TSTP Solution File: GRP002-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 22:25:20 EDT 2022
% Result : Unsatisfiable 34.59s 22.42s
% Output : Proof 34.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 102
% Syntax : Number of formulae : 419 ( 324 unt; 6 typ; 0 def)
% Number of atoms : 514 ( 507 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 177 ( 82 ~; 75 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 263 ( 255 !; 0 ?; 263 :)
% Comments :
%------------------------------------------------------------------------------
tff(identity_type,type,
identity: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(k_type,type,
k: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( multiply(X,inverse(X)) = identity )
<=> ( multiply(X,inverse(X)) = identity ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
tff(5,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
| ( multiply(a,inverse(a)) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(a,inverse(a)) = identity,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( ( multiply(X,identity) = X )
<=> ( multiply(X,identity) = X ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : ( multiply(X,identity) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
tff(14,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(a,identity) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
multiply(a,identity) = a,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X: $i] :
refl(
( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(23,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(b),b) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
multiply(inverse(b),b) = identity,
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
multiply(a,multiply(inverse(b),b)) = multiply(a,identity),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,inverse(b)),b) = multiply(a,multiply(inverse(b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
multiply(multiply(a,inverse(b)),b) = multiply(a,multiply(inverse(b),b)),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
^ [X: $i] :
refl(
( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(42,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
multiply(identity,b) = b,
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),inverse(a)),inverse(b)) = multiply(multiply(a,b),multiply(inverse(a),inverse(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
multiply(multiply(multiply(a,b),inverse(a)),inverse(b)) = multiply(multiply(a,b),multiply(inverse(a),inverse(b))),
inference(unit_resolution,[status(thm)],[47,35]) ).
tff(49,plain,
multiply(multiply(a,b),multiply(inverse(a),inverse(b))) = multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),inverse(a)),inverse(b))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),inverse(a)),inverse(b))) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),inverse(a)),inverse(b))) = identity,
inference(unit_resolution,[status(thm)],[52,25]) ).
tff(54,plain,
identity = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
identity = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),
inference(transitivity,[status(thm)],[54,51]) ).
tff(56,plain,
multiply(identity,b) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),b),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),b) = multiply(identity,b),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),b) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),b) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),b)),
inference(unit_resolution,[status(thm)],[58,35]) ).
tff(60,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),b)) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),b),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(multiply(a,multiply(b,inverse(a))),identity) = multiply(a,multiply(b,inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
multiply(multiply(a,multiply(b,inverse(a))),identity) = multiply(a,multiply(b,inverse(a))),
inference(unit_resolution,[status(thm)],[61,16]) ).
tff(63,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),inverse(a)) = multiply(a,multiply(b,inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
multiply(multiply(a,b),inverse(a)) = multiply(a,multiply(b,inverse(a))),
inference(unit_resolution,[status(thm)],[63,35]) ).
tff(65,plain,
multiply(multiply(multiply(a,b),inverse(a)),multiply(inverse(b),b)) = multiply(multiply(a,multiply(b,inverse(a))),identity),
inference(monotonicity,[status(thm)],[64,27]) ).
tff(66,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b) = multiply(multiply(multiply(a,b),inverse(a)),multiply(inverse(b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b) = multiply(multiply(multiply(a,b),inverse(a)),multiply(inverse(b),b)),
inference(unit_resolution,[status(thm)],[66,35]) ).
tff(68,plain,
multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),b) = multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),
inference(monotonicity,[status(thm)],[49]) ).
tff(69,plain,
multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),b) = multiply(a,multiply(b,inverse(a))),
inference(transitivity,[status(thm)],[68,67,65,62]) ).
tff(70,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),b)) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),b)),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))) = b,
inference(transitivity,[status(thm)],[71,60,57,46]) ).
tff(73,plain,
multiply(multiply(a,inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a))))) = multiply(multiply(a,inverse(b)),b),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
multiply(multiply(a,inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a))))) = a,
inference(transitivity,[status(thm)],[73,37,28,18]) ).
tff(75,plain,
multiply(multiply(multiply(a,inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a))))),inverse(a)) = multiply(a,inverse(a)),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a))))),inverse(a)) = multiply(multiply(a,inverse(b)),multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
multiply(multiply(multiply(a,inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a))))),inverse(a)) = multiply(multiply(a,inverse(b)),multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),inverse(a))),
inference(unit_resolution,[status(thm)],[76,35]) ).
tff(78,plain,
multiply(multiply(a,inverse(b)),multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),inverse(a))) = multiply(multiply(multiply(a,inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a))))),inverse(a)),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),inverse(a)) = multiply(b,inverse(a)),
inference(monotonicity,[status(thm)],[72]) ).
tff(80,plain,
multiply(b,inverse(a)) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),inverse(a)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
multiply(multiply(a,inverse(b)),multiply(b,inverse(a))) = multiply(multiply(a,inverse(b)),multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),inverse(a))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),inverse(a)) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,multiply(b,inverse(a))),inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),inverse(a)) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,multiply(b,inverse(a))),inverse(a))),
inference(unit_resolution,[status(thm)],[82,35]) ).
tff(84,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,multiply(b,inverse(a))),inverse(a))) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),inverse(a)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,inverse(a))),inverse(a)) = multiply(a,multiply(multiply(b,inverse(a)),inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
multiply(multiply(a,multiply(b,inverse(a))),inverse(a)) = multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),
inference(unit_resolution,[status(thm)],[85,35]) ).
tff(87,plain,
multiply(a,multiply(multiply(b,inverse(a)),inverse(a))) = multiply(multiply(a,multiply(b,inverse(a))),inverse(a)),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,multiply(b,inverse(a))),inverse(a))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))) = multiply(b,inverse(a)),
inference(transitivity,[status(thm)],[88,84,79]) ).
tff(90,plain,
multiply(multiply(a,inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a))))) = multiply(multiply(a,inverse(b)),multiply(b,inverse(a))),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))) = multiply(multiply(a,inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
multiply(multiply(multiply(a,inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))) = multiply(multiply(a,inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a))))),
inference(unit_resolution,[status(thm)],[91,35]) ).
tff(93,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(a,multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
multiply(multiply(a,inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(a,multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(unit_resolution,[status(thm)],[93,35]) ).
tff(95,plain,
multiply(a,multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(a,inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
multiply(multiply(a,multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))) = multiply(multiply(multiply(a,inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)) = multiply(multiply(inverse(a),inverse(b)),multiply(b,inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)) = multiply(multiply(inverse(a),inverse(b)),multiply(b,inverse(a))),
inference(unit_resolution,[status(thm)],[97,35]) ).
tff(99,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(inverse(a),identity) = inverse(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
multiply(inverse(a),identity) = inverse(a),
inference(unit_resolution,[status(thm)],[99,16]) ).
tff(101,plain,
multiply(inverse(a),multiply(inverse(b),b)) = multiply(inverse(a),identity),
inference(monotonicity,[status(thm)],[27]) ).
tff(102,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),inverse(b)),b) = multiply(inverse(a),multiply(inverse(b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
multiply(multiply(inverse(a),inverse(b)),b) = multiply(inverse(a),multiply(inverse(b),b)),
inference(unit_resolution,[status(thm)],[102,35]) ).
tff(104,plain,
multiply(multiply(inverse(a),inverse(b)),b) = inverse(a),
inference(transitivity,[status(thm)],[103,101,100]) ).
tff(105,plain,
multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)) = multiply(inverse(a),inverse(a)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
multiply(inverse(a),inverse(a)) = multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),inverse(a)),a) = multiply(inverse(a),multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
multiply(multiply(inverse(a),inverse(a)),a) = multiply(inverse(a),multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[107,35]) ).
tff(109,plain,
multiply(inverse(a),multiply(inverse(a),a)) = multiply(multiply(inverse(a),inverse(a)),a),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[110,25]) ).
tff(112,plain,
multiply(inverse(a),multiply(inverse(a),a)) = multiply(inverse(a),identity),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
multiply(inverse(a),identity) = multiply(inverse(a),multiply(inverse(a),a)),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
inverse(a) = multiply(inverse(a),identity),
inference(symmetry,[status(thm)],[100]) ).
tff(115,plain,
inverse(a) = multiply(multiply(inverse(a),inverse(a)),a),
inference(transitivity,[status(thm)],[114,113,109]) ).
tff(116,plain,
multiply(inverse(a),inverse(a)) = multiply(inverse(a),multiply(multiply(inverse(a),inverse(a)),a)),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
multiply(inverse(a),multiply(multiply(inverse(a),inverse(a)),a)) = multiply(inverse(a),inverse(a)),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),multiply(inverse(a),inverse(a))),a) = multiply(inverse(a),multiply(multiply(inverse(a),inverse(a)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
multiply(multiply(inverse(a),multiply(inverse(a),inverse(a))),a) = multiply(inverse(a),multiply(multiply(inverse(a),inverse(a)),a)),
inference(unit_resolution,[status(thm)],[118,35]) ).
tff(120,plain,
^ [X: $i] :
refl(
( ( multiply(X,multiply(X,X)) = identity )
<=> ( multiply(X,multiply(X,X)) = identity ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [X: $i] : ( multiply(X,multiply(X,X)) = identity )
<=> ! [X: $i] : ( multiply(X,multiply(X,X)) = identity ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [X: $i] : ( multiply(X,multiply(X,X)) = identity )
<=> ! [X: $i] : ( multiply(X,multiply(X,X)) = identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,axiom,
! [X: $i] : ( multiply(X,multiply(X,X)) = identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
tff(124,plain,
! [X: $i] : ( multiply(X,multiply(X,X)) = identity ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [X: $i] : ( multiply(X,multiply(X,X)) = identity ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [X: $i] : ( multiply(X,multiply(X,X)) = identity ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
( ~ ! [X: $i] : ( multiply(X,multiply(X,X)) = identity )
| ( multiply(inverse(a),multiply(inverse(a),inverse(a))) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
multiply(inverse(a),multiply(inverse(a),inverse(a))) = identity,
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
multiply(multiply(inverse(a),multiply(inverse(a),inverse(a))),a) = multiply(identity,a),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
multiply(identity,a) = multiply(multiply(inverse(a),multiply(inverse(a),inverse(a))),a),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[131,44]) ).
tff(133,plain,
a = multiply(identity,a),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
a = multiply(multiply(inverse(a),inverse(b)),multiply(b,inverse(a))),
inference(transitivity,[status(thm)],[133,130,119,117,106,98]) ).
tff(135,plain,
multiply(a,multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(multiply(inverse(a),inverse(b)),multiply(b,inverse(a))),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
multiply(multiply(multiply(inverse(a),inverse(b)),multiply(b,inverse(a))),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(a,multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(inverse(a),inverse(b)),multiply(b,inverse(a))),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(inverse(a),inverse(b)),multiply(multiply(b,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
multiply(multiply(multiply(inverse(a),inverse(b)),multiply(b,inverse(a))),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(inverse(a),inverse(b)),multiply(multiply(b,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(unit_resolution,[status(thm)],[137,35]) ).
tff(139,plain,
multiply(multiply(inverse(a),inverse(b)),multiply(multiply(b,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(multiply(inverse(a),inverse(b)),multiply(b,inverse(a))),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
| ( multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = identity,
inference(unit_resolution,[status(thm)],[140,7]) ).
tff(142,plain,
multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(monotonicity,[status(thm)],[49]) ).
tff(143,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(a,b),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,plain,
multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(a,b),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(unit_resolution,[status(thm)],[143,35]) ).
tff(145,plain,
multiply(multiply(a,b),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
multiply(multiply(a,b),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = identity,
inference(transitivity,[status(thm)],[145,142,141]) ).
tff(147,plain,
multiply(inverse(a),multiply(multiply(a,b),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(inverse(a),identity),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(inverse(a),multiply(multiply(a,b),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
multiply(multiply(inverse(a),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(inverse(a),multiply(multiply(a,b),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(unit_resolution,[status(thm)],[148,35]) ).
tff(150,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),a),b) = multiply(inverse(a),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
multiply(multiply(inverse(a),a),b) = multiply(inverse(a),multiply(a,b)),
inference(unit_resolution,[status(thm)],[150,35]) ).
tff(152,plain,
multiply(multiply(inverse(a),a),b) = multiply(identity,b),
inference(monotonicity,[status(thm)],[111]) ).
tff(153,plain,
multiply(identity,b) = multiply(multiply(inverse(a),a),b),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
b = multiply(identity,b),
inference(symmetry,[status(thm)],[46]) ).
tff(155,plain,
b = multiply(inverse(a),multiply(a,b)),
inference(transitivity,[status(thm)],[154,153,151]) ).
tff(156,plain,
multiply(b,multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(inverse(a),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(b,multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
multiply(multiply(b,multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(b,multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(unit_resolution,[status(thm)],[157,35]) ).
tff(159,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,inverse(a)),inverse(b)) = multiply(b,multiply(inverse(a),inverse(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
multiply(multiply(b,inverse(a)),inverse(b)) = multiply(b,multiply(inverse(a),inverse(b))),
inference(unit_resolution,[status(thm)],[159,35]) ).
tff(161,plain,
multiply(multiply(multiply(b,inverse(a)),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(b,multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,inverse(a)),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(b,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
multiply(multiply(multiply(b,inverse(a)),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(b,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(unit_resolution,[status(thm)],[162,35]) ).
tff(164,plain,
multiply(multiply(b,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(multiply(b,inverse(a)),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
multiply(multiply(b,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = inverse(a),
inference(transitivity,[status(thm)],[164,161,158,156,149,147,100]) ).
tff(166,plain,
multiply(multiply(inverse(a),inverse(b)),multiply(multiply(b,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(inverse(a),inverse(b)),inverse(a)),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
multiply(multiply(inverse(a),inverse(b)),inverse(a)) = multiply(multiply(inverse(a),inverse(b)),multiply(multiply(b,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
multiply(multiply(inverse(a),inverse(b)),inverse(a)) = multiply(a,multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(transitivity,[status(thm)],[167,139,136]) ).
tff(169,plain,
multiply(multiply(multiply(inverse(a),inverse(b)),inverse(a)),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))) = multiply(multiply(a,multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,inverse(a)),inverse(b)) = multiply(identity,multiply(inverse(a),inverse(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
multiply(multiply(identity,inverse(a)),inverse(b)) = multiply(identity,multiply(inverse(a),inverse(b))),
inference(unit_resolution,[status(thm)],[170,35]) ).
tff(172,plain,
multiply(inverse(a),multiply(a,inverse(a))) = multiply(inverse(a),identity),
inference(monotonicity,[status(thm)],[9]) ).
tff(173,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),a),inverse(a)) = multiply(inverse(a),multiply(a,inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
multiply(multiply(inverse(a),a),inverse(a)) = multiply(inverse(a),multiply(a,inverse(a))),
inference(unit_resolution,[status(thm)],[173,35]) ).
tff(175,plain,
identity = multiply(inverse(a),a),
inference(symmetry,[status(thm)],[111]) ).
tff(176,plain,
multiply(identity,inverse(a)) = multiply(multiply(inverse(a),a),inverse(a)),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
multiply(identity,inverse(a)) = inverse(a),
inference(transitivity,[status(thm)],[176,174,172,100]) ).
tff(178,plain,
multiply(multiply(identity,inverse(a)),inverse(b)) = multiply(inverse(a),inverse(b)),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
multiply(inverse(a),inverse(b)) = multiply(multiply(identity,inverse(a)),inverse(b)),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
multiply(inverse(a),inverse(b)) = multiply(identity,multiply(inverse(a),inverse(b))),
inference(transitivity,[status(thm)],[179,171]) ).
tff(181,plain,
multiply(multiply(inverse(a),inverse(b)),inverse(a)) = multiply(multiply(identity,multiply(inverse(a),inverse(b))),inverse(a)),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
multiply(multiply(identity,multiply(inverse(a),inverse(b))),inverse(a)) = multiply(multiply(inverse(a),inverse(b)),inverse(a)),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,multiply(inverse(a),inverse(b))),inverse(a)) = multiply(identity,multiply(multiply(inverse(a),inverse(b)),inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
multiply(multiply(identity,multiply(inverse(a),inverse(b))),inverse(a)) = multiply(identity,multiply(multiply(inverse(a),inverse(b)),inverse(a))),
inference(unit_resolution,[status(thm)],[183,35]) ).
tff(185,plain,
multiply(identity,multiply(multiply(inverse(a),inverse(b)),inverse(a))) = multiply(multiply(identity,multiply(inverse(a),inverse(b))),inverse(a)),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,inverse(a)),inverse(a)) = multiply(b,multiply(inverse(a),inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(187,plain,
multiply(multiply(b,inverse(a)),inverse(a)) = multiply(b,multiply(inverse(a),inverse(a))),
inference(unit_resolution,[status(thm)],[186,35]) ).
tff(188,plain,
multiply(b,multiply(inverse(a),inverse(a))) = multiply(multiply(b,inverse(a)),inverse(a)),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
multiply(inverse(a),multiply(multiply(inverse(a),inverse(a)),a)) = multiply(multiply(inverse(a),multiply(inverse(a),inverse(a))),a),
inference(symmetry,[status(thm)],[119]) ).
tff(190,plain,
multiply(inverse(a),inverse(a)) = a,
inference(transitivity,[status(thm)],[116,189,129,132]) ).
tff(191,plain,
b = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),
inference(transitivity,[status(thm)],[154,56,59,70]) ).
tff(192,plain,
multiply(b,multiply(inverse(a),inverse(a))) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),a),
inference(monotonicity,[status(thm)],[191,190]) ).
tff(193,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),a) = multiply(b,multiply(inverse(a),inverse(a))),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),a) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,multiply(b,inverse(a))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(195,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),a) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,multiply(b,inverse(a))),a)),
inference(unit_resolution,[status(thm)],[194,35]) ).
tff(196,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,multiply(b,inverse(a))),a)) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),a),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,inverse(a))),a) = multiply(a,multiply(multiply(b,inverse(a)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(198,plain,
multiply(multiply(a,multiply(b,inverse(a))),a) = multiply(a,multiply(multiply(b,inverse(a)),a)),
inference(unit_resolution,[status(thm)],[197,35]) ).
tff(199,plain,
multiply(a,multiply(multiply(b,inverse(a)),a)) = multiply(multiply(a,multiply(b,inverse(a))),a),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(multiply(b,inverse(a)),a))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,multiply(b,inverse(a))),a)),
inference(monotonicity,[status(thm)],[199]) ).
tff(201,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),a),multiply(multiply(b,inverse(a)),a)) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(multiply(b,inverse(a)),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(202,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),a),multiply(multiply(b,inverse(a)),a)) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(multiply(b,inverse(a)),a))),
inference(unit_resolution,[status(thm)],[201,35]) ).
tff(203,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,inverse(a)),a) = multiply(b,multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
multiply(multiply(b,inverse(a)),a) = multiply(b,multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[203,35]) ).
tff(205,plain,
multiply(b,multiply(inverse(a),a)) = multiply(multiply(b,inverse(a)),a),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
multiply(b,multiply(inverse(a),a)) = multiply(b,identity),
inference(monotonicity,[status(thm)],[111]) ).
tff(207,plain,
multiply(b,identity) = multiply(b,multiply(inverse(a),a)),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(b,identity) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(209,plain,
multiply(b,identity) = b,
inference(unit_resolution,[status(thm)],[208,16]) ).
tff(210,plain,
b = multiply(b,identity),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
b = multiply(multiply(b,inverse(a)),a),
inference(transitivity,[status(thm)],[210,207,205]) ).
tff(212,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),a),b) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),a),multiply(multiply(b,inverse(a)),a)),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),a),b) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(214,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),a),b) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),
inference(unit_resolution,[status(thm)],[213,35]) ).
tff(215,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),a),b),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)) = multiply(multiply(b,inverse(a)),inverse(a)),
inference(transitivity,[status(thm)],[215,212,202,200,196,193,188]) ).
tff(217,plain,
multiply(a,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))) = multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
multiply(a,multiply(multiply(b,inverse(a)),inverse(a))) = multiply(a,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)))),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),a),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(222,plain,
multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),a),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)))),
inference(unit_resolution,[status(thm)],[221,35]) ).
tff(223,plain,
identity = multiply(inverse(b),b),
inference(symmetry,[status(thm)],[27]) ).
tff(224,plain,
multiply(inverse(a),a) = multiply(inverse(b),b),
inference(transitivity,[status(thm)],[111,223]) ).
tff(225,plain,
multiply(a,multiply(b,inverse(a))) = multiply(multiply(a,b),inverse(a)),
inference(symmetry,[status(thm)],[64]) ).
tff(226,plain,
multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(a),a)) = multiply(multiply(multiply(a,b),inverse(a)),multiply(inverse(b),b)),
inference(monotonicity,[status(thm)],[225,224]) ).
tff(227,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(a)),a) = multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(a)),a) = multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[227,35]) ).
tff(229,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),a) = multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(a)),a),
inference(monotonicity,[status(thm)],[87]) ).
tff(230,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),a) = multiply(a,multiply(b,inverse(a))),
inference(transitivity,[status(thm)],[229,228,226,65,62]) ).
tff(231,plain,
multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),a),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))) = multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))) = multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),a),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(a,b)) = multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(234,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(a,b)) = multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))),
inference(unit_resolution,[status(thm)],[233,35]) ).
tff(235,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(236,plain,
multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(unit_resolution,[status(thm)],[235,35]) ).
tff(237,plain,
multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b) = multiply(a,multiply(b,inverse(a))),
inference(transitivity,[status(thm)],[67,65,62]) ).
tff(238,plain,
multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(transitivity,[status(thm)],[239,236]) ).
tff(241,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(a,b)) = multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)) = multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(a,b)),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)) = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))),
inference(transitivity,[status(thm)],[242,234,232,222,220]) ).
tff(244,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a))))),
inference(monotonicity,[status(thm)],[243]) ).
tff(245,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a))))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
( ~ ! [X: $i] : ( multiply(X,multiply(X,X)) = identity )
| ( multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a))))) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(247,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a))))) = identity,
inference(unit_resolution,[status(thm)],[246,126]) ).
tff(248,plain,
identity = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a))))),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
identity = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b))),
inference(transitivity,[status(thm)],[248,245]) ).
tff(250,plain,
multiply(identity,multiply(multiply(inverse(a),inverse(b)),inverse(a))) = multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b))),multiply(multiply(inverse(a),inverse(b)),inverse(a))),
inference(monotonicity,[status(thm)],[249]) ).
tff(251,plain,
multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b))),multiply(multiply(inverse(a),inverse(b)),inverse(a))) = multiply(identity,multiply(multiply(inverse(a),inverse(b)),inverse(a))),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b))),multiply(multiply(inverse(a),inverse(b)),inverse(a))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(253,plain,
multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b))),multiply(multiply(inverse(a),inverse(b)),inverse(a))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(a)))),
inference(unit_resolution,[status(thm)],[252,35]) ).
tff(254,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(a)))) = multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b))),multiply(multiply(inverse(a),inverse(b)),inverse(a))),
inference(symmetry,[status(thm)],[253]) ).
tff(255,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))) = multiply(inverse(b),b),
inference(transitivity,[status(thm)],[50,53,223]) ).
tff(256,plain,
multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b))))) = multiply(multiply(multiply(a,b),inverse(a)),multiply(inverse(b),b)),
inference(monotonicity,[status(thm)],[225,255]) ).
tff(257,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))) = multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(258,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))) = multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b))))),
inference(unit_resolution,[status(thm)],[257,35]) ).
tff(259,plain,
multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(symmetry,[status(thm)],[236]) ).
tff(260,plain,
multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(transitivity,[status(thm)],[259,238]) ).
tff(261,plain,
multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))) = multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(inverse(a),inverse(b))) = multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(inverse(a),inverse(b))) = multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),
inference(unit_resolution,[status(thm)],[262,35]) ).
tff(264,plain,
multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(inverse(a),inverse(b))) = multiply(a,multiply(b,inverse(a))),
inference(transitivity,[status(thm)],[263,261,258,256,65,62]) ).
tff(265,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(inverse(a),inverse(b))),inverse(a)) = multiply(multiply(a,multiply(b,inverse(a))),inverse(a)),
inference(monotonicity,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(inverse(a),inverse(b))),inverse(a)) = multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(267,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(inverse(a),inverse(b))),inverse(a)) = multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(a))),
inference(unit_resolution,[status(thm)],[266,35]) ).
tff(268,plain,
multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(a))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(inverse(a),inverse(b))),inverse(a)),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(a))) = multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),
inference(transitivity,[status(thm)],[268,265,86]) ).
tff(270,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(a)))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(a)))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)) = multiply(multiply(inverse(a),inverse(b)),inverse(a)),
inference(transitivity,[status(thm)],[242,234,232,222,220,271,254,251,185,182]) ).
tff(273,plain,
multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))) = multiply(multiply(multiply(inverse(a),inverse(b)),inverse(a)),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
multiply(a,inverse(a)) = multiply(inverse(b),b),
inference(transitivity,[status(thm)],[9,223]) ).
tff(275,plain,
multiply(multiply(a,multiply(b,inverse(a))),multiply(a,inverse(a))) = multiply(multiply(multiply(a,b),inverse(a)),multiply(inverse(b),b)),
inference(monotonicity,[status(thm)],[225,274]) ).
tff(276,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)) = multiply(multiply(a,multiply(b,inverse(a))),multiply(a,inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(277,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)) = multiply(multiply(a,multiply(b,inverse(a))),multiply(a,inverse(a))),
inference(unit_resolution,[status(thm)],[276,35]) ).
tff(278,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)) = multiply(a,multiply(b,inverse(a))),
inference(transitivity,[status(thm)],[277,275,65,62]) ).
tff(279,plain,
multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),inverse(a)) = multiply(multiply(a,multiply(b,inverse(a))),inverse(a)),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),inverse(a)) = multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(281,plain,
multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),inverse(a)) = multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),inverse(a))),
inference(unit_resolution,[status(thm)],[280,35]) ).
tff(282,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),inverse(a))) = multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),inverse(a)),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
a = multiply(inverse(a),inverse(a)),
inference(transitivity,[status(thm)],[133,130,119,117]) ).
tff(284,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),a) = multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),inverse(a))),
inference(monotonicity,[status(thm)],[199,283]) ).
tff(285,plain,
multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),a) = multiply(multiply(a,multiply(b,inverse(a))),a),
inference(monotonicity,[status(thm)],[278]) ).
tff(286,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),a) = multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(287,plain,
multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),a) = multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[286,35]) ).
tff(288,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),a)) = multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),a),
inference(symmetry,[status(thm)],[287]) ).
tff(289,plain,
multiply(multiply(a,multiply(b,inverse(a))),inverse(b)) = multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),
inference(monotonicity,[status(thm)],[225]) ).
tff(290,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(monotonicity,[status(thm)],[289]) ).
tff(291,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(292,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(unit_resolution,[status(thm)],[291,35]) ).
tff(293,plain,
multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(monotonicity,[status(thm)],[278]) ).
tff(295,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(296,plain,
multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(unit_resolution,[status(thm)],[295,35]) ).
tff(297,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(monotonicity,[status(thm)],[199]) ).
tff(299,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(inverse(a),a),
inference(transitivity,[status(thm)],[298,297,294,293,290,141,175]) ).
tff(300,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))) = multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),a)),
inference(monotonicity,[status(thm)],[199,299]) ).
tff(301,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(302,plain,
multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))),
inference(unit_resolution,[status(thm)],[301,35]) ).
tff(303,plain,
multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(a,multiply(multiply(b,inverse(a)),a)),
inference(transitivity,[status(thm)],[302,300,288,285,198]) ).
tff(304,plain,
multiply(multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),a) = multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),a),
inference(monotonicity,[status(thm)],[303]) ).
tff(305,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),a) = multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(306,plain,
multiply(multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),a) = multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),a)),
inference(unit_resolution,[status(thm)],[305,35]) ).
tff(307,plain,
multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),a)) = multiply(multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),a),
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(309,plain,
multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(unit_resolution,[status(thm)],[308,35]) ).
tff(310,plain,
multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
multiply(multiply(inverse(a),multiply(a,b)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(inverse(a),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(monotonicity,[status(thm)],[310]) ).
tff(312,plain,
multiply(multiply(inverse(a),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(inverse(a),multiply(a,b)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(symmetry,[status(thm)],[311]) ).
tff(313,plain,
multiply(inverse(a),multiply(multiply(a,b),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(inverse(a),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(symmetry,[status(thm)],[149]) ).
tff(314,plain,
multiply(inverse(a),identity) = multiply(inverse(a),multiply(multiply(a,b),multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(symmetry,[status(thm)],[147]) ).
tff(315,plain,
inverse(a) = multiply(multiply(inverse(a),multiply(a,b)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(transitivity,[status(thm)],[114,314,313,312]) ).
tff(316,plain,
multiply(inverse(b),inverse(a)) = multiply(inverse(b),multiply(multiply(inverse(a),multiply(a,b)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))),
inference(monotonicity,[status(thm)],[315]) ).
tff(317,plain,
multiply(inverse(b),multiply(multiply(inverse(a),multiply(a,b)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))) = multiply(inverse(b),inverse(a)),
inference(symmetry,[status(thm)],[316]) ).
tff(318,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(b),multiply(inverse(a),multiply(a,b))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(inverse(b),multiply(multiply(inverse(a),multiply(a,b)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(319,plain,
multiply(multiply(inverse(b),multiply(inverse(a),multiply(a,b))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(inverse(b),multiply(multiply(inverse(a),multiply(a,b)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))),
inference(unit_resolution,[status(thm)],[318,35]) ).
tff(320,plain,
multiply(inverse(b),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a))))) = multiply(inverse(b),b),
inference(monotonicity,[status(thm)],[72]) ).
tff(321,plain,
multiply(inverse(a),multiply(a,b)) = multiply(multiply(inverse(a),a),b),
inference(symmetry,[status(thm)],[151]) ).
tff(322,plain,
multiply(inverse(a),multiply(a,b)) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a)))),
inference(transitivity,[status(thm)],[321,152,56,59,70]) ).
tff(323,plain,
multiply(inverse(b),multiply(inverse(a),multiply(a,b))) = multiply(inverse(b),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,multiply(b,inverse(a))))),
inference(monotonicity,[status(thm)],[322]) ).
tff(324,plain,
multiply(inverse(b),multiply(inverse(a),multiply(a,b))) = identity,
inference(transitivity,[status(thm)],[323,320,27]) ).
tff(325,plain,
multiply(multiply(inverse(b),multiply(inverse(a),multiply(a,b))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(monotonicity,[status(thm)],[324]) ).
tff(326,plain,
multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(inverse(b),multiply(inverse(a),multiply(a,b))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(328,plain,
multiply(multiply(identity,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(unit_resolution,[status(thm)],[327,35]) ).
tff(329,plain,
multiply(multiply(identity,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(monotonicity,[status(thm)],[177]) ).
tff(330,plain,
multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(multiply(identity,inverse(a)),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),
inference(symmetry,[status(thm)],[329]) ).
tff(331,plain,
multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))) = multiply(inverse(b),inverse(a)),
inference(transitivity,[status(thm)],[330,328,326,319,317]) ).
tff(332,plain,
multiply(multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),a) = multiply(multiply(inverse(b),inverse(a)),a),
inference(monotonicity,[status(thm)],[331]) ).
tff(333,plain,
multiply(multiply(inverse(b),inverse(a)),a) = multiply(multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),a),
inference(symmetry,[status(thm)],[332]) ).
tff(334,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(b),inverse(a)),a) = multiply(inverse(b),multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(335,plain,
multiply(multiply(inverse(b),inverse(a)),a) = multiply(inverse(b),multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[334,35]) ).
tff(336,plain,
multiply(inverse(b),multiply(inverse(a),a)) = multiply(multiply(inverse(b),inverse(a)),a),
inference(symmetry,[status(thm)],[335]) ).
tff(337,plain,
multiply(inverse(b),multiply(inverse(a),a)) = multiply(inverse(b),identity),
inference(monotonicity,[status(thm)],[111]) ).
tff(338,plain,
multiply(inverse(b),identity) = multiply(inverse(b),multiply(inverse(a),a)),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(inverse(b),identity) = inverse(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(340,plain,
multiply(inverse(b),identity) = inverse(b),
inference(unit_resolution,[status(thm)],[339,16]) ).
tff(341,plain,
inverse(b) = multiply(inverse(b),identity),
inference(symmetry,[status(thm)],[340]) ).
tff(342,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,inverse(b)) = inverse(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(343,plain,
multiply(identity,inverse(b)) = inverse(b),
inference(unit_resolution,[status(thm)],[342,44]) ).
tff(344,plain,
multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(symmetry,[status(thm)],[142]) ).
tff(345,plain,
identity = multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(symmetry,[status(thm)],[141]) ).
tff(346,plain,
identity = multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(transitivity,[status(thm)],[345,344]) ).
tff(347,plain,
multiply(identity,inverse(b)) = multiply(multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),inverse(b)),
inference(monotonicity,[status(thm)],[346]) ).
tff(348,plain,
multiply(multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),inverse(b)) = multiply(identity,inverse(b)),
inference(symmetry,[status(thm)],[347]) ).
tff(349,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),inverse(b)) = multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(350,plain,
multiply(multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),inverse(b)) = multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))),
inference(unit_resolution,[status(thm)],[349,35]) ).
tff(351,plain,
multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),inverse(b)),
inference(symmetry,[status(thm)],[350]) ).
tff(352,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(353,plain,
multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)),
inference(unit_resolution,[status(thm)],[352,44]) ).
tff(354,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)) = multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))),
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))),
inference(monotonicity,[status(thm)],[354]) ).
tff(356,plain,
multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))) = multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))),
inference(symmetry,[status(thm)],[355]) ).
tff(357,plain,
multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))) = multiply(multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),a),
inference(transitivity,[status(thm)],[356,351,348,343,341,338,336,333]) ).
tff(358,plain,
multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))) = multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),a)),
inference(monotonicity,[status(thm)],[357]) ).
tff(359,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))) = multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(symmetry,[status(thm)],[302]) ).
tff(360,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),a),multiply(inverse(a),a)) = multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))),
inference(symmetry,[status(thm)],[300]) ).
tff(361,plain,
multiply(multiply(a,multiply(b,inverse(a))),a) = multiply(multiply(multiply(multiply(a,multiply(b,inverse(a))),a),inverse(a)),a),
inference(symmetry,[status(thm)],[285]) ).
tff(362,plain,
multiply(a,multiply(multiply(b,inverse(a)),a)) = multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(transitivity,[status(thm)],[199,361,287,360,359]) ).
tff(363,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))),
inference(monotonicity,[status(thm)],[362]) ).
tff(364,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),
inference(symmetry,[status(thm)],[363]) ).
tff(365,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a)))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(366,plain,
multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a)))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))))),
inference(unit_resolution,[status(thm)],[365,35]) ).
tff(367,plain,
( ~ ! [X: $i] : ( multiply(X,multiply(X,X)) = identity )
| ( multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a)))) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(368,plain,
multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a)))) = identity,
inference(unit_resolution,[status(thm)],[367,126]) ).
tff(369,plain,
multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a)))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(monotonicity,[status(thm)],[368]) ).
tff(370,plain,
multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))) = multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a)))),multiply(inverse(a),multiply(inverse(b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))))),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))) = multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),
inference(transitivity,[status(thm)],[309,330,328,370,366,364]) ).
tff(372,plain,
multiply(multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))) = multiply(multiply(multiply(a,multiply(multiply(b,inverse(a)),a)),multiply(a,multiply(multiply(b,inverse(a)),a))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))),
inference(monotonicity,[status(thm)],[371]) ).
tff(373,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))) = multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(374,plain,
multiply(multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))) = multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))))),
inference(unit_resolution,[status(thm)],[373,35]) ).
tff(375,plain,
multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))))) = multiply(multiply(multiply(inverse(a),inverse(b)),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))),
inference(symmetry,[status(thm)],[374]) ).
tff(376,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))),
inference(monotonicity,[status(thm)],[356]) ).
tff(377,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))),
inference(symmetry,[status(thm)],[376]) ).
tff(378,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(379,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))),
inference(unit_resolution,[status(thm)],[378,35]) ).
tff(380,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))) = identity,
inference(transitivity,[status(thm)],[50,53]) ).
tff(381,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))),
inference(monotonicity,[status(thm)],[380]) ).
tff(382,plain,
multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))),
inference(transitivity,[status(thm)],[354,382,379,377]) ).
tff(384,plain,
multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(multiply(a,b),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))))),
inference(monotonicity,[status(thm)],[383]) ).
tff(385,plain,
multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),
inference(transitivity,[status(thm)],[384,375,372,358,307,304,284,282,279,86]) ).
tff(386,plain,
multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))) = multiply(multiply(multiply(a,multiply(b,inverse(a))),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),multiply(a,b)),
inference(symmetry,[status(thm)],[234]) ).
tff(387,plain,
multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))) = multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),
inference(transitivity,[status(thm)],[386,241]) ).
tff(388,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))),multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))) = multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),multiply(b,inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))))),multiply(a,b)),multiply(a,multiply(multiply(b,inverse(a)),inverse(a)))),
inference(monotonicity,[status(thm)],[387,385]) ).
tff(389,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))),multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))) = multiply(multiply(a,multiply(b,inverse(a))),multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(390,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))),multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))) = multiply(multiply(a,multiply(b,inverse(a))),multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))),
inference(unit_resolution,[status(thm)],[389,35]) ).
tff(391,plain,
multiply(multiply(a,multiply(b,inverse(a))),multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))) = multiply(multiply(multiply(a,multiply(b,inverse(a))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b))),multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(393,plain,
multiply(multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))),
inference(unit_resolution,[status(thm)],[392,35]) ).
tff(394,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(inverse(a),inverse(b))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(395,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(inverse(a),inverse(b))) = multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(multiply(a,b),multiply(inverse(a),inverse(b)))),
inference(unit_resolution,[status(thm)],[394,35]) ).
tff(396,plain,
multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(inverse(a),inverse(b))) = identity,
inference(transitivity,[status(thm)],[395,50,53]) ).
tff(397,plain,
multiply(multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))),
inference(monotonicity,[status(thm)],[396]) ).
tff(398,plain,
multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(inverse(a),inverse(b))),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))),
inference(symmetry,[status(thm)],[397]) ).
tff(399,plain,
multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))),
inference(transitivity,[status(thm)],[398,393]) ).
tff(400,plain,
multiply(multiply(a,multiply(b,inverse(a))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))) = multiply(multiply(a,multiply(b,inverse(a))),multiply(multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),multiply(a,b)),multiply(multiply(inverse(a),inverse(b)),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))))),
inference(monotonicity,[status(thm)],[399]) ).
tff(401,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,inverse(a))),identity),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(multiply(a,multiply(b,inverse(a))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(402,plain,
multiply(multiply(multiply(a,multiply(b,inverse(a))),identity),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(multiply(a,multiply(b,inverse(a))),multiply(identity,multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b)))),
inference(unit_resolution,[status(thm)],[401,35]) ).
tff(403,plain,
multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b) = multiply(multiply(a,multiply(b,inverse(a))),identity),
inference(transitivity,[status(thm)],[67,65]) ).
tff(404,plain,
multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) = multiply(multiply(multiply(a,multiply(b,inverse(a))),identity),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))),
inference(monotonicity,[status(thm)],[403]) ).
tff(405,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),inverse(b)) = multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(406,plain,
multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),inverse(b)) = multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),multiply(inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b))),inverse(b))),
inference(unit_resolution,[status(thm)],[405,35]) ).
tff(407,plain,
multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),inverse(b)) = identity,
inference(transitivity,[status(thm)],[406,404,402,400,391,388,273,169,96,92,90,81,78,75,9]) ).
tff(408,plain,
( ( multiply(k,inverse(b)) != identity )
<=> ( multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),inverse(b)) != identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(409,plain,
( ( multiply(k,inverse(b)) != identity )
<=> ( multiply(k,inverse(b)) != identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(410,axiom,
multiply(k,inverse(b)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
tff(411,plain,
multiply(k,inverse(b)) != identity,
inference(modus_ponens,[status(thm)],[410,409]) ).
tff(412,plain,
multiply(multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),inverse(b)) != identity,
inference(modus_ponens,[status(thm)],[411,408]) ).
tff(413,plain,
$false,
inference(unit_resolution,[status(thm)],[412,407]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 31 14:10:30 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.37 Usage: tptp [options] [-file:]file
% 0.15/0.37 -h, -? prints this message.
% 0.15/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.37 -m, -model generate model.
% 0.15/0.37 -p, -proof generate proof.
% 0.15/0.37 -c, -core generate unsat core of named formulas.
% 0.15/0.37 -st, -statistics display statistics.
% 0.15/0.37 -t:timeout set timeout (in second).
% 0.15/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.37 -<param>:<value> configuration parameter and value.
% 0.15/0.37 -o:<output-file> file to place output in.
% 34.59/22.42 % SZS status Unsatisfiable
% 34.59/22.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------