,identity) = inverse(a3),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
double_divide(a3,double_divide(a3,identity)) = double_divide(a3,inverse(a3)),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
double_divide(a3,double_divide(a3,identity)) = identity,
inference(transitivity,[status(thm)],[138,134]) ).
tff(140,plain,
double_divide(a3,double_divide(a3,identity)) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(transitivity,[status(thm)],[138,134,30]) ).
tff(141,plain,
double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[140,52]) ).
tff(142,plain,
double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[141,46]) ).
tff(143,plain,
double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[142,139]) ).
tff(144,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity))),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
double_divide(a3,double_divide(a3,identity)) = double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity))),
inference(transitivity,[status(thm)],[138,134,30,85,82,19,144]) ).
tff(146,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(double_divide(double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,identity)),double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(identity,a3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(double_divide(double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,identity)),double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(identity,a3),
inference(unit_resolution,[status(thm)],[146,17]) ).
tff(148,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(unit_resolution,[status(thm)],[148,17]) ).
tff(150,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = identity,
inference(transitivity,[status(thm)],[149,31]) ).
tff(151,plain,
double_divide(double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[149,52]) ).
tff(152,plain,
double_divide(double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[151,46]) ).
tff(153,plain,
double_divide(double_divide(double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,identity)),double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[152,150]) ).
tff(154,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,identity)),double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)))) = double_divide(identity,double_divide(identity,a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)))) = double_divide(identity,double_divide(identity,a3)),
inference(unit_resolution,[status(thm)],[155,17]) ).
tff(157,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))) = a3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))) = a3,
inference(unit_resolution,[status(thm)],[157,17]) ).
tff(159,plain,
double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(double_divide(double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,identity)),double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))),
inference(monotonicity,[status(thm)],[154]) ).
tff(160,plain,
double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)) = double_divide(identity,a3),
inference(transitivity,[status(thm)],[159,147]) ).
tff(161,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))),
inference(monotonicity,[status(thm)],[160,144]) ).
tff(162,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)) = a3,
inference(transitivity,[status(thm)],[161,158]) ).
tff(163,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity))) = double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(monotonicity,[status(thm)],[162,63]) ).
tff(164,plain,
double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
double_divide(a3,identity) = double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(monotonicity,[status(thm)],[30]) ).
tff(166,plain,
double_divide(a3,identity) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity))),
inference(transitivity,[status(thm)],[165,164]) ).
tff(167,plain,
double_divide(double_divide(identity,identity),double_divide(a3,identity)) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[69,166]) ).
tff(168,plain,
double_divide(double_divide(identity,identity),double_divide(a3,identity)) = double_divide(identity,double_divide(identity,a3)),
inference(transitivity,[status(thm)],[167,156]) ).
tff(169,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(a3,identity)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(double_divide(double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,identity)),double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))),
inference(monotonicity,[status(thm)],[168,154]) ).
tff(170,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(a3,identity)),double_divide(identity,identity)) = double_divide(identity,a3),
inference(transitivity,[status(thm)],[169,147]) ).
tff(171,plain,
double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity))) = double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))),
inference(monotonicity,[status(thm)],[170,145]) ).
tff(172,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity))),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
a3 = double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))),
inference(symmetry,[status(thm)],[158]) ).
tff(174,plain,
a3 = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity))),
inference(transitivity,[status(thm)],[173,172]) ).
tff(175,plain,
double_divide(double_divide(identity,a3),a3) = double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
double_divide(double_divide(identity,a3),a3) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[175,131,73]) ).
tff(177,plain,
double_divide(double_divide(double_divide(identity,a3),a3),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
double_divide(double_divide(double_divide(identity,a3),a3),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[177,72,60,31]) ).
tff(179,plain,
double_divide(double_divide(double_divide(double_divide(identity,a3),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)) = double_divide(identity,double_divide(multiply(b3,c3),a3)),
inference(monotonicity,[status(thm)],[178,129]) ).
tff(180,plain,
double_divide(identity,double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(double_divide(double_divide(identity,a3),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3)),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),
inference(unit_resolution,[status(thm)],[181,17]) ).
tff(183,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(unit_resolution,[status(thm)],[183,17]) ).
tff(185,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))) = double_divide(double_divide(c3,b3),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))) = double_divide(double_divide(c3,b3),identity),
inference(unit_resolution,[status(thm)],[185,17]) ).
tff(187,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(c3,b3),identity),inverse(double_divide(double_divide(c3,b3),identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
identity = double_divide(double_divide(double_divide(c3,b3),identity),inverse(double_divide(double_divide(c3,b3),identity))),
inference(unit_resolution,[status(thm)],[187,28]) ).
tff(189,plain,
double_divide(double_divide(double_divide(c3,b3),identity),inverse(double_divide(double_divide(c3,b3),identity))) = identity,
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(double_divide(c3,b3),identity),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
inverse(double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
inference(unit_resolution,[status(thm)],[190,38]) ).
tff(192,plain,
double_divide(double_divide(double_divide(c3,b3),identity),identity) = inverse(double_divide(double_divide(c3,b3),identity)),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)) = double_divide(double_divide(double_divide(c3,b3),identity),inverse(double_divide(double_divide(c3,b3),identity))),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)) = identity,
inference(transitivity,[status(thm)],[193,189]) ).
tff(195,plain,
double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(transitivity,[status(thm)],[193,189,30]) ).
tff(196,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[195,52]) ).
tff(197,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[196,46]) ).
tff(198,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[197,194]) ).
tff(199,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity))),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),
inference(monotonicity,[status(thm)],[199]) ).
tff(201,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)) = double_divide(double_divide(c3,b3),identity),
inference(transitivity,[status(thm)],[200,186]) ).
tff(202,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(monotonicity,[status(thm)],[65,201]) ).
tff(203,plain,
double_divide(identity,double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[204,184,85,82,19]) ).
tff(206,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[204,184,85,82,19,73]) ).
tff(207,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[207,72,60,85,82,19,73]) ).
tff(209,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[208,205]) ).
tff(210,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity)))) = identity,
inference(transitivity,[status(thm)],[209,72,60,31]) ).
tff(211,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(c3,b3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(212,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(c3,b3),
inference(unit_resolution,[status(thm)],[211,17]) ).
tff(213,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)))),
inference(symmetry,[status(thm)],[82]) ).
tff(214,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)))),
inference(symmetry,[status(thm)],[19]) ).
tff(215,plain,
double_divide(identity,identity) = identity,
inference(transitivity,[status(thm)],[214,213,84,31]) ).
tff(216,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity)) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(218,plain,
identity = double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))),
inference(unit_resolution,[status(thm)],[217,28]) ).
tff(219,plain,
double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))) = identity,
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(c3,b3)) = double_divide(double_divide(c3,b3),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(221,plain,
inverse(double_divide(c3,b3)) = double_divide(double_divide(c3,b3),identity),
inference(unit_resolution,[status(thm)],[220,38]) ).
tff(222,plain,
double_divide(double_divide(c3,b3),identity) = inverse(double_divide(c3,b3)),
inference(symmetry,[status(thm)],[221]) ).
tff(223,plain,
double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(transitivity,[status(thm)],[223,219,30]) ).
tff(225,plain,
double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[224,52]) ).
tff(226,plain,
double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[225,46]) ).
tff(227,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity))) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),
inference(monotonicity,[status(thm)],[226,216]) ).
tff(228,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity))),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[30,52]) ).
tff(230,plain,
double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(identity,identity)),
inference(symmetry,[status(thm)],[229]) ).
tff(231,plain,
identity = double_divide(identity,double_divide(identity,identity)),
inference(transitivity,[status(thm)],[45,230]) ).
tff(232,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity)))),
inference(monotonicity,[status(thm)],[231,228]) ).
tff(233,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))) = double_divide(c3,b3),
inference(transitivity,[status(thm)],[232,212]) ).
tff(234,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))))) = double_divide(double_divide(c3,b3),identity),
inference(monotonicity,[status(thm)],[233,210]) ).
tff(235,plain,
double_divide(double_divide(c3,b3),identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(c3,b3),identity))))),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
double_divide(double_divide(c3,b3),identity) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),
inference(transitivity,[status(thm)],[235,182]) ).
tff(237,plain,
double_divide(identity,double_divide(double_divide(c3,b3),identity)) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(symmetry,[status(thm)],[237]) ).
tff(239,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),
inference(symmetry,[status(thm)],[232]) ).
tff(240,plain,
double_divide(c3,b3) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(c3,b3),identity)))),
inference(symmetry,[status(thm)],[212]) ).
tff(241,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))) = double_divide(c3,b3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(242,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))) = double_divide(c3,b3),
inference(unit_resolution,[status(thm)],[241,17]) ).
tff(243,plain,
double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)) = identity,
inference(transitivity,[status(thm)],[223,219]) ).
tff(244,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[226,243]) ).
tff(245,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))) = identity,
inference(transitivity,[status(thm)],[244,214,213,84,31]) ).
tff(246,plain,
double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
inference(monotonicity,[status(thm)],[215]) ).
tff(247,plain,
double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)) = inverse(double_divide(double_divide(c3,b3),identity)),
inference(transitivity,[status(thm)],[246,192]) ).
tff(248,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))),
inference(symmetry,[status(thm)],[244]) ).
tff(249,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)) = double_divide(c3,b3),
inference(transitivity,[status(thm)],[249,242]) ).
tff(251,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(double_divide(c3,b3),identity),
inference(monotonicity,[status(thm)],[250,215]) ).
tff(252,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))) = double_divide(double_divide(double_divide(c3,b3),identity),inverse(double_divide(double_divide(c3,b3),identity))),
inference(monotonicity,[status(thm)],[251,247]) ).
tff(253,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity))),
inference(transitivity,[status(thm)],[252,189,30,85,82,19,199]) ).
tff(254,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),
inference(monotonicity,[status(thm)],[253]) ).
tff(255,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)))) = double_divide(identity,double_divide(c3,b3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(256,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)))) = double_divide(identity,double_divide(c3,b3)),
inference(unit_resolution,[status(thm)],[255,17]) ).
tff(257,plain,
double_divide(identity,double_divide(c3,b3)) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)))),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
double_divide(identity,double_divide(c3,b3)) = double_divide(double_divide(c3,b3),identity),
inference(transitivity,[status(thm)],[257,254,186]) ).
tff(259,plain,
double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
inference(monotonicity,[status(thm)],[258,245]) ).
tff(260,plain,
double_divide(double_divide(double_divide(c3,b3),identity),identity) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
double_divide(double_divide(double_divide(c3,b3),identity),identity) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(transitivity,[status(thm)],[260,242,240,239,238]) ).
tff(262,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(identity,double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(identity,a3),a3),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),a3))),
inference(monotonicity,[status(thm)],[261,180]) ).
tff(263,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(identity,double_divide(multiply(b3,c3),a3))) = double_divide(identity,a3),
inference(transitivity,[status(thm)],[262,125]) ).
tff(264,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(265,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(unit_resolution,[status(thm)],[264,17]) ).
tff(266,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(double_divide(double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)),double_divide(identity,identity)),double_divide(double_divide(multiply(b3,c3),a3),double_divide(double_divide(multiply(b3,c3),a3),identity)))),
inference(monotonicity,[status(thm)],[104]) ).
tff(267,plain,
double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)) = double_divide(multiply(b3,c3),a3),
inference(transitivity,[status(thm)],[266,109]) ).
tff(268,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))) = double_divide(identity,double_divide(multiply(b3,c3),a3)),
inference(monotonicity,[status(thm)],[65,267]) ).
tff(269,plain,
double_divide(identity,double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[268]) ).
tff(270,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[270,265,85,82,19,73]) ).
tff(272,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[271]) ).
tff(273,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[272,72,60,31]) ).
tff(274,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(identity,double_divide(multiply(b3,c3),a3)))) = double_divide(identity,double_divide(identity,a3)),
inference(monotonicity,[status(thm)],[273,263]) ).
tff(275,plain,
double_divide(identity,double_divide(identity,a3)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(identity,double_divide(multiply(b3,c3),a3)))),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(identity,identity)))) = double_divide(identity,double_divide(identity,a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(277,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(identity,identity)))) = double_divide(identity,double_divide(identity,a3)),
inference(unit_resolution,[status(thm)],[276,17]) ).
tff(278,plain,
double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(a3,identity),
inference(symmetry,[status(thm)],[165]) ).
tff(279,plain,
double_divide(identity,identity) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(transitivity,[status(thm)],[214,213,84]) ).
tff(280,plain,
double_divide(a3,double_divide(identity,identity)) = double_divide(a3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
double_divide(a3,double_divide(identity,identity)) = inverse(a3),
inference(transitivity,[status(thm)],[280,278,137]) ).
tff(282,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(identity,identity))) = double_divide(a3,inverse(a3)),
inference(monotonicity,[status(thm)],[162,281]) ).
tff(283,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(identity,identity))) = double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity))),
inference(transitivity,[status(thm)],[282,134,30,85,82,19,144]) ).
tff(284,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(identity,identity)))) = double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))),
inference(monotonicity,[status(thm)],[283]) ).
tff(285,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))) = double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(identity,identity)))),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
a3 = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(identity,double_divide(multiply(b3,c3),a3)))),
inference(transitivity,[status(thm)],[173,285,277,275]) ).
tff(287,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[74,72,60,31]) ).
tff(288,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(identity,identity))) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
inference(monotonicity,[status(thm)],[251,287]) ).
tff(289,plain,
double_divide(double_divide(double_divide(c3,b3),identity),identity) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),identity)) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[231,289]) ).
tff(291,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(identity,identity)))) = double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),identity)),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(identity,identity)))) = double_divide(identity,double_divide(c3,b3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(293,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(identity,identity)))) = double_divide(identity,double_divide(c3,b3)),
inference(unit_resolution,[status(thm)],[292,17]) ).
tff(294,plain,
double_divide(identity,double_divide(c3,b3)) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(identity,identity)))),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,identity)))),
inference(symmetry,[status(thm)],[254]) ).
tff(296,plain,
double_divide(double_divide(c3,b3),identity) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(identity,identity)),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),
inference(symmetry,[status(thm)],[186]) ).
tff(297,plain,
multiply(b3,c3) = double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),identity)),
inference(transitivity,[status(thm)],[127,296,295,256,294,291]) ).
tff(298,plain,
double_divide(multiply(b3,c3),a3) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(identity,double_divide(multiply(b3,c3),a3))))),
inference(monotonicity,[status(thm)],[297,286]) ).
tff(299,plain,
double_divide(multiply(b3,c3),a3) = double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),
inference(transitivity,[status(thm)],[298,123]) ).
tff(300,plain,
double_divide(double_divide(multiply(b3,c3),a3),identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)))),
inference(monotonicity,[status(thm)],[299,121]) ).
tff(301,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)))) = double_divide(double_divide(multiply(b3,c3),a3),identity),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)))) = double_divide(identity,double_divide(multiply(b3,c3),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(303,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)))) = double_divide(identity,double_divide(multiply(b3,c3),a3)),
inference(unit_resolution,[status(thm)],[302,17]) ).
tff(304,plain,
double_divide(identity,double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(identity,double_divide(identity,double_divide(multiply(b3,c3),a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)))),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(a3,double_divide(multiply(b3,c3),a3)))) = double_divide(identity,double_divide(multiply(b3,c3),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(306,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(a3,double_divide(multiply(b3,c3),a3)))) = double_divide(identity,double_divide(multiply(b3,c3),a3)),
inference(unit_resolution,[status(thm)],[305,17]) ).
tff(307,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(identity,a3),a3))) = b3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(308,plain,
double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(identity,a3),a3))) = b3,
inference(unit_resolution,[status(thm)],[307,17]) ).
tff(309,plain,
double_divide(double_divide(identity,a3),a3) = double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))),
inference(transitivity,[status(thm)],[175,131,56]) ).
tff(310,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)))) = double_divide(identity,double_divide(b3,a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(311,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)))) = double_divide(identity,double_divide(b3,a3)),
inference(unit_resolution,[status(thm)],[310,17]) ).
tff(312,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(identity,double_divide(b3,a3)),inverse(double_divide(identity,double_divide(b3,a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(313,plain,
identity = double_divide(double_divide(identity,double_divide(b3,a3)),inverse(double_divide(identity,double_divide(b3,a3)))),
inference(unit_resolution,[status(thm)],[312,28]) ).
tff(314,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),inverse(double_divide(identity,double_divide(b3,a3)))) = identity,
inference(symmetry,[status(thm)],[313]) ).
tff(315,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(identity,double_divide(b3,a3)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(316,plain,
inverse(double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(identity,double_divide(b3,a3)),identity),
inference(unit_resolution,[status(thm)],[315,38]) ).
tff(317,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),identity) = inverse(double_divide(identity,double_divide(b3,a3))),
inference(symmetry,[status(thm)],[316]) ).
tff(318,plain,
identity = double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))),
inference(transitivity,[status(thm)],[30,85,82,19,56]) ).
tff(319,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),identity) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),
inference(monotonicity,[status(thm)],[318]) ).
tff(320,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(identity,double_divide(b3,a3)),identity),
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
double_divide(b3,a3) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),
inference(symmetry,[status(thm)],[21]) ).
tff(322,plain,
double_divide(b3,a3) = inverse(double_divide(identity,double_divide(b3,a3))),
inference(transitivity,[status(thm)],[321,320,317]) ).
tff(323,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)) = double_divide(double_divide(identity,double_divide(b3,a3)),inverse(double_divide(identity,double_divide(b3,a3)))),
inference(monotonicity,[status(thm)],[322]) ).
tff(324,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[323,314,30,85,82,19]) ).
tff(325,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[323,314,30,85,82,19,73]) ).
tff(326,plain,
double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[325]) ).
tff(327,plain,
double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[326,72,60,85,82,19,73]) ).
tff(328,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[327,324]) ).
tff(329,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3))),
inference(symmetry,[status(thm)],[328]) ).
tff(330,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3))),
inference(transitivity,[status(thm)],[214,213,84,120,119,329]) ).
tff(331,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))))) = double_divide(identity,double_divide(identity,double_divide(b3,a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(332,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))))) = double_divide(identity,double_divide(identity,double_divide(b3,a3))),
inference(unit_resolution,[status(thm)],[331,17]) ).
tff(333,plain,
double_divide(identity,double_divide(b3,a3)) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[80]) ).
tff(334,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[333]) ).
tff(335,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[334,82,19]) ).
tff(336,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[334,82,19,73]) ).
tff(337,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[336]) ).
tff(338,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[337,72,60,85,82,19,73]) ).
tff(339,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[338,335]) ).
tff(340,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3)))),
inference(symmetry,[status(thm)],[339]) ).
tff(341,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[55,214,213,84,120,119,340]) ).
tff(342,plain,
double_divide(double_divide(identity,identity),double_divide(b3,a3)) = double_divide(identity,double_divide(b3,a3)),
inference(monotonicity,[status(thm)],[215]) ).
tff(343,plain,
double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[326,72,60,31]) ).
tff(344,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(b3,a3))) = double_divide(identity,double_divide(identity,double_divide(b3,a3))),
inference(monotonicity,[status(thm)],[343,342]) ).
tff(345,plain,
double_divide(identity,double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(b3,a3))),
inference(symmetry,[status(thm)],[344]) ).
tff(346,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(b3,a3)))),
inference(monotonicity,[status(thm)],[231,345]) ).
tff(347,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(b3,a3)))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(b3,a3)))),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(b3,a3)))) = double_divide(identity,double_divide(b3,a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(349,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(b3,a3)))) = double_divide(identity,double_divide(b3,a3)),
inference(unit_resolution,[status(thm)],[348,17]) ).
tff(350,plain,
double_divide(identity,double_divide(b3,a3)) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(b3,a3)))),
inference(symmetry,[status(thm)],[349]) ).
tff(351,plain,
double_divide(identity,double_divide(b3,a3)) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[350,347]) ).
tff(352,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[351,341]) ).
tff(353,plain,
double_divide(b3,a3) = double_divide(identity,double_divide(identity,double_divide(b3,a3))),
inference(transitivity,[status(thm)],[321,352,332]) ).
tff(354,plain,
double_divide(double_divide(b3,a3),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)))),
inference(monotonicity,[status(thm)],[353,330]) ).
tff(355,plain,
double_divide(double_divide(b3,a3),double_divide(identity,identity)) = double_divide(identity,double_divide(b3,a3)),
inference(transitivity,[status(thm)],[354,311]) ).
tff(356,plain,
double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(identity,a3),a3)) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),
inference(monotonicity,[status(thm)],[355,309]) ).
tff(357,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(identity,a3),a3)),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))))) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),
inference(symmetry,[status(thm)],[352]) ).
tff(359,plain,
double_divide(identity,double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))))),
inference(symmetry,[status(thm)],[332]) ).
tff(360,plain,
double_divide(identity,double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(identity,a3),a3)),
inference(transitivity,[status(thm)],[359,358,357]) ).
tff(361,plain,
a3 = double_divide(identity,double_divide(identity,a3)),
inference(transitivity,[status(thm)],[173,285,277]) ).
tff(362,plain,
double_divide(a3,double_divide(identity,double_divide(identity,double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(double_divide(double_divide(b3,a3),double_divide(identity,identity)),double_divide(double_divide(identity,a3),a3))),
inference(monotonicity,[status(thm)],[361,360]) ).
tff(363,plain,
double_divide(a3,double_divide(identity,double_divide(identity,double_divide(b3,a3)))) = b3,
inference(transitivity,[status(thm)],[362,308]) ).
tff(364,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,c3),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = c3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(365,plain,
double_divide(double_divide(identity,c3),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))) = c3,
inference(unit_resolution,[status(thm)],[364,17]) ).
tff(366,plain,
double_divide(c3,b3) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))),
inference(symmetry,[status(thm)],[242]) ).
tff(367,plain,
double_divide(c3,b3) = inverse(double_divide(double_divide(c3,b3),identity)),
inference(transitivity,[status(thm)],[366,259,192]) ).
tff(368,plain,
double_divide(double_divide(c3,b3),double_divide(identity,identity)) = double_divide(double_divide(c3,b3),identity),
inference(monotonicity,[status(thm)],[215]) ).
tff(369,plain,
double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)) = double_divide(double_divide(double_divide(c3,b3),identity),inverse(double_divide(double_divide(c3,b3),identity))),
inference(monotonicity,[status(thm)],[368,367]) ).
tff(370,plain,
double_divide(double_divide(double_divide(c3,b3),identity),inverse(double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3)),
inference(transitivity,[status(thm)],[214,213,84,31,188,370]) ).
tff(372,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))))) = double_divide(identity,c3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(373,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))))) = double_divide(identity,c3),
inference(unit_resolution,[status(thm)],[372,17]) ).
tff(374,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(375,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(unit_resolution,[status(thm)],[374,17]) ).
tff(376,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(c3,multiply(a3,b3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(377,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(c3,multiply(a3,b3)),
inference(unit_resolution,[status(thm)],[376,17]) ).
tff(378,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(c3,multiply(a3,b3)),inverse(double_divide(c3,multiply(a3,b3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(379,plain,
identity = double_divide(double_divide(c3,multiply(a3,b3)),inverse(double_divide(c3,multiply(a3,b3)))),
inference(unit_resolution,[status(thm)],[378,28]) ).
tff(380,plain,
double_divide(double_divide(c3,multiply(a3,b3)),inverse(double_divide(c3,multiply(a3,b3)))) = identity,
inference(symmetry,[status(thm)],[379]) ).
tff(381,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(c3,multiply(a3,b3))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(382,plain,
inverse(double_divide(c3,multiply(a3,b3))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
inference(unit_resolution,[status(thm)],[381,38]) ).
tff(383,plain,
double_divide(double_divide(c3,multiply(a3,b3)),identity) = inverse(double_divide(c3,multiply(a3,b3))),
inference(symmetry,[status(thm)],[382]) ).
tff(384,plain,
double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)) = double_divide(double_divide(c3,multiply(a3,b3)),inverse(double_divide(c3,multiply(a3,b3)))),
inference(monotonicity,[status(thm)],[383]) ).
tff(385,plain,
double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)) = identity,
inference(transitivity,[status(thm)],[384,380]) ).
tff(386,plain,
double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
inference(transitivity,[status(thm)],[384,380,30]) ).
tff(387,plain,
double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
inference(monotonicity,[status(thm)],[386,52]) ).
tff(388,plain,
double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[387,46]) ).
tff(389,plain,
double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[388,385]) ).
tff(390,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
inference(monotonicity,[status(thm)],[390]) ).
tff(392,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)) = double_divide(c3,multiply(a3,b3)),
inference(transitivity,[status(thm)],[391,377]) ).
tff(393,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,identity))) = double_divide(identity,double_divide(c3,multiply(a3,b3))),
inference(monotonicity,[status(thm)],[65,392]) ).
tff(394,plain,
double_divide(identity,double_divide(c3,multiply(a3,b3))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[394]) ).
tff(396,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))),
inference(transitivity,[status(thm)],[395,375,85,82,19,56]) ).
tff(397,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,c3),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(c3,double_divide(double_divide(b3,a3),identity)))) = double_divide(b3,a3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(398,plain,
double_divide(double_divide(identity,c3),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(c3,double_divide(double_divide(b3,a3),identity)))) = double_divide(b3,a3),
inference(unit_resolution,[status(thm)],[397,17]) ).
tff(399,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(a3,b3) = double_divide(double_divide(b3,a3),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(400,plain,
multiply(a3,b3) = double_divide(double_divide(b3,a3),identity),
inference(unit_resolution,[status(thm)],[399,7]) ).
tff(401,plain,
double_divide(double_divide(b3,a3),identity) = multiply(a3,b3),
inference(symmetry,[status(thm)],[400]) ).
tff(402,plain,
double_divide(c3,double_divide(double_divide(b3,a3),identity)) = double_divide(c3,multiply(a3,b3)),
inference(monotonicity,[status(thm)],[401]) ).
tff(403,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(c3,double_divide(double_divide(b3,a3),identity))) = double_divide(identity,double_divide(c3,multiply(a3,b3))),
inference(monotonicity,[status(thm)],[54,402]) ).
tff(404,plain,
double_divide(identity,double_divide(c3,multiply(a3,b3))) = double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(c3,double_divide(double_divide(b3,a3),identity))),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
double_divide(double_divide(identity,c3),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(identity,c3),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),
inference(monotonicity,[status(thm)],[404]) ).
tff(406,plain,
double_divide(double_divide(identity,c3),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(identity,double_divide(identity,double_divide(b3,a3))),
inference(transitivity,[status(thm)],[405,398,321,352,332]) ).
tff(407,plain,
double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(identity,double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(b3,a3)))),
inference(monotonicity,[status(thm)],[406,330]) ).
tff(408,plain,
double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)) = double_divide(identity,double_divide(b3,a3)),
inference(transitivity,[status(thm)],[407,311]) ).
tff(409,plain,
double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3))))) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),
inference(monotonicity,[status(thm)],[408,396]) ).
tff(410,plain,
double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),double_divide(identity,identity)),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3))))),
inference(symmetry,[status(thm)],[409]) ).
tff(411,plain,
double_divide(identity,double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3))))),
inference(transitivity,[status(thm)],[359,358,410]) ).
tff(412,plain,
double_divide(double_divide(identity,identity),double_divide(c3,multiply(a3,b3))) = double_divide(identity,double_divide(c3,multiply(a3,b3))),
inference(monotonicity,[status(thm)],[215]) ).
tff(413,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),inverse(double_divide(identity,double_divide(c3,multiply(a3,b3))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(414,plain,
identity = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),inverse(double_divide(identity,double_divide(c3,multiply(a3,b3))))),
inference(unit_resolution,[status(thm)],[413,28]) ).
tff(415,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),inverse(double_divide(identity,double_divide(c3,multiply(a3,b3))))) = identity,
inference(symmetry,[status(thm)],[414]) ).
tff(416,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(417,plain,
inverse(double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),
inference(unit_resolution,[status(thm)],[416,38]) ).
tff(418,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity) = inverse(double_divide(identity,double_divide(c3,multiply(a3,b3)))),
inference(symmetry,[status(thm)],[417]) ).
tff(419,plain,
identity = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
inference(transitivity,[status(thm)],[30,85,82,19,390]) ).
tff(420,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
inference(monotonicity,[status(thm)],[419]) ).
tff(421,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
double_divide(c3,multiply(a3,b3)) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
inference(symmetry,[status(thm)],[377]) ).
tff(423,plain,
double_divide(c3,multiply(a3,b3)) = inverse(double_divide(identity,double_divide(c3,multiply(a3,b3)))),
inference(transitivity,[status(thm)],[422,421,418]) ).
tff(424,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),inverse(double_divide(identity,double_divide(c3,multiply(a3,b3))))),
inference(monotonicity,[status(thm)],[423]) ).
tff(425,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[424,415,30,85,82,19,73]) ).
tff(426,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[425]) ).
tff(427,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[426,72,60,31]) ).
tff(428,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(c3,multiply(a3,b3)))) = double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),
inference(monotonicity,[status(thm)],[427,412]) ).
tff(429,plain,
double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(c3,multiply(a3,b3)))),
inference(symmetry,[status(thm)],[428]) ).
tff(430,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(c3,multiply(a3,b3))))),
inference(monotonicity,[status(thm)],[231,429]) ).
tff(431,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(c3,multiply(a3,b3))))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),
inference(symmetry,[status(thm)],[430]) ).
tff(432,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(c3,multiply(a3,b3))))) = double_divide(identity,double_divide(c3,multiply(a3,b3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(433,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(c3,multiply(a3,b3))))) = double_divide(identity,double_divide(c3,multiply(a3,b3))),
inference(unit_resolution,[status(thm)],[432,17]) ).
tff(434,plain,
double_divide(identity,double_divide(c3,multiply(a3,b3))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(c3,multiply(a3,b3))))),
inference(symmetry,[status(thm)],[433]) ).
tff(435,plain,
double_divide(identity,double_divide(c3,multiply(a3,b3))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),
inference(transitivity,[status(thm)],[434,431]) ).
tff(436,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))))),
inference(monotonicity,[status(thm)],[435,411]) ).
tff(437,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))) = double_divide(identity,c3),
inference(transitivity,[status(thm)],[436,373]) ).
tff(438,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(identity,c3),double_divide(double_divide(double_divide(c3,b3),double_divide(identity,identity)),double_divide(c3,b3))),
inference(monotonicity,[status(thm)],[437,371]) ).
tff(439,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)) = c3,
inference(transitivity,[status(thm)],[438,365]) ).
tff(440,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(identity,double_divide(identity,double_divide(b3,a3))))) = double_divide(c3,b3),
inference(monotonicity,[status(thm)],[439,363]) ).
tff(441,plain,
double_divide(c3,b3) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(identity,double_divide(identity,double_divide(b3,a3))))),
inference(symmetry,[status(thm)],[440]) ).
tff(442,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,a3),double_divide(identity,identity)))) = double_divide(identity,double_divide(c3,b3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(443,plain,
double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,a3),double_divide(identity,identity)))) = double_divide(identity,double_divide(c3,b3)),
inference(unit_resolution,[status(thm)],[442,17]) ).
tff(444,plain,
double_divide(double_divide(identity,a3),double_divide(identity,identity)) = double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(a3,double_divide(a3,identity)),double_divide(identity,identity)),double_divide(a3,double_divide(a3,identity)))),
inference(monotonicity,[status(thm)],[144]) ).
tff(445,plain,
double_divide(double_divide(identity,a3),double_divide(identity,identity)) = a3,
inference(transitivity,[status(thm)],[444,158]) ).
tff(446,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)) = multiply(b3,c3),
inference(transitivity,[status(thm)],[251,128]) ).
tff(447,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,a3),double_divide(identity,identity))) = double_divide(multiply(b3,c3),a3),
inference(monotonicity,[status(thm)],[446,445]) ).
tff(448,plain,
double_divide(multiply(b3,c3),a3) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,a3),double_divide(identity,identity))),
inference(symmetry,[status(thm)],[447]) ).
tff(449,plain,
double_divide(a3,double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(identity,double_divide(identity,a3)),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,identity)),double_divide(identity,identity)),double_divide(double_divide(identity,a3),double_divide(identity,identity)))),
inference(monotonicity,[status(thm)],[361,448]) ).
tff(450,plain,
double_divide(a3,double_divide(multiply(b3,c3),a3)) = double_divide(double_divide(c3,b3),identity),
inference(transitivity,[status(thm)],[449,443,257,254,186]) ).
tff(451,plain,
double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[115,72,60,31]) ).
tff(452,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(a3,double_divide(multiply(b3,c3),a3))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
inference(monotonicity,[status(thm)],[451,450]) ).
tff(453,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(a3,double_divide(multiply(b3,c3),a3))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(identity,double_divide(identity,double_divide(b3,a3))))),
inference(transitivity,[status(thm)],[452,237,232,212,441]) ).
tff(454,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(a3,double_divide(multiply(b3,c3),a3)))) = double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(identity,double_divide(identity,double_divide(b3,a3)))))),
inference(monotonicity,[status(thm)],[453]) ).
tff(455,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(identity,double_divide(identity,double_divide(b3,a3)))))) = double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(multiply(b3,c3),a3)),double_divide(multiply(b3,c3),a3)),double_divide(identity,identity)),double_divide(a3,double_divide(multiply(b3,c3),a3)))),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(identity,double_divide(identity,double_divide(b3,a3)))))) = double_divide(identity,double_divide(c3,multiply(a3,b3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(457,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(identity,double_divide(identity,double_divide(b3,a3)))))) = double_divide(identity,double_divide(c3,multiply(a3,b3))),
inference(unit_resolution,[status(thm)],[456,17]) ).
tff(458,plain,
double_divide(identity,double_divide(c3,multiply(a3,b3))) = double_divide(double_divide(identity,a3),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,identity)),double_divide(a3,double_divide(identity,double_divide(identity,double_divide(b3,a3)))))),
inference(symmetry,[status(thm)],[457]) ).
tff(459,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))))) = double_divide(identity,double_divide(c3,multiply(a3,b3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(460,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))))) = double_divide(identity,double_divide(c3,multiply(a3,b3))),
inference(unit_resolution,[status(thm)],[459,17]) ).
tff(461,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[424,415,30,85,82,19]) ).
tff(462,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[426,72,60,85,82,19,73]) ).
tff(463,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[462,461]) ).
tff(464,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3)))),
inference(symmetry,[status(thm)],[463]) ).
tff(465,plain,
identity = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3)))),
inference(transitivity,[status(thm)],[30,120,119,464]) ).
tff(466,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))))) = double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(467,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))))) = double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),
inference(unit_resolution,[status(thm)],[466,17]) ).
tff(468,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[395,375,85,82,19]) ).
tff(469,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[395,375,85,82,19,73]) ).
tff(470,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[469]) ).
tff(471,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
inference(transitivity,[status(thm)],[470,72,60,85,82,19,73]) ).
tff(472,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[471,468]) ).
tff(473,plain,
double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3))))),
inference(symmetry,[status(thm)],[472]) ).
tff(474,plain,
double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3))))),
inference(transitivity,[status(thm)],[389,214,213,84,120,119,473]) ).
tff(475,plain,
double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(identity,identity)),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(c3,multiply(a3,b3)))))),
inference(monotonicity,[status(thm)],[435,474]) ).
tff(476,plain,
double_divide(c3,multiply(a3,b3)) = double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),
inference(transitivity,[status(thm)],[422,475,467]) ).
tff(477,plain,
double_divide(double_divide(c3,multiply(a3,b3)),identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(c3,multiply(a3,b3))))),
inference(monotonicity,[status(thm)],[476,465]) ).
tff(478,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(multiply(a3,b3),c3) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(479,plain,
multiply(multiply(a3,b3),c3) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
inference(unit_resolution,[status(thm)],[478,7]) ).
tff(480,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(transitivity,[status(thm)],[479,477,460,458,455,306,304,301,10]) ).
tff(481,plain,
( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
<=> ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(482,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
tff(483,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(modus_ponens,[status(thm)],[482,481]) ).
tff(484,plain,
$false,
inference(unit_resolution,[status(thm)],[483,480]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP495-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 17:13:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------