%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : BOO029-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:00:10 AM UTC 2025
% Result : Unsatisfiable 25.58s 25.75s
% Output : Proof 25.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 110
% Syntax : Number of formulae : 479 ( 380 unt; 0 typ; 0 def)
% Number of atoms : 598 ( 587 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 191 ( 82 ~; 78 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 430 ( 404 !; 0 ?; 430 :)
% Comments :
%------------------------------------------------------------------------------
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y )
<=> ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y )
| ( add(add(multiply(add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),add(a,inverse(a))),multiply(add(a,inverse(a)),multiply(inverse(a),add(a,b)))),add(a,inverse(a))) = add(a,inverse(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
add(add(multiply(add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),add(a,inverse(a))),multiply(add(a,inverse(a)),multiply(inverse(a),add(a,b)))),add(a,inverse(a))) = add(a,inverse(a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(X,Y) = multiply(Y,X) )
<=> ( multiply(X,Y) = multiply(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
<=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
<=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
tff(14,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(add(a,b),inverse(a)) = multiply(inverse(a),add(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiply(add(a,b),inverse(a)) = multiply(inverse(a),add(a,b)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiply(inverse(a),add(a,b)) = multiply(add(a,b),inverse(a)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
<=> ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
| ( multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)) = inverse(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)) = inverse(a),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
^ [Y: $i,X: $i] :
refl(( ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
<=> ( add(multiply(X,Y),multiply(X,inverse(Y))) = X ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
<=> ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
<=> ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
tff(33,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
| ( add(multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),a),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a))) = multiply(add(a,inverse(a)),add(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
add(multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),a),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a))) = multiply(add(a,inverse(a)),add(inverse(a),a)),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
| ( multiply(multiply(add(inverse(a),a),add(a,inverse(a))),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
multiply(multiply(add(inverse(a),a),add(a,inverse(a))),a) = a,
inference(unit_resolution,[status(thm)],[38,26]) ).
tff(40,plain,
^ [Y: $i,X: $i] :
refl(( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
tff(44,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(inverse(a),a) = add(a,inverse(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
add(inverse(a),a) = add(a,inverse(a)),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
add(a,inverse(a)) = add(inverse(a),a),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
multiply(add(inverse(a),a),add(a,inverse(a))) = multiply(add(a,inverse(a)),add(inverse(a),a)),
inference(monotonicity,[status(thm)],[48,49]) ).
tff(51,plain,
multiply(add(a,inverse(a)),add(inverse(a),a)) = multiply(add(inverse(a),a),add(a,inverse(a))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),a) = multiply(multiply(add(inverse(a),a),add(a,inverse(a))),a),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),a) = a,
inference(transitivity,[status(thm)],[52,39]) ).
tff(54,plain,
add(multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),a),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a))) = add(a,inverse(a)),
inference(monotonicity,[status(thm)],[53,28]) ).
tff(55,plain,
add(a,inverse(a)) = add(multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),a),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
add(a,inverse(a)) = multiply(add(a,inverse(a)),add(inverse(a),a)),
inference(transitivity,[status(thm)],[55,37]) ).
tff(57,plain,
multiply(add(a,inverse(a)),inverse(a)) = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
multiply(add(a,inverse(a)),inverse(a)) = inverse(a),
inference(transitivity,[status(thm)],[57,28]) ).
tff(59,plain,
multiply(multiply(add(a,inverse(a)),inverse(a)),add(a,b)) = multiply(inverse(a),add(a,b)),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,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(61,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)],[60]) ).
tff(62,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(63,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiply) ).
tff(64,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(add(a,inverse(a)),inverse(a)),add(a,b)) = multiply(add(a,inverse(a)),multiply(inverse(a),add(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
multiply(multiply(add(a,inverse(a)),inverse(a)),add(a,b)) = multiply(add(a,inverse(a)),multiply(inverse(a),add(a,b))),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
multiply(add(a,inverse(a)),multiply(inverse(a),add(a,b))) = multiply(multiply(add(a,inverse(a)),inverse(a)),add(a,b)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
multiply(add(a,inverse(a)),multiply(inverse(a),add(a,b))) = multiply(add(a,b),inverse(a)),
inference(transitivity,[status(thm)],[69,59,19]) ).
tff(71,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(add(a,b),a) = multiply(a,add(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
multiply(add(a,b),a) = multiply(a,add(a,b)),
inference(unit_resolution,[status(thm)],[71,16]) ).
tff(73,plain,
multiply(a,add(a,b)) = multiply(add(a,b),a),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
| ( multiply(multiply(add(a,a),add(a,inverse(a))),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
multiply(multiply(add(a,a),add(a,inverse(a))),a) = a,
inference(unit_resolution,[status(thm)],[74,26]) ).
tff(76,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(add(X,Y),add(X,inverse(Y))) = X )
<=> ( multiply(add(X,Y),add(X,inverse(Y))) = X ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [Y: $i,X: $i] : ( multiply(add(X,Y),add(X,inverse(Y))) = X )
<=> ! [Y: $i,X: $i] : ( multiply(add(X,Y),add(X,inverse(Y))) = X ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [Y: $i,X: $i] : ( multiply(add(X,Y),add(X,inverse(Y))) = X )
<=> ! [Y: $i,X: $i] : ( multiply(add(X,Y),add(X,inverse(Y))) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
! [Y: $i,X: $i] : ( multiply(add(X,Y),add(X,inverse(Y))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
tff(80,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),add(X,inverse(Y))) = X ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),add(X,inverse(Y))) = X ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),add(X,inverse(Y))) = X ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),add(X,inverse(Y))) = X )
| ( multiply(add(a,a),add(a,inverse(a))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
multiply(add(a,a),add(a,inverse(a))) = a,
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
a = multiply(add(a,a),add(a,inverse(a))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
multiply(a,a) = multiply(multiply(add(a,a),add(a,inverse(a))),a),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
multiply(a,a) = a,
inference(transitivity,[status(thm)],[86,75]) ).
tff(88,plain,
multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(a,a)) = multiply(multiply(add(inverse(a),a),add(a,inverse(a))),a),
inference(monotonicity,[status(thm)],[51,87]) ).
tff(89,plain,
multiply(multiply(add(inverse(a),a),add(a,inverse(a))),a) = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(a,a)),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
a = multiply(multiply(add(inverse(a),a),add(a,inverse(a))),a),
inference(symmetry,[status(thm)],[39]) ).
tff(91,plain,
a = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(a,a)),
inference(transitivity,[status(thm)],[90,89]) ).
tff(92,plain,
add(a,a) = add(a,multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(a,a))),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
add(a,multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(a,a))) = add(a,a),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( add(X,multiply(Y,multiply(X,Z))) = X )
<=> ( add(X,multiply(Y,multiply(X,Z))) = X ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
tff(98,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X )
| ( add(a,multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(a,a))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
add(a,multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(a,a))) = a,
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
a = add(a,multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(a,a))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
a = add(a,a),
inference(transitivity,[status(thm)],[103,93]) ).
tff(105,plain,
multiply(a,add(a,b)) = multiply(add(a,a),add(a,b)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
multiply(add(a,a),add(a,b)) = multiply(a,add(a,b)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(108,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
tff(111,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),a),b) = add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),add(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
add(add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),a),b) = add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),add(a,b)),
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X )
| ( add(a,multiply(multiply(inverse(b),b),multiply(a,multiply(inverse(a),a)))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
add(a,multiply(multiply(inverse(b),b),multiply(a,multiply(inverse(a),a)))) = a,
inference(unit_resolution,[status(thm)],[116,100]) ).
tff(118,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(multiply(multiply(inverse(b),b),multiply(a,multiply(inverse(a),a))),a) = add(a,multiply(multiply(inverse(b),b),multiply(a,multiply(inverse(a),a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
add(multiply(multiply(inverse(b),b),multiply(a,multiply(inverse(a),a))),a) = add(a,multiply(multiply(inverse(b),b),multiply(a,multiply(inverse(a),a)))),
inference(unit_resolution,[status(thm)],[118,46]) ).
tff(120,plain,
multiply(inverse(a),multiply(a,a)) = multiply(inverse(a),a),
inference(monotonicity,[status(thm)],[87]) ).
tff(121,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),a),a) = multiply(inverse(a),multiply(a,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
multiply(multiply(inverse(a),a),a) = multiply(inverse(a),multiply(a,a)),
inference(unit_resolution,[status(thm)],[121,66]) ).
tff(123,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(a,multiply(inverse(a),a)) = multiply(multiply(inverse(a),a),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
multiply(a,multiply(inverse(a),a)) = multiply(multiply(inverse(a),a),a),
inference(unit_resolution,[status(thm)],[123,16]) ).
tff(125,plain,
multiply(a,multiply(inverse(a),a)) = multiply(inverse(a),a),
inference(transitivity,[status(thm)],[124,122,120]) ).
tff(126,plain,
multiply(multiply(inverse(b),b),multiply(a,multiply(inverse(a),a))) = multiply(multiply(inverse(b),b),multiply(inverse(a),a)),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
multiply(multiply(inverse(b),b),multiply(inverse(a),a)) = multiply(multiply(inverse(b),b),multiply(a,multiply(inverse(a),a))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(b),b),multiply(inverse(a),a)) = multiply(inverse(b),multiply(b,multiply(inverse(a),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
multiply(multiply(inverse(b),b),multiply(inverse(a),a)) = multiply(inverse(b),multiply(b,multiply(inverse(a),a))),
inference(unit_resolution,[status(thm)],[128,66]) ).
tff(130,plain,
multiply(inverse(b),multiply(b,multiply(inverse(a),a))) = multiply(multiply(inverse(b),b),multiply(inverse(a),a)),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
multiply(inverse(b),multiply(b,multiply(inverse(a),a))) = multiply(multiply(inverse(b),b),multiply(a,multiply(inverse(a),a))),
inference(transitivity,[status(thm)],[130,127]) ).
tff(132,plain,
add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),a) = add(multiply(multiply(inverse(b),b),multiply(a,multiply(inverse(a),a))),a),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),a) = a,
inference(transitivity,[status(thm)],[132,119,117]) ).
tff(134,plain,
add(add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),a),b) = add(a,b),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
add(a,b) = add(add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),a),b),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
add(a,b) = add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),add(a,b)),
inference(transitivity,[status(thm)],[135,115]) ).
tff(137,plain,
add(a,a) = a,
inference(transitivity,[status(thm)],[92,102]) ).
tff(138,plain,
multiply(add(a,a),add(a,b)) = multiply(a,add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),add(a,b))),
inference(monotonicity,[status(thm)],[137,136]) ).
tff(139,plain,
multiply(a,add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),add(a,b))) = multiply(add(a,a),add(a,b)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(X,add(Y,add(X,Z))) = X )
<=> ( multiply(X,add(Y,add(X,Z))) = X ) )),
inference(bind,[status(th)],[]) ).
tff(141,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).
tff(144,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X ),
inference(skolemize,[status(sab)],[144]) ).
tff(146,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[145,141]) ).
tff(147,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X )
| ( multiply(a,add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),add(a,b))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
multiply(a,add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),add(a,b))) = a,
inference(unit_resolution,[status(thm)],[147,146]) ).
tff(149,plain,
a = multiply(a,add(multiply(inverse(b),multiply(b,multiply(inverse(a),a))),add(a,b))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),add(X,inverse(Y))) = X )
| ( multiply(add(a,inverse(a)),add(a,inverse(inverse(a)))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
multiply(add(a,inverse(a)),add(a,inverse(inverse(a)))) = a,
inference(unit_resolution,[status(thm)],[150,82]) ).
tff(152,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
| ( add(multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),a),multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),inverse(a))) = multiply(add(a,inverse(a)),inverse(inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
add(multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),a),multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),inverse(a))) = multiply(add(a,inverse(a)),inverse(inverse(a))),
inference(unit_resolution,[status(thm)],[152,35]) ).
tff(154,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),inverse(a)) = multiply(inverse(a),multiply(add(a,inverse(a)),inverse(inverse(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),inverse(a)) = multiply(inverse(a),multiply(add(a,inverse(a)),inverse(inverse(a)))),
inference(unit_resolution,[status(thm)],[154,16]) ).
tff(156,plain,
multiply(inverse(a),multiply(add(a,inverse(a)),inverse(inverse(a)))) = multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),inverse(a)),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),add(a,inverse(a))),inverse(inverse(a))) = multiply(inverse(a),multiply(add(a,inverse(a)),inverse(inverse(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
multiply(multiply(inverse(a),add(a,inverse(a))),inverse(inverse(a))) = multiply(inverse(a),multiply(add(a,inverse(a)),inverse(inverse(a)))),
inference(unit_resolution,[status(thm)],[157,66]) ).
tff(159,plain,
multiply(inverse(a),add(a,inverse(a))) = multiply(inverse(a),multiply(add(a,inverse(a)),add(inverse(a),a))),
inference(monotonicity,[status(thm)],[56]) ).
tff(160,plain,
multiply(inverse(a),multiply(add(a,inverse(a)),add(inverse(a),a))) = multiply(inverse(a),add(a,inverse(a))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(inverse(a),multiply(add(a,inverse(a)),add(inverse(a),a))) = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
multiply(inverse(a),multiply(add(a,inverse(a)),add(inverse(a),a))) = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)),
inference(unit_resolution,[status(thm)],[161,16]) ).
tff(163,plain,
multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)) = multiply(inverse(a),multiply(add(a,inverse(a)),add(inverse(a),a))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
inverse(a) = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)),
inference(symmetry,[status(thm)],[28]) ).
tff(165,plain,
inverse(a) = multiply(inverse(a),add(a,inverse(a))),
inference(transitivity,[status(thm)],[164,163,160]) ).
tff(166,plain,
multiply(inverse(a),inverse(inverse(a))) = multiply(multiply(inverse(a),add(a,inverse(a))),inverse(inverse(a))),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(inverse(inverse(a)),inverse(a)) = multiply(inverse(a),inverse(inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
multiply(inverse(inverse(a)),inverse(a)) = multiply(inverse(a),inverse(inverse(a))),
inference(unit_resolution,[status(thm)],[167,16]) ).
tff(169,plain,
multiply(inverse(inverse(a)),inverse(a)) = multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),inverse(a)),
inference(transitivity,[status(thm)],[168,166,158,156]) ).
tff(170,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(inverse(inverse(a)),add(a,inverse(a))) = multiply(add(a,inverse(a)),inverse(inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(171,plain,
multiply(inverse(inverse(a)),add(a,inverse(a))) = multiply(add(a,inverse(a)),inverse(inverse(a))),
inference(unit_resolution,[status(thm)],[170,16]) ).
tff(172,plain,
multiply(add(a,inverse(a)),inverse(inverse(a))) = multiply(inverse(inverse(a)),add(a,inverse(a))),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),a) = multiply(multiply(inverse(inverse(a)),add(a,inverse(a))),a),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
multiply(multiply(inverse(inverse(a)),add(a,inverse(a))),a) = multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),a),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(inverse(a)),add(a,inverse(a))),a) = multiply(inverse(inverse(a)),multiply(add(a,inverse(a)),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
multiply(multiply(inverse(inverse(a)),add(a,inverse(a))),a) = multiply(inverse(inverse(a)),multiply(add(a,inverse(a)),a)),
inference(unit_resolution,[status(thm)],[175,66]) ).
tff(177,plain,
multiply(inverse(inverse(a)),multiply(add(a,inverse(a)),a)) = multiply(multiply(inverse(inverse(a)),add(a,inverse(a))),a),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
add(a,inverse(a)) = multiply(add(inverse(a),a),add(a,inverse(a))),
inference(transitivity,[status(thm)],[55,37,51]) ).
tff(179,plain,
multiply(add(a,inverse(a)),a) = multiply(multiply(add(inverse(a),a),add(a,inverse(a))),a),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
multiply(add(a,inverse(a)),a) = a,
inference(transitivity,[status(thm)],[179,39]) ).
tff(181,plain,
multiply(inverse(inverse(a)),multiply(add(a,inverse(a)),a)) = multiply(inverse(inverse(a)),a),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
multiply(inverse(inverse(a)),a) = multiply(inverse(inverse(a)),multiply(add(a,inverse(a)),a)),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
multiply(inverse(inverse(a)),a) = multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),a),
inference(transitivity,[status(thm)],[182,177,174]) ).
tff(184,plain,
add(multiply(inverse(inverse(a)),a),multiply(inverse(inverse(a)),inverse(a))) = add(multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),a),multiply(multiply(add(a,inverse(a)),inverse(inverse(a))),inverse(a))),
inference(monotonicity,[status(thm)],[183,169]) ).
tff(185,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
| ( add(multiply(inverse(inverse(a)),a),multiply(inverse(inverse(a)),inverse(a))) = inverse(inverse(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
add(multiply(inverse(inverse(a)),a),multiply(inverse(inverse(a)),inverse(a))) = inverse(inverse(a)),
inference(unit_resolution,[status(thm)],[185,35]) ).
tff(187,plain,
inverse(inverse(a)) = add(multiply(inverse(inverse(a)),a),multiply(inverse(inverse(a)),inverse(a))),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
inverse(inverse(a)) = multiply(add(a,inverse(a)),inverse(inverse(a))),
inference(transitivity,[status(thm)],[187,184,153]) ).
tff(189,plain,
multiply(a,add(a,inverse(a))) = multiply(a,multiply(add(a,inverse(a)),add(inverse(a),a))),
inference(monotonicity,[status(thm)],[56]) ).
tff(190,plain,
multiply(a,multiply(add(a,inverse(a)),add(inverse(a),a))) = multiply(a,add(a,inverse(a))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(a,multiply(add(a,inverse(a)),add(inverse(a),a))) = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
multiply(a,multiply(add(a,inverse(a)),add(inverse(a),a))) = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),a),
inference(unit_resolution,[status(thm)],[191,16]) ).
tff(193,plain,
multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),a) = multiply(a,multiply(add(a,inverse(a)),add(inverse(a),a))),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
multiply(multiply(add(inverse(a),a),add(a,inverse(a))),a) = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),a),
inference(symmetry,[status(thm)],[52]) ).
tff(195,plain,
a = multiply(a,add(a,inverse(a))),
inference(transitivity,[status(thm)],[90,194,193,190]) ).
tff(196,plain,
add(a,inverse(inverse(a))) = add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),
inference(monotonicity,[status(thm)],[195,188]) ).
tff(197,plain,
add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))) = add(a,inverse(inverse(a))),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
add(a,multiply(add(a,inverse(a)),inverse(inverse(a)))) = add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),
inference(monotonicity,[status(thm)],[195]) ).
tff(199,plain,
add(a,multiply(add(a,inverse(a)),inverse(inverse(a)))) = add(a,inverse(inverse(a))),
inference(transitivity,[status(thm)],[198,197]) ).
tff(200,plain,
multiply(add(inverse(a),a),add(a,multiply(add(a,inverse(a)),inverse(inverse(a))))) = multiply(add(a,inverse(a)),add(a,inverse(inverse(a)))),
inference(monotonicity,[status(thm)],[48,199]) ).
tff(201,plain,
add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))) = add(a,multiply(add(a,inverse(a)),inverse(inverse(a)))),
inference(symmetry,[status(thm)],[198]) ).
tff(202,plain,
multiply(add(a,inverse(a)),add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a))))) = multiply(add(inverse(a),a),add(a,multiply(add(a,inverse(a)),inverse(inverse(a))))),
inference(monotonicity,[status(thm)],[49,201]) ).
tff(203,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(add(a,inverse(a)),add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a))))) = multiply(add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),add(a,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
multiply(add(a,inverse(a)),add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a))))) = multiply(add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),add(a,inverse(a))),
inference(unit_resolution,[status(thm)],[203,16]) ).
tff(205,plain,
multiply(add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),add(a,inverse(a))) = multiply(add(a,inverse(a)),add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a))))),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
multiply(add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),add(a,inverse(a))) = multiply(add(a,b),a),
inference(transitivity,[status(thm)],[205,202,200,151,149,139,106,73]) ).
tff(207,plain,
add(multiply(add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),add(a,inverse(a))),multiply(add(a,inverse(a)),multiply(inverse(a),add(a,b)))) = add(multiply(add(a,b),a),multiply(add(a,b),inverse(a))),
inference(monotonicity,[status(thm)],[206,70]) ).
tff(208,plain,
add(multiply(add(a,b),a),multiply(add(a,b),inverse(a))) = add(multiply(add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),add(a,inverse(a))),multiply(add(a,inverse(a)),multiply(inverse(a),add(a,b)))),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
| ( add(multiply(add(a,b),a),multiply(add(a,b),inverse(a))) = add(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
add(multiply(add(a,b),a),multiply(add(a,b),inverse(a))) = add(a,b),
inference(unit_resolution,[status(thm)],[209,35]) ).
tff(211,plain,
add(a,b) = add(multiply(add(a,b),a),multiply(add(a,b),inverse(a))),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
add(a,b) = add(multiply(add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),add(a,inverse(a))),multiply(add(a,inverse(a)),multiply(inverse(a),add(a,b)))),
inference(transitivity,[status(thm)],[211,208]) ).
tff(213,plain,
add(add(a,b),add(a,inverse(a))) = add(add(multiply(add(multiply(a,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(inverse(a)))),add(a,inverse(a))),multiply(add(a,inverse(a)),multiply(inverse(a),add(a,b)))),add(a,inverse(a))),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(a,b),a),inverse(a)) = add(add(a,b),add(a,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(215,plain,
add(add(add(a,b),a),inverse(a)) = add(add(a,b),add(a,inverse(a))),
inference(unit_resolution,[status(thm)],[214,113]) ).
tff(216,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),add(X,inverse(Y))) = X )
| ( multiply(add(a,b),add(a,inverse(b))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
multiply(add(a,b),add(a,inverse(b))) = a,
inference(unit_resolution,[status(thm)],[216,82]) ).
tff(218,plain,
multiply(multiply(add(inverse(a),a),add(a,inverse(b))),multiply(add(a,b),add(a,inverse(b)))) = multiply(multiply(add(inverse(a),a),add(a,inverse(b))),a),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
multiply(multiply(add(inverse(a),a),add(a,inverse(b))),a) = multiply(multiply(add(inverse(a),a),add(a,inverse(b))),multiply(add(a,b),add(a,inverse(b)))),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
| ( multiply(multiply(add(inverse(a),a),add(a,inverse(b))),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(221,plain,
multiply(multiply(add(inverse(a),a),add(a,inverse(b))),a) = a,
inference(unit_resolution,[status(thm)],[220,26]) ).
tff(222,plain,
a = multiply(multiply(add(inverse(a),a),add(a,inverse(b))),a),
inference(symmetry,[status(thm)],[221]) ).
tff(223,plain,
a = multiply(multiply(add(inverse(a),a),add(a,inverse(b))),multiply(add(a,b),add(a,inverse(b)))),
inference(transitivity,[status(thm)],[222,219]) ).
tff(224,plain,
add(add(a,b),a) = add(add(a,b),multiply(multiply(add(inverse(a),a),add(a,inverse(b))),multiply(add(a,b),add(a,inverse(b))))),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
add(add(a,b),multiply(multiply(add(inverse(a),a),add(a,inverse(b))),multiply(add(a,b),add(a,inverse(b))))) = add(add(a,b),a),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X )
| ( add(add(a,b),multiply(multiply(add(inverse(a),a),add(a,inverse(b))),multiply(add(a,b),add(a,inverse(b))))) = add(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(227,plain,
add(add(a,b),multiply(multiply(add(inverse(a),a),add(a,inverse(b))),multiply(add(a,b),add(a,inverse(b))))) = add(a,b),
inference(unit_resolution,[status(thm)],[226,100]) ).
tff(228,plain,
add(a,b) = add(add(a,b),multiply(multiply(add(inverse(a),a),add(a,inverse(b))),multiply(add(a,b),add(a,inverse(b))))),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
add(a,b) = add(add(a,b),a),
inference(transitivity,[status(thm)],[228,225]) ).
tff(230,plain,
add(add(a,b),inverse(a)) = add(add(add(a,b),a),inverse(a)),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(inverse(a),add(a,b)) = add(add(a,b),inverse(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(232,plain,
add(inverse(a),add(a,b)) = add(add(a,b),inverse(a)),
inference(unit_resolution,[status(thm)],[231,46]) ).
tff(233,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(inverse(a),a),b) = add(inverse(a),add(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,plain,
add(add(inverse(a),a),b) = add(inverse(a),add(a,b)),
inference(unit_resolution,[status(thm)],[233,113]) ).
tff(235,plain,
add(add(a,inverse(a)),b) = add(add(inverse(a),a),b),
inference(monotonicity,[status(thm)],[49]) ).
tff(236,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(b,add(a,inverse(a))) = add(add(a,inverse(a)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(237,plain,
add(b,add(a,inverse(a))) = add(add(a,inverse(a)),b),
inference(unit_resolution,[status(thm)],[236,46]) ).
tff(238,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
| ( add(multiply(add(a,inverse(a)),b),multiply(add(a,inverse(a)),inverse(b))) = add(a,inverse(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
add(multiply(add(a,inverse(a)),b),multiply(add(a,inverse(a)),inverse(b))) = add(a,inverse(a)),
inference(unit_resolution,[status(thm)],[238,35]) ).
tff(240,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(add(a,inverse(a)),b) = multiply(b,add(a,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,plain,
multiply(add(a,inverse(a)),b) = multiply(b,add(a,inverse(a))),
inference(unit_resolution,[status(thm)],[240,16]) ).
tff(242,plain,
multiply(b,add(a,inverse(a))) = multiply(add(a,inverse(a)),b),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
add(multiply(b,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(b))) = add(multiply(add(a,inverse(a)),b),multiply(add(a,inverse(a)),inverse(b))),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(add(a,inverse(a)),inverse(b)) = multiply(inverse(b),add(a,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(245,plain,
multiply(add(a,inverse(a)),inverse(b)) = multiply(inverse(b),add(a,inverse(a))),
inference(unit_resolution,[status(thm)],[244,16]) ).
tff(246,plain,
multiply(inverse(b),add(a,inverse(a))) = multiply(add(a,inverse(a)),inverse(b)),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
add(multiply(inverse(a),a),add(a,inverse(a))) = add(multiply(inverse(a),a),add(inverse(a),a)),
inference(monotonicity,[status(thm)],[49]) ).
tff(248,plain,
add(multiply(inverse(a),a),add(inverse(a),a)) = add(multiply(inverse(a),a),add(a,inverse(a))),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(multiply(inverse(a),a),inverse(a)),a) = add(multiply(inverse(a),a),add(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
add(add(multiply(inverse(a),a),inverse(a)),a) = add(multiply(inverse(a),a),add(inverse(a),a)),
inference(unit_resolution,[status(thm)],[249,113]) ).
tff(251,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
| ( add(multiply(inverse(a),a),multiply(inverse(a),inverse(a))) = inverse(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(252,plain,
add(multiply(inverse(a),a),multiply(inverse(a),inverse(a))) = inverse(a),
inference(unit_resolution,[status(thm)],[251,35]) ).
tff(253,plain,
multiply(inverse(a),add(a,inverse(a))) = inverse(a),
inference(transitivity,[status(thm)],[159,162,28]) ).
tff(254,plain,
multiply(add(a,inverse(a)),multiply(inverse(a),add(a,inverse(a)))) = multiply(add(a,inverse(a)),inverse(a)),
inference(monotonicity,[status(thm)],[253]) ).
tff(255,plain,
multiply(add(a,inverse(a)),inverse(a)) = multiply(add(a,inverse(a)),multiply(inverse(a),add(a,inverse(a)))),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)) = multiply(add(a,inverse(a)),inverse(a)),
inference(symmetry,[status(thm)],[57]) ).
tff(257,plain,
inverse(a) = multiply(add(a,inverse(a)),multiply(inverse(a),add(a,inverse(a)))),
inference(transitivity,[status(thm)],[164,256,255]) ).
tff(258,plain,
add(inverse(a),inverse(a)) = add(inverse(a),multiply(add(a,inverse(a)),multiply(inverse(a),add(a,inverse(a))))),
inference(monotonicity,[status(thm)],[257]) ).
tff(259,plain,
add(inverse(a),multiply(add(a,inverse(a)),multiply(inverse(a),add(a,inverse(a))))) = add(inverse(a),inverse(a)),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X )
| ( add(inverse(a),multiply(add(a,inverse(a)),multiply(inverse(a),add(a,inverse(a))))) = inverse(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(261,plain,
add(inverse(a),multiply(add(a,inverse(a)),multiply(inverse(a),add(a,inverse(a))))) = inverse(a),
inference(unit_resolution,[status(thm)],[260,100]) ).
tff(262,plain,
inverse(a) = add(inverse(a),multiply(add(a,inverse(a)),multiply(inverse(a),add(a,inverse(a))))),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
inverse(a) = add(inverse(a),inverse(a)),
inference(transitivity,[status(thm)],[262,259]) ).
tff(264,plain,
multiply(inverse(a),inverse(a)) = multiply(add(inverse(a),inverse(a)),add(inverse(a),inverse(a))),
inference(monotonicity,[status(thm)],[263,263]) ).
tff(265,plain,
multiply(add(inverse(a),inverse(a)),add(inverse(a),inverse(a))) = multiply(inverse(a),inverse(a)),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
add(inverse(a),inverse(a)) = inverse(a),
inference(transitivity,[status(thm)],[258,261]) ).
tff(267,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X )
| ( add(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)))) = multiply(add(a,inverse(a)),add(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(268,plain,
add(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)))) = multiply(add(a,inverse(a)),add(inverse(a),a)),
inference(unit_resolution,[status(thm)],[267,100]) ).
tff(269,plain,
multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a))) = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)),
inference(monotonicity,[status(thm)],[28]) ).
tff(270,plain,
multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)) = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a))),
inference(symmetry,[status(thm)],[269]) ).
tff(271,plain,
inverse(a) = multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a))),
inference(transitivity,[status(thm)],[164,270]) ).
tff(272,plain,
add(inverse(a),a) = multiply(add(a,inverse(a)),add(inverse(a),a)),
inference(transitivity,[status(thm)],[48,55,37]) ).
tff(273,plain,
add(add(inverse(a),a),inverse(a)) = add(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a)))),
inference(monotonicity,[status(thm)],[272,271]) ).
tff(274,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(inverse(a),a),inverse(a)) = add(inverse(a),add(a,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(275,plain,
add(add(inverse(a),a),inverse(a)) = add(inverse(a),add(a,inverse(a))),
inference(unit_resolution,[status(thm)],[274,113]) ).
tff(276,plain,
add(inverse(a),add(a,inverse(a))) = add(add(inverse(a),a),inverse(a)),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
add(inverse(a),add(a,inverse(a))) = multiply(add(a,inverse(a)),add(inverse(a),a)),
inference(transitivity,[status(thm)],[276,273,268]) ).
tff(278,plain,
multiply(add(inverse(a),inverse(a)),add(inverse(a),add(a,inverse(a)))) = multiply(inverse(a),multiply(add(a,inverse(a)),add(inverse(a),a))),
inference(monotonicity,[status(thm)],[266,277]) ).
tff(279,plain,
multiply(inverse(a),multiply(add(a,inverse(a)),add(inverse(a),a))) = multiply(add(inverse(a),inverse(a)),add(inverse(a),add(a,inverse(a)))),
inference(symmetry,[status(thm)],[278]) ).
tff(280,plain,
add(inverse(a),inverse(a)) = multiply(add(inverse(a),inverse(a)),add(inverse(a),add(a,inverse(a)))),
inference(transitivity,[status(thm)],[258,261,164,163,279]) ).
tff(281,plain,
multiply(add(inverse(a),inverse(a)),add(inverse(a),inverse(a))) = multiply(multiply(add(inverse(a),inverse(a)),add(inverse(a),add(a,inverse(a)))),inverse(a)),
inference(monotonicity,[status(thm)],[280,266]) ).
tff(282,plain,
multiply(multiply(add(inverse(a),inverse(a)),add(inverse(a),add(a,inverse(a)))),inverse(a)) = multiply(add(inverse(a),inverse(a)),add(inverse(a),inverse(a))),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
| ( multiply(multiply(add(inverse(a),inverse(a)),add(inverse(a),add(a,inverse(a)))),inverse(a)) = inverse(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(284,plain,
multiply(multiply(add(inverse(a),inverse(a)),add(inverse(a),add(a,inverse(a)))),inverse(a)) = inverse(a),
inference(unit_resolution,[status(thm)],[283,26]) ).
tff(285,plain,
inverse(a) = multiply(multiply(add(inverse(a),inverse(a)),add(inverse(a),add(a,inverse(a)))),inverse(a)),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
inverse(a) = multiply(inverse(a),inverse(a)),
inference(transitivity,[status(thm)],[285,282,265]) ).
tff(287,plain,
add(multiply(inverse(a),a),inverse(a)) = add(multiply(inverse(a),a),multiply(inverse(a),inverse(a))),
inference(monotonicity,[status(thm)],[286]) ).
tff(288,plain,
add(multiply(inverse(a),a),inverse(a)) = inverse(a),
inference(transitivity,[status(thm)],[287,252]) ).
tff(289,plain,
add(add(multiply(inverse(a),a),inverse(a)),a) = add(inverse(a),a),
inference(monotonicity,[status(thm)],[288]) ).
tff(290,plain,
add(inverse(a),a) = add(add(multiply(inverse(a),a),inverse(a)),a),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
add(a,inverse(a)) = add(multiply(inverse(a),a),add(a,inverse(a))),
inference(transitivity,[status(thm)],[49,290,250,248]) ).
tff(292,plain,
add(inverse(b),add(a,inverse(a))) = add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),
inference(monotonicity,[status(thm)],[291]) ).
tff(293,plain,
add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))) = add(inverse(b),add(a,inverse(a))),
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
| ( add(multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),a),multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),inverse(a))) = add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
add(multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),a),multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),inverse(a))) = add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),
inference(unit_resolution,[status(thm)],[294,35]) ).
tff(296,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),a) = multiply(a,add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(297,plain,
multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),a) = multiply(a,add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))),
inference(unit_resolution,[status(thm)],[296,16]) ).
tff(298,plain,
add(multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),a),multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),inverse(a))) = add(multiply(a,add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))),multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),inverse(a))),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
add(multiply(a,add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))),multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),inverse(a))) = add(multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),a),multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),inverse(a))),
inference(symmetry,[status(thm)],[298]) ).
tff(300,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X )
| ( multiply(inverse(a),add(inverse(b),add(inverse(a),add(a,inverse(a))))) = inverse(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(301,plain,
multiply(inverse(a),add(inverse(b),add(inverse(a),add(a,inverse(a))))) = inverse(a),
inference(unit_resolution,[status(thm)],[300,146]) ).
tff(302,plain,
multiply(add(a,inverse(a)),add(inverse(a),a)) = add(multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),a),multiply(multiply(add(a,inverse(a)),add(inverse(a),a)),inverse(a))),
inference(symmetry,[status(thm)],[37]) ).
tff(303,plain,
add(inverse(a),add(a,inverse(a))) = add(multiply(inverse(a),a),add(a,inverse(a))),
inference(transitivity,[status(thm)],[276,273,268,302,54,49,290,250,248]) ).
tff(304,plain,
add(inverse(b),add(inverse(a),add(a,inverse(a)))) = add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),
inference(monotonicity,[status(thm)],[303]) ).
tff(305,plain,
add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))) = add(inverse(b),add(inverse(a),add(a,inverse(a)))),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
multiply(inverse(a),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))) = multiply(inverse(a),add(inverse(b),add(inverse(a),add(a,inverse(a))))),
inference(monotonicity,[status(thm)],[305]) ).
tff(307,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),inverse(a)) = multiply(inverse(a),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(308,plain,
multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),inverse(a)) = multiply(inverse(a),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))),
inference(unit_resolution,[status(thm)],[307,16]) ).
tff(309,plain,
multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),inverse(a)) = inverse(a),
inference(transitivity,[status(thm)],[308,306,301]) ).
tff(310,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X )
| ( multiply(a,add(inverse(b),add(a,inverse(a)))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(311,plain,
multiply(a,add(inverse(b),add(a,inverse(a)))) = a,
inference(unit_resolution,[status(thm)],[310,146]) ).
tff(312,plain,
multiply(a,add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))) = multiply(a,add(inverse(b),add(a,inverse(a)))),
inference(monotonicity,[status(thm)],[293]) ).
tff(313,plain,
multiply(a,add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))) = a,
inference(transitivity,[status(thm)],[312,311]) ).
tff(314,plain,
add(multiply(a,add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))),multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),inverse(a))) = add(a,inverse(a)),
inference(monotonicity,[status(thm)],[313,309]) ).
tff(315,plain,
add(a,inverse(a)) = add(multiply(a,add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))),multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),inverse(a))),
inference(symmetry,[status(thm)],[314]) ).
tff(316,plain,
add(a,inverse(a)) = add(inverse(b),add(a,inverse(a))),
inference(transitivity,[status(thm)],[315,299,295,293]) ).
tff(317,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
| ( multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)) = inverse(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(318,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)) = inverse(b),
inference(unit_resolution,[status(thm)],[317,26]) ).
tff(319,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(inverse(b),multiply(add(b,inverse(b)),add(inverse(b),b))) = multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(320,plain,
multiply(inverse(b),multiply(add(b,inverse(b)),add(inverse(b),b))) = multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)),
inference(unit_resolution,[status(thm)],[319,16]) ).
tff(321,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
| ( add(multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),b),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b))) = multiply(add(b,inverse(b)),add(inverse(b),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
add(multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),b),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b))) = multiply(add(b,inverse(b)),add(inverse(b),b)),
inference(unit_resolution,[status(thm)],[321,35]) ).
tff(323,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
| ( multiply(multiply(add(inverse(b),b),add(b,inverse(b))),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(324,plain,
multiply(multiply(add(inverse(b),b),add(b,inverse(b))),b) = b,
inference(unit_resolution,[status(thm)],[323,26]) ).
tff(325,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(inverse(b),b) = add(b,inverse(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(326,plain,
add(inverse(b),b) = add(b,inverse(b)),
inference(unit_resolution,[status(thm)],[325,46]) ).
tff(327,plain,
add(b,inverse(b)) = add(inverse(b),b),
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
multiply(add(inverse(b),b),add(b,inverse(b))) = multiply(add(b,inverse(b)),add(inverse(b),b)),
inference(monotonicity,[status(thm)],[326,327]) ).
tff(329,plain,
multiply(add(b,inverse(b)),add(inverse(b),b)) = multiply(add(inverse(b),b),add(b,inverse(b))),
inference(symmetry,[status(thm)],[328]) ).
tff(330,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),b) = multiply(multiply(add(inverse(b),b),add(b,inverse(b))),b),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),b) = b,
inference(transitivity,[status(thm)],[330,324]) ).
tff(332,plain,
add(multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),b),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b))) = add(b,inverse(b)),
inference(monotonicity,[status(thm)],[331,318]) ).
tff(333,plain,
add(b,inverse(b)) = add(multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),b),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b))),
inference(symmetry,[status(thm)],[332]) ).
tff(334,plain,
add(b,inverse(b)) = multiply(add(b,inverse(b)),add(inverse(b),b)),
inference(transitivity,[status(thm)],[333,322]) ).
tff(335,plain,
multiply(inverse(b),add(b,inverse(b))) = multiply(inverse(b),multiply(add(b,inverse(b)),add(inverse(b),b))),
inference(monotonicity,[status(thm)],[334]) ).
tff(336,plain,
multiply(inverse(b),add(b,inverse(b))) = inverse(b),
inference(transitivity,[status(thm)],[335,320,318]) ).
tff(337,plain,
multiply(add(b,inverse(b)),multiply(inverse(b),add(b,inverse(b)))) = multiply(add(b,inverse(b)),inverse(b)),
inference(monotonicity,[status(thm)],[336]) ).
tff(338,plain,
multiply(add(b,inverse(b)),inverse(b)) = multiply(add(b,inverse(b)),multiply(inverse(b),add(b,inverse(b)))),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
multiply(add(b,inverse(b)),inverse(b)) = multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)),
inference(monotonicity,[status(thm)],[334]) ).
tff(340,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)) = multiply(add(b,inverse(b)),inverse(b)),
inference(symmetry,[status(thm)],[339]) ).
tff(341,plain,
inverse(b) = multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)),
inference(symmetry,[status(thm)],[318]) ).
tff(342,plain,
inverse(b) = multiply(add(b,inverse(b)),multiply(inverse(b),add(b,inverse(b)))),
inference(transitivity,[status(thm)],[341,340,338]) ).
tff(343,plain,
add(inverse(b),inverse(b)) = add(inverse(b),multiply(add(b,inverse(b)),multiply(inverse(b),add(b,inverse(b))))),
inference(monotonicity,[status(thm)],[342]) ).
tff(344,plain,
add(inverse(b),multiply(add(b,inverse(b)),multiply(inverse(b),add(b,inverse(b))))) = add(inverse(b),inverse(b)),
inference(symmetry,[status(thm)],[343]) ).
tff(345,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X )
| ( add(inverse(b),multiply(add(b,inverse(b)),multiply(inverse(b),add(b,inverse(b))))) = inverse(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(346,plain,
add(inverse(b),multiply(add(b,inverse(b)),multiply(inverse(b),add(b,inverse(b))))) = inverse(b),
inference(unit_resolution,[status(thm)],[345,100]) ).
tff(347,plain,
inverse(b) = add(inverse(b),multiply(add(b,inverse(b)),multiply(inverse(b),add(b,inverse(b))))),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
inverse(b) = add(inverse(b),inverse(b)),
inference(transitivity,[status(thm)],[347,344]) ).
tff(349,plain,
multiply(inverse(b),add(a,inverse(a))) = multiply(add(inverse(b),inverse(b)),add(inverse(b),add(a,inverse(a)))),
inference(monotonicity,[status(thm)],[348,316]) ).
tff(350,plain,
multiply(add(inverse(b),inverse(b)),add(inverse(b),add(a,inverse(a)))) = multiply(inverse(b),add(a,inverse(a))),
inference(symmetry,[status(thm)],[349]) ).
tff(351,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(multiply(inverse(b),b),inverse(b)),add(a,inverse(a))) = add(multiply(inverse(b),b),add(inverse(b),add(a,inverse(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(352,plain,
add(add(multiply(inverse(b),b),inverse(b)),add(a,inverse(a))) = add(multiply(inverse(b),b),add(inverse(b),add(a,inverse(a)))),
inference(unit_resolution,[status(thm)],[351,113]) ).
tff(353,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
| ( add(multiply(inverse(b),b),multiply(inverse(b),inverse(b))) = inverse(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(354,plain,
add(multiply(inverse(b),b),multiply(inverse(b),inverse(b))) = inverse(b),
inference(unit_resolution,[status(thm)],[353,35]) ).
tff(355,plain,
multiply(inverse(b),inverse(b)) = multiply(add(inverse(b),inverse(b)),add(inverse(b),inverse(b))),
inference(monotonicity,[status(thm)],[348,348]) ).
tff(356,plain,
multiply(add(inverse(b),inverse(b)),add(inverse(b),inverse(b))) = multiply(inverse(b),inverse(b)),
inference(symmetry,[status(thm)],[355]) ).
tff(357,plain,
add(inverse(b),inverse(b)) = inverse(b),
inference(transitivity,[status(thm)],[343,346]) ).
tff(358,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X )
| ( add(multiply(add(b,inverse(b)),add(inverse(b),b)),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)))) = multiply(add(b,inverse(b)),add(inverse(b),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(359,plain,
add(multiply(add(b,inverse(b)),add(inverse(b),b)),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)))) = multiply(add(b,inverse(b)),add(inverse(b),b)),
inference(unit_resolution,[status(thm)],[358,100]) ).
tff(360,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b))) = multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)),
inference(monotonicity,[status(thm)],[318]) ).
tff(361,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)) = multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b))),
inference(symmetry,[status(thm)],[360]) ).
tff(362,plain,
inverse(b) = multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b))),
inference(transitivity,[status(thm)],[341,361]) ).
tff(363,plain,
add(inverse(b),b) = multiply(add(b,inverse(b)),add(inverse(b),b)),
inference(transitivity,[status(thm)],[326,333,322]) ).
tff(364,plain,
add(add(inverse(b),b),inverse(b)) = add(multiply(add(b,inverse(b)),add(inverse(b),b)),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)))),
inference(monotonicity,[status(thm)],[363,362]) ).
tff(365,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(inverse(b),b),inverse(b)) = add(inverse(b),add(b,inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(366,plain,
add(add(inverse(b),b),inverse(b)) = add(inverse(b),add(b,inverse(b))),
inference(unit_resolution,[status(thm)],[365,113]) ).
tff(367,plain,
add(inverse(b),add(b,inverse(b))) = add(add(inverse(b),b),inverse(b)),
inference(symmetry,[status(thm)],[366]) ).
tff(368,plain,
add(inverse(b),add(b,inverse(b))) = multiply(add(b,inverse(b)),add(inverse(b),b)),
inference(transitivity,[status(thm)],[367,364,359]) ).
tff(369,plain,
multiply(add(inverse(b),inverse(b)),add(inverse(b),add(b,inverse(b)))) = multiply(inverse(b),multiply(add(b,inverse(b)),add(inverse(b),b))),
inference(monotonicity,[status(thm)],[357,368]) ).
tff(370,plain,
multiply(inverse(b),multiply(add(b,inverse(b)),add(inverse(b),b))) = multiply(add(inverse(b),inverse(b)),add(inverse(b),add(b,inverse(b)))),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b)) = multiply(inverse(b),multiply(add(b,inverse(b)),add(inverse(b),b))),
inference(symmetry,[status(thm)],[320]) ).
tff(372,plain,
add(inverse(b),inverse(b)) = multiply(add(inverse(b),inverse(b)),add(inverse(b),add(b,inverse(b)))),
inference(transitivity,[status(thm)],[343,346,341,371,370]) ).
tff(373,plain,
multiply(add(inverse(b),inverse(b)),add(inverse(b),inverse(b))) = multiply(multiply(add(inverse(b),inverse(b)),add(inverse(b),add(b,inverse(b)))),inverse(b)),
inference(monotonicity,[status(thm)],[372,357]) ).
tff(374,plain,
multiply(multiply(add(inverse(b),inverse(b)),add(inverse(b),add(b,inverse(b)))),inverse(b)) = multiply(add(inverse(b),inverse(b)),add(inverse(b),inverse(b))),
inference(symmetry,[status(thm)],[373]) ).
tff(375,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
| ( multiply(multiply(add(inverse(b),inverse(b)),add(inverse(b),add(b,inverse(b)))),inverse(b)) = inverse(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(376,plain,
multiply(multiply(add(inverse(b),inverse(b)),add(inverse(b),add(b,inverse(b)))),inverse(b)) = inverse(b),
inference(unit_resolution,[status(thm)],[375,26]) ).
tff(377,plain,
inverse(b) = multiply(multiply(add(inverse(b),inverse(b)),add(inverse(b),add(b,inverse(b)))),inverse(b)),
inference(symmetry,[status(thm)],[376]) ).
tff(378,plain,
inverse(b) = multiply(inverse(b),inverse(b)),
inference(transitivity,[status(thm)],[377,374,356]) ).
tff(379,plain,
add(multiply(inverse(b),b),inverse(b)) = add(multiply(inverse(b),b),multiply(inverse(b),inverse(b))),
inference(monotonicity,[status(thm)],[378]) ).
tff(380,plain,
add(multiply(inverse(b),b),inverse(b)) = inverse(b),
inference(transitivity,[status(thm)],[379,354]) ).
tff(381,plain,
add(add(multiply(inverse(b),b),inverse(b)),add(a,inverse(a))) = add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),
inference(monotonicity,[status(thm)],[380,291]) ).
tff(382,plain,
add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))) = add(add(multiply(inverse(b),b),inverse(b)),add(a,inverse(a))),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
add(inverse(b),add(a,inverse(a))) = add(multiply(inverse(b),b),add(inverse(b),add(a,inverse(a)))),
inference(transitivity,[status(thm)],[292,382,352]) ).
tff(384,plain,
multiply(add(inverse(b),inverse(b)),add(inverse(b),add(a,inverse(a)))) = multiply(inverse(b),add(multiply(inverse(b),b),add(inverse(b),add(a,inverse(a))))),
inference(monotonicity,[status(thm)],[357,383]) ).
tff(385,plain,
multiply(inverse(b),add(multiply(inverse(b),b),add(inverse(b),add(a,inverse(a))))) = multiply(add(inverse(b),inverse(b)),add(inverse(b),add(a,inverse(a)))),
inference(symmetry,[status(thm)],[384]) ).
tff(386,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,add(X,Z))) = X )
| ( multiply(inverse(b),add(multiply(inverse(b),b),add(inverse(b),add(a,inverse(a))))) = inverse(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(387,plain,
multiply(inverse(b),add(multiply(inverse(b),b),add(inverse(b),add(a,inverse(a))))) = inverse(b),
inference(unit_resolution,[status(thm)],[386,146]) ).
tff(388,plain,
inverse(b) = multiply(inverse(b),add(multiply(inverse(b),b),add(inverse(b),add(a,inverse(a))))),
inference(symmetry,[status(thm)],[387]) ).
tff(389,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y )
| ( multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)) = inverse(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(390,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)) = inverse(b),
inference(unit_resolution,[status(thm)],[389,26]) ).
tff(391,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)) = multiply(add(a,inverse(a)),inverse(b)),
inference(transitivity,[status(thm)],[390,388,385,350,246]) ).
tff(392,plain,
add(b,inverse(b)) = multiply(add(inverse(b),b),add(b,inverse(b))),
inference(transitivity,[status(thm)],[333,322,329]) ).
tff(393,plain,
multiply(add(b,inverse(b)),b) = multiply(multiply(add(inverse(b),b),add(b,inverse(b))),b),
inference(monotonicity,[status(thm)],[392]) ).
tff(394,plain,
multiply(add(b,inverse(b)),b) = b,
inference(transitivity,[status(thm)],[393,324]) ).
tff(395,plain,
multiply(add(a,inverse(a)),multiply(add(b,inverse(b)),b)) = multiply(add(a,inverse(a)),b),
inference(monotonicity,[status(thm)],[394]) ).
tff(396,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(add(a,inverse(a)),add(b,inverse(b))),b) = multiply(add(a,inverse(a)),multiply(add(b,inverse(b)),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(397,plain,
multiply(multiply(add(a,inverse(a)),add(b,inverse(b))),b) = multiply(add(a,inverse(a)),multiply(add(b,inverse(b)),b)),
inference(unit_resolution,[status(thm)],[396,66]) ).
tff(398,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(a,inverse(a)),inverse(b)) = add(inverse(b),add(a,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(399,plain,
add(add(a,inverse(a)),inverse(b)) = add(inverse(b),add(a,inverse(a))),
inference(unit_resolution,[status(thm)],[398,46]) ).
tff(400,plain,
add(inverse(b),add(a,inverse(a))) = add(add(a,inverse(a)),inverse(b)),
inference(symmetry,[status(thm)],[399]) ).
tff(401,plain,
add(a,inverse(a)) = add(add(a,inverse(a)),inverse(b)),
inference(transitivity,[status(thm)],[315,299,295,293,400]) ).
tff(402,plain,
multiply(add(a,inverse(a)),add(b,inverse(b))) = multiply(add(add(a,inverse(a)),inverse(b)),add(inverse(b),b)),
inference(monotonicity,[status(thm)],[401,327]) ).
tff(403,plain,
multiply(add(add(a,inverse(a)),inverse(b)),add(inverse(b),b)) = multiply(add(a,inverse(a)),add(b,inverse(b))),
inference(symmetry,[status(thm)],[402]) ).
tff(404,plain,
add(add(a,inverse(a)),inverse(b)) = add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),
inference(transitivity,[status(thm)],[399,292]) ).
tff(405,plain,
multiply(add(add(a,inverse(a)),inverse(b)),add(inverse(b),b)) = multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),add(b,inverse(b))),
inference(monotonicity,[status(thm)],[404,326]) ).
tff(406,plain,
multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),add(b,inverse(b))) = multiply(add(add(a,inverse(a)),inverse(b)),add(inverse(b),b)),
inference(symmetry,[status(thm)],[405]) ).
tff(407,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),add(b,inverse(b))) = multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(408,plain,
multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),add(b,inverse(b))) = multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))),
inference(unit_resolution,[status(thm)],[407,16]) ).
tff(409,plain,
multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))) = multiply(add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))),add(b,inverse(b))),
inference(symmetry,[status(thm)],[408]) ).
tff(410,plain,
multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))) = multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),
inference(monotonicity,[status(thm)],[293]) ).
tff(411,plain,
multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))) = multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))),
inference(symmetry,[status(thm)],[410]) ).
tff(412,plain,
multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))) = multiply(add(a,inverse(a)),add(b,inverse(b))),
inference(transitivity,[status(thm)],[411,409,406,403]) ).
tff(413,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),b) = multiply(multiply(add(a,inverse(a)),add(b,inverse(b))),b),
inference(monotonicity,[status(thm)],[412]) ).
tff(414,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(b,multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))) = multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(415,plain,
multiply(b,multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))) = multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),b),
inference(unit_resolution,[status(thm)],[414,16]) ).
tff(416,plain,
multiply(b,multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))) = multiply(b,add(a,inverse(a))),
inference(transitivity,[status(thm)],[415,413,397,395,241]) ).
tff(417,plain,
add(multiply(b,multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b))) = add(multiply(b,add(a,inverse(a))),multiply(add(a,inverse(a)),inverse(b))),
inference(monotonicity,[status(thm)],[416,391]) ).
tff(418,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),b) = multiply(b,multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))),
inference(symmetry,[status(thm)],[415]) ).
tff(419,plain,
add(multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),b),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b))) = add(multiply(b,multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b))),
inference(monotonicity,[status(thm)],[418]) ).
tff(420,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),multiply(X,inverse(Y))) = X )
| ( add(multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),b),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b))) = multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(421,plain,
add(multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),b),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b))) = multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),
inference(unit_resolution,[status(thm)],[420,35]) ).
tff(422,plain,
multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))) = add(multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),b),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b))),
inference(symmetry,[status(thm)],[421]) ).
tff(423,plain,
multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))) = add(a,inverse(a)),
inference(transitivity,[status(thm)],[410,422,419,417,243,239]) ).
tff(424,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(b,multiply(add(b,inverse(b)),add(inverse(b),b))) = multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(425,plain,
multiply(b,multiply(add(b,inverse(b)),add(inverse(b),b))) = multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),b),
inference(unit_resolution,[status(thm)],[424,16]) ).
tff(426,plain,
multiply(b,add(b,inverse(b))) = multiply(b,multiply(add(b,inverse(b)),add(inverse(b),b))),
inference(monotonicity,[status(thm)],[334]) ).
tff(427,plain,
multiply(b,add(b,inverse(b))) = b,
inference(transitivity,[status(thm)],[426,425,330,324]) ).
tff(428,plain,
add(multiply(b,add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))))) = add(b,add(a,inverse(a))),
inference(monotonicity,[status(thm)],[427,423]) ).
tff(429,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X )
| ( add(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)))) = multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(430,plain,
add(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)))) = multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),
inference(unit_resolution,[status(thm)],[429,100]) ).
tff(431,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b))) = multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)),
inference(monotonicity,[status(thm)],[390]) ).
tff(432,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)) = multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b))),
inference(symmetry,[status(thm)],[431]) ).
tff(433,plain,
inverse(b) = multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)),
inference(symmetry,[status(thm)],[390]) ).
tff(434,plain,
inverse(b) = multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b))),
inference(transitivity,[status(thm)],[433,432]) ).
tff(435,plain,
add(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)) = add(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),multiply(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)))),
inference(monotonicity,[status(thm)],[434]) ).
tff(436,plain,
add(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)) = multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))),
inference(transitivity,[status(thm)],[435,430,411]) ).
tff(437,plain,
multiply(b,multiply(add(b,inverse(b)),add(inverse(b),b))) = multiply(b,add(b,inverse(b))),
inference(symmetry,[status(thm)],[426]) ).
tff(438,plain,
multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),b) = multiply(b,multiply(add(b,inverse(b)),add(inverse(b),b))),
inference(symmetry,[status(thm)],[425]) ).
tff(439,plain,
multiply(multiply(add(inverse(b),b),add(b,inverse(b))),b) = multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),b),
inference(symmetry,[status(thm)],[330]) ).
tff(440,plain,
b = multiply(multiply(add(inverse(b),b),add(b,inverse(b))),b),
inference(symmetry,[status(thm)],[324]) ).
tff(441,plain,
b = multiply(b,add(b,inverse(b))),
inference(transitivity,[status(thm)],[440,439,438,437]) ).
tff(442,plain,
add(b,add(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b))) = add(multiply(b,add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))))),
inference(monotonicity,[status(thm)],[441,436]) ).
tff(443,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(inverse(b),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))) = add(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(444,plain,
add(inverse(b),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))) = add(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b)),
inference(unit_resolution,[status(thm)],[443,46]) ).
tff(445,plain,
add(b,add(inverse(b),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))))) = add(b,add(multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))),inverse(b))),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(b,inverse(b)),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))) = add(b,add(inverse(b),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(447,plain,
add(add(b,inverse(b)),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))) = add(b,add(inverse(b),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))))),
inference(unit_resolution,[status(thm)],[446,113]) ).
tff(448,plain,
multiply(add(b,inverse(b)),add(inverse(b),b)) = add(multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),b),multiply(multiply(add(b,inverse(b)),add(inverse(b),b)),inverse(b))),
inference(symmetry,[status(thm)],[322]) ).
tff(449,plain,
multiply(add(b,inverse(b)),add(b,inverse(b))) = multiply(add(b,inverse(b)),add(inverse(b),b)),
inference(monotonicity,[status(thm)],[327]) ).
tff(450,plain,
multiply(add(b,inverse(b)),add(b,inverse(b))) = add(b,inverse(b)),
inference(transitivity,[status(thm)],[449,448,332]) ).
tff(451,plain,
add(multiply(add(b,inverse(b)),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))))) = add(add(b,inverse(b)),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))),
inference(monotonicity,[status(thm)],[450,410]) ).
tff(452,plain,
multiply(add(b,inverse(b)),add(inverse(b),b)) = multiply(add(b,inverse(b)),add(b,inverse(b))),
inference(symmetry,[status(thm)],[449]) ).
tff(453,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,multiply(X,Z))) = X )
| ( add(add(b,inverse(b)),multiply(inverse(b),multiply(add(b,inverse(b)),b))) = add(b,inverse(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(454,plain,
add(add(b,inverse(b)),multiply(inverse(b),multiply(add(b,inverse(b)),b))) = add(b,inverse(b)),
inference(unit_resolution,[status(thm)],[453,100]) ).
tff(455,plain,
multiply(inverse(b),multiply(add(b,inverse(b)),b)) = multiply(inverse(b),b),
inference(monotonicity,[status(thm)],[394]) ).
tff(456,plain,
multiply(inverse(b),b) = multiply(inverse(b),multiply(add(b,inverse(b)),b)),
inference(symmetry,[status(thm)],[455]) ).
tff(457,plain,
add(add(b,inverse(b)),multiply(inverse(b),b)) = add(add(b,inverse(b)),multiply(inverse(b),multiply(add(b,inverse(b)),b))),
inference(monotonicity,[status(thm)],[456]) ).
tff(458,plain,
add(add(b,inverse(b)),multiply(inverse(b),b)) = multiply(add(b,inverse(b)),add(b,inverse(b))),
inference(transitivity,[status(thm)],[457,454,333,322,452]) ).
tff(459,plain,
add(add(add(b,inverse(b)),multiply(inverse(b),b)),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))) = add(multiply(add(b,inverse(b)),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))))),
inference(monotonicity,[status(thm)],[458,411]) ).
tff(460,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(b,inverse(b)),multiply(inverse(b),b)),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))) = add(add(b,inverse(b)),add(multiply(inverse(b),b),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(461,plain,
add(add(add(b,inverse(b)),multiply(inverse(b),b)),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))) = add(add(b,inverse(b)),add(multiply(inverse(b),b),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))))),
inference(unit_resolution,[status(thm)],[460,113]) ).
tff(462,plain,
add(add(b,inverse(b)),add(multiply(inverse(b),b),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))))) = add(add(add(b,inverse(b)),multiply(inverse(b),b)),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))),
inference(symmetry,[status(thm)],[461]) ).
tff(463,plain,
multiply(inverse(b),multiply(b,add(b,inverse(b)))) = multiply(inverse(b),b),
inference(monotonicity,[status(thm)],[427]) ).
tff(464,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(b),b),add(b,inverse(b))) = multiply(inverse(b),multiply(b,add(b,inverse(b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(465,plain,
multiply(multiply(inverse(b),b),add(b,inverse(b))) = multiply(inverse(b),multiply(b,add(b,inverse(b)))),
inference(unit_resolution,[status(thm)],[464,66]) ).
tff(466,plain,
multiply(multiply(inverse(b),b),add(b,inverse(b))) = multiply(inverse(b),b),
inference(transitivity,[status(thm)],[465,463]) ).
tff(467,plain,
add(multiply(multiply(inverse(b),b),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))))) = add(multiply(inverse(b),b),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a))))),
inference(monotonicity,[status(thm)],[466,410]) ).
tff(468,plain,
add(add(b,inverse(b)),add(multiply(multiply(inverse(b),b),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))))) = add(add(b,inverse(b)),add(multiply(inverse(b),b),multiply(add(b,inverse(b)),add(inverse(b),add(a,inverse(a)))))),
inference(monotonicity,[status(thm)],[467]) ).
tff(469,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(b,inverse(b)),add(multiply(multiply(inverse(b),b),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))))) = add(add(multiply(multiply(inverse(b),b),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))))),add(b,inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(470,plain,
add(add(b,inverse(b)),add(multiply(multiply(inverse(b),b),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))))) = add(add(multiply(multiply(inverse(b),b),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))))),add(b,inverse(b))),
inference(unit_resolution,[status(thm)],[469,46]) ).
tff(471,plain,
add(add(multiply(multiply(inverse(b),b),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))))),add(b,inverse(b))) = add(add(b,inverse(b)),add(multiply(multiply(inverse(b),b),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a))))))),
inference(symmetry,[status(thm)],[470]) ).
tff(472,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y )
| ( add(add(multiply(multiply(inverse(b),b),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))))),add(b,inverse(b))) = add(b,inverse(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(473,plain,
add(add(multiply(multiply(inverse(b),b),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))))),add(b,inverse(b))) = add(b,inverse(b)),
inference(unit_resolution,[status(thm)],[472,7]) ).
tff(474,plain,
add(b,inverse(b)) = add(add(multiply(multiply(inverse(b),b),add(b,inverse(b))),multiply(add(b,inverse(b)),add(inverse(b),add(multiply(inverse(a),a),add(a,inverse(a)))))),add(b,inverse(b))),
inference(symmetry,[status(thm)],[473]) ).
tff(475,plain,
add(b,inverse(b)) = add(a,inverse(a)),
inference(transitivity,[status(thm)],[474,471,468,462,459,451,447,445,442,428,237,235,234,232,230,215,213,9]) ).
tff(476,plain,
( ( add(b,inverse(b)) != add(a,inverse(a)) )
<=> ( add(b,inverse(b)) != add(a,inverse(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(477,axiom,
add(b,inverse(b)) != add(a,inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_inverse) ).
tff(478,plain,
add(b,inverse(b)) != add(a,inverse(a)),
inference(modus_ponens,[status(thm)],[477,476]) ).
tff(479,plain,
$false,
inference(unit_resolution,[status(thm)],[478,475]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : BOO029-1 : TPTP v9.0.0. Released v2.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n013.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Jun 19 11:35:38 EDT 2025
% 0.13/0.36 % CPUTime :
% 25.58/25.75 % SZS status Unsatisfiable
% 25.58/25.75 % SZS output start Proof
% See solution above
% 25.58/25.81 % E exiting
%------------------------------------------------------------------------------