TSTP Solution File: GRP681-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP681-1 : TPTP v8.1.0. Released v4.0.0.
% 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 22:29:26 EDT 2022
% Result : Unsatisfiable 100.38s 64.50s
% Output : Proof 100.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 222
% Syntax : Number of formulae : 1184 ( 972 unt; 7 typ; 0 def)
% Number of atoms : 1400 (1390 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 404 ( 190 ~; 186 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 601 ( 586 !; 0 ?; 601 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(op_d_type,type,
op_d: $i ).
tff(op_c_type,type,
op_c: $i ).
tff(a_type,type,
a: $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(unit_type,type,
unit: $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
tff(5,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d)))) = mult(a,mult(mult(op_c,op_c),op_d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d)))) = mult(a,mult(mult(op_c,op_c),op_d)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) = mult(rd(op_c,mult(a,mult(unit,a))),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(11,plain,
ld(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) = mult(rd(op_c,mult(a,mult(unit,a))),a),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [B: $i,A: $i] :
refl(
( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
tff(16,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),a),a) = mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
rd(mult(mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),a),a) = mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
^ [A: $i] :
refl(
( ( mult(op_c,A) = mult(A,op_c) )
<=> ( mult(op_c,A) = mult(A,op_c) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
<=> ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
<=> ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
tff(25,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,a) = mult(a,op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
mult(op_c,a) = mult(a,op_c),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
mult(a,op_c) = mult(op_c,a),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
^ [B: $i,A: $i] :
refl(
( ( mult(rd(A,B),B) = A )
<=> ( mult(rd(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
tff(35,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(op_c,mult(a,mult(unit,a))),mult(a,mult(unit,a))) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
mult(rd(op_c,mult(a,mult(unit,a))),mult(a,mult(unit,a))) = op_c,
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
^ [A: $i] :
refl(
( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
tff(44,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
mult(unit,a) = a,
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
a = mult(unit,a),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
mult(a,a) = mult(a,mult(unit,a)),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
mult(rd(op_c,mult(a,mult(unit,a))),mult(a,a)) = mult(rd(op_c,mult(a,mult(unit,a))),mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
mult(rd(op_c,mult(a,mult(unit,a))),mult(a,a)) = op_c,
inference(transitivity,[status(thm)],[51,39]) ).
tff(53,plain,
mult(a,mult(rd(op_c,mult(a,mult(unit,a))),mult(a,a))) = mult(a,op_c),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
tff(58,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(rd(op_c,mult(a,mult(unit,a))),mult(a,a))) = mult(mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
mult(a,mult(rd(op_c,mult(a,mult(unit,a))),mult(a,a))) = mult(mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),a),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
mult(mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),a) = mult(a,mult(rd(op_c,mult(a,mult(unit,a))),mult(a,a))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
mult(mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),a) = mult(op_c,a),
inference(transitivity,[status(thm)],[63,53,30]) ).
tff(65,plain,
rd(mult(mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),a),a) = rd(mult(op_c,a),a),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
rd(mult(op_c,a),a) = rd(mult(mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),a),a),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(op_c,a),a) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
rd(mult(op_c,a),a) = op_c,
inference(unit_resolution,[status(thm)],[67,18]) ).
tff(69,plain,
op_c = rd(mult(op_c,a),a),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,op_c) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
mult(unit,op_c) = op_c,
inference(unit_resolution,[status(thm)],[70,46]) ).
tff(72,plain,
^ [B: $i,A: $i] :
refl(
( ( mult(A,ld(A,B)) = B )
<=> ( mult(A,ld(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
tff(76,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)) = unit ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)) = unit,
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)),
inference(unit_resolution,[status(thm)],[81,60]) ).
tff(83,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
ld(a,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),
inference(unit_resolution,[status(thm)],[83,7]) ).
tff(85,plain,
mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)) = mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(symmetry,[status(thm)],[82]) ).
tff(86,plain,
unit = mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)),
inference(symmetry,[status(thm)],[80]) ).
tff(87,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(unit,a),a) = unit ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
rd(mult(unit,a),a) = unit,
inference(unit_resolution,[status(thm)],[87,18]) ).
tff(89,plain,
^ [A: $i] :
refl(
( ( mult(A,unit) = A )
<=> ( mult(A,unit) = A ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
tff(93,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(a,unit) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
mult(a,unit) = a,
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))) = unit ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))) = unit,
inference(unit_resolution,[status(thm)],[98,37]) ).
tff(100,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(a,a)) = mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[50]) ).
tff(101,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(a,a)) = unit,
inference(transitivity,[status(thm)],[100,99]) ).
tff(102,plain,
mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(a,a))) = mult(a,unit),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(a,a))) = mult(mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(a,a))) = mult(mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)),a),
inference(unit_resolution,[status(thm)],[103,60]) ).
tff(105,plain,
mult(mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)),a) = mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(a,a))),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
mult(mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)),a) = mult(unit,a),
inference(transitivity,[status(thm)],[105,102,97,49]) ).
tff(107,plain,
rd(mult(mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)),a),a) = rd(mult(unit,a),a),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)),a),a) = mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
rd(mult(mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)),a),a) = mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)),
inference(unit_resolution,[status(thm)],[108,18]) ).
tff(110,plain,
mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)) = rd(mult(mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)),a),a),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
mult(a,mult(rd(unit,mult(a,mult(unit,a))),a)) = mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(transitivity,[status(thm)],[110,107,88,86,85]) ).
tff(112,plain,
ld(a,mult(a,mult(rd(unit,mult(a,mult(unit,a))),a))) = ld(a,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(rd(unit,mult(a,mult(unit,a))),a))) = mult(rd(unit,mult(a,mult(unit,a))),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
ld(a,mult(a,mult(rd(unit,mult(a,mult(unit,a))),a))) = mult(rd(unit,mult(a,mult(unit,a))),a),
inference(unit_resolution,[status(thm)],[113,7]) ).
tff(115,plain,
mult(rd(unit,mult(a,mult(unit,a))),a) = ld(a,mult(a,mult(rd(unit,mult(a,mult(unit,a))),a))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(rd(unit,mult(a,mult(unit,a))),unit) = rd(unit,mult(a,mult(unit,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
mult(rd(unit,mult(a,mult(unit,a))),unit) = rd(unit,mult(a,mult(unit,a))),
inference(unit_resolution,[status(thm)],[116,95]) ).
tff(118,plain,
mult(rd(unit,mult(a,mult(unit,a))),unit) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(monotonicity,[status(thm)],[86]) ).
tff(119,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))) = mult(rd(unit,mult(a,mult(unit,a))),unit),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))) = rd(unit,mult(a,mult(unit,a))),
inference(transitivity,[status(thm)],[119,117]) ).
tff(121,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a) = mult(rd(unit,mult(a,mult(unit,a))),a),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a) = mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),
inference(transitivity,[status(thm)],[121,115,112,84]) ).
tff(123,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)) = mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)) = unit,
inference(transitivity,[status(thm)],[123,82,80]) ).
tff(125,plain,
mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),op_c) = mult(unit,op_c),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),op_c),
inference(unit_resolution,[status(thm)],[126,60]) ).
tff(128,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))) = mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(transitivity,[status(thm)],[127,125,71,69,66,20]) ).
tff(129,plain,
ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)))) = ld(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)),
inference(unit_resolution,[status(thm)],[130,7]) ).
tff(132,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)) = ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)))),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(a,unit)) = mult(a,unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
mult(unit,mult(a,unit)) = mult(a,unit),
inference(unit_resolution,[status(thm)],[133,46]) ).
tff(135,plain,
mult(unit,mult(a,unit)) = mult(unit,a),
inference(transitivity,[status(thm)],[134,97,49]) ).
tff(136,plain,
mult(a,mult(unit,mult(a,unit))) = mult(a,mult(unit,a)),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(unit,mult(a,unit))) = mult(mult(a,mult(unit,a)),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
mult(a,mult(unit,mult(a,unit))) = mult(mult(a,mult(unit,a)),unit),
inference(unit_resolution,[status(thm)],[137,60]) ).
tff(139,plain,
mult(mult(a,mult(unit,a)),unit) = mult(a,mult(unit,mult(a,unit))),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,unit) = unit ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
mult(unit,unit) = unit,
inference(unit_resolution,[status(thm)],[140,46]) ).
tff(142,plain,
mult(unit,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))) = mult(unit,unit),
inference(monotonicity,[status(thm)],[80]) ).
tff(143,plain,
mult(unit,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))) = unit,
inference(transitivity,[status(thm)],[142,141]) ).
tff(144,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(a,mult(unit,a)),unit),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)),
inference(unit_resolution,[status(thm)],[145,60]) ).
tff(147,plain,
mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)) = mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)),
inference(unit_resolution,[status(thm)],[148,60]) ).
tff(150,plain,
mult(mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)) = mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))) = mult(mult(a,mult(unit,a)),unit),
inference(monotonicity,[status(thm)],[99]) ).
tff(152,plain,
mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))) = mult(a,mult(unit,a)),
inference(transitivity,[status(thm)],[151,139,136]) ).
tff(153,plain,
mult(mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)) = mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)) = mult(mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
unit = mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(transitivity,[status(thm)],[86,154,150]) ).
tff(156,plain,
ld(mult(a,mult(unit,a)),unit) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = ld(mult(a,mult(unit,a)),unit),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(unit_resolution,[status(thm)],[158,7]) ).
tff(160,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))) = ld(mult(a,mult(unit,a)),unit),
inference(transitivity,[status(thm)],[160,157]) ).
tff(162,plain,
mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(a,mult(unit,a)),
inference(transitivity,[status(thm)],[162,147,144,139,136]) ).
tff(164,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[120,163]) ).
tff(165,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = unit,
inference(transitivity,[status(thm)],[164,99]) ).
tff(166,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),a) = mult(unit,a),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),a),
inference(unit_resolution,[status(thm)],[167,60]) ).
tff(169,plain,
mult(unit,mult(a,unit)) = a,
inference(transitivity,[status(thm)],[134,97]) ).
tff(170,plain,
mult(mult(unit,mult(a,unit)),a) = mult(a,mult(unit,a)),
inference(monotonicity,[status(thm)],[169,49]) ).
tff(171,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(a,mult(unit,a))) = mult(mult(unit,mult(a,unit)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(172,plain,
mult(unit,mult(a,mult(unit,a))) = mult(mult(unit,mult(a,unit)),a),
inference(unit_resolution,[status(thm)],[171,60]) ).
tff(173,plain,
mult(unit,mult(a,mult(unit,a))) = mult(a,mult(unit,a)),
inference(transitivity,[status(thm)],[172,170]) ).
tff(174,plain,
mult(a,mult(unit,mult(a,mult(unit,a)))) = mult(a,mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
mult(a,mult(a,mult(unit,a))) = mult(a,mult(unit,mult(a,mult(unit,a)))),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
mult(unit,mult(a,mult(a,mult(unit,a)))) = mult(unit,mult(a,mult(unit,mult(a,mult(unit,a))))),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
mult(unit,mult(a,mult(unit,mult(a,mult(unit,a))))) = mult(unit,mult(a,mult(a,mult(unit,a)))),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(a,mult(unit,mult(a,mult(unit,a))))) = mult(mult(unit,mult(a,unit)),mult(a,mult(unit,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(179,plain,
mult(unit,mult(a,mult(unit,mult(a,mult(unit,a))))) = mult(mult(unit,mult(a,unit)),mult(a,mult(unit,a))),
inference(unit_resolution,[status(thm)],[178,60]) ).
tff(180,plain,
mult(mult(unit,mult(a,unit)),mult(a,mult(unit,a))) = mult(unit,mult(a,mult(unit,mult(a,mult(unit,a))))),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
mult(mult(unit,mult(a,unit)),mult(a,mult(unit,a))) = mult(a,mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[169]) ).
tff(182,plain,
mult(a,mult(a,mult(unit,a))) = mult(mult(unit,mult(a,unit)),mult(a,mult(unit,a))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
mult(unit,mult(a,a)) = mult(unit,mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[50]) ).
tff(184,plain,
mult(unit,mult(a,a)) = mult(a,mult(unit,a)),
inference(transitivity,[status(thm)],[183,172,170]) ).
tff(185,plain,
mult(a,mult(unit,mult(a,a))) = mult(a,mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(unit,mult(a,a))) = mult(mult(a,mult(unit,a)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(187,plain,
mult(a,mult(unit,mult(a,a))) = mult(mult(a,mult(unit,a)),a),
inference(unit_resolution,[status(thm)],[186,60]) ).
tff(188,plain,
mult(mult(a,mult(unit,a)),a) = mult(a,mult(unit,mult(a,a))),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
mult(mult(a,mult(unit,a)),a) = mult(unit,mult(a,mult(a,mult(unit,a)))),
inference(transitivity,[status(thm)],[188,185,182,180,177]) ).
tff(190,plain,
mult(a,mult(mult(a,mult(unit,a)),a)) = mult(a,mult(unit,mult(a,mult(a,mult(unit,a))))),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
mult(a,mult(unit,mult(a,mult(a,mult(unit,a))))) = mult(a,mult(mult(a,mult(unit,a)),a)),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(unit,mult(a,mult(a,mult(unit,a))))) = mult(mult(a,mult(unit,a)),mult(a,mult(unit,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(193,plain,
mult(a,mult(unit,mult(a,mult(a,mult(unit,a))))) = mult(mult(a,mult(unit,a)),mult(a,mult(unit,a))),
inference(unit_resolution,[status(thm)],[192,60]) ).
tff(194,plain,
mult(mult(a,mult(unit,a)),mult(a,mult(unit,a))) = mult(a,mult(unit,mult(a,mult(a,mult(unit,a))))),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
mult(mult(unit,mult(a,unit)),a) = mult(unit,mult(a,mult(unit,a))),
inference(symmetry,[status(thm)],[172]) ).
tff(196,plain,
mult(a,mult(unit,a)) = mult(mult(unit,mult(a,unit)),a),
inference(symmetry,[status(thm)],[170]) ).
tff(197,plain,
mult(a,mult(unit,a)) = mult(unit,mult(a,mult(unit,a))),
inference(transitivity,[status(thm)],[196,195]) ).
tff(198,plain,
mult(mult(a,mult(unit,a)),mult(a,mult(unit,a))) = mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))) = mult(mult(a,mult(unit,a)),mult(a,mult(unit,a))),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))) = mult(a,mult(mult(a,mult(unit,a)),a)),
inference(transitivity,[status(thm)],[199,194,191]) ).
tff(201,plain,
mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)) = mult(mult(a,mult(mult(a,mult(unit,a)),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[200,122]) ).
tff(202,plain,
mult(mult(a,mult(mult(a,mult(unit,a)),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(a,mult(unit,a)),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(mult(a,mult(unit,a)),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
mult(a,mult(mult(a,mult(unit,a)),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(mult(a,mult(unit,a)),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[203,60]) ).
tff(205,plain,
mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = unit,
inference(transitivity,[status(thm)],[82,80]) ).
tff(206,plain,
mult(mult(a,mult(unit,a)),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(mult(a,mult(unit,a)),unit),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
mult(mult(a,mult(unit,a)),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(a,mult(unit,a)),
inference(transitivity,[status(thm)],[206,139,136]) ).
tff(208,plain,
mult(a,mult(mult(a,mult(unit,a)),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(a,mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
mult(a,mult(a,mult(unit,a))) = mult(a,mult(mult(a,mult(unit,a)),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
mult(a,mult(a,mult(unit,a))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),
inference(transitivity,[status(thm)],[209,204,202]) ).
tff(211,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a))),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a)))) = a,
inference(transitivity,[status(thm)],[211,168,166,48]) ).
tff(213,plain,
mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a))))) = mult(op_c,a),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a))))) = mult(a,op_c),
inference(transitivity,[status(thm)],[213,29]) ).
tff(215,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(a,mult(unit,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(217,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(a,mult(unit,a)))),
inference(unit_resolution,[status(thm)],[216,60]) ).
tff(218,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(a,mult(unit,a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a)))))),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
op_c = mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(transitivity,[status(thm)],[69,66,20]) ).
tff(220,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),op_c) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(222,plain,
mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),op_c),
inference(unit_resolution,[status(thm)],[221,27]) ).
tff(223,plain,
mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(transitivity,[status(thm)],[222,220]) ).
tff(224,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)) = rd(mult(mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),a),a),
inference(symmetry,[status(thm)],[20]) ).
tff(227,plain,
mult(mult(unit,mult(a,unit)),mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(monotonicity,[status(thm)],[169]) ).
tff(228,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(a,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(unit,mult(a,unit)),mult(rd(op_c,mult(a,mult(unit,a))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(229,plain,
mult(unit,mult(a,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(unit,mult(a,unit)),mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(unit_resolution,[status(thm)],[228,60]) ).
tff(230,plain,
mult(unit,mult(a,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = op_c,
inference(transitivity,[status(thm)],[229,227,226,65,68]) ).
tff(231,plain,
mult(a,mult(unit,mult(a,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(a,op_c),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(unit,mult(a,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(233,plain,
mult(a,mult(unit,mult(a,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(unit_resolution,[status(thm)],[232,60]) ).
tff(234,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))) = mult(a,mult(unit,mult(a,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))))),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))) = mult(op_c,a),
inference(transitivity,[status(thm)],[234,231,30]) ).
tff(236,plain,
rd(unit,mult(a,mult(unit,a))) = mult(rd(unit,mult(a,mult(unit,a))),unit),
inference(symmetry,[status(thm)],[117]) ).
tff(237,plain,
rd(unit,mult(a,mult(unit,a))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(transitivity,[status(thm)],[236,118]) ).
tff(238,plain,
mult(a,rd(unit,mult(a,mult(unit,a)))) = mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(a,rd(unit,mult(a,mult(unit,a)))),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),
inference(monotonicity,[status(thm)],[120,239]) ).
tff(241,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(op_c,a)),
inference(monotonicity,[status(thm)],[241,235]) ).
tff(243,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(op_c,a)) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a)))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(op_c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(245,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a)))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(op_c,a)),
inference(unit_resolution,[status(thm)],[244,60]) ).
tff(246,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a)) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)),
inference(monotonicity,[status(thm)],[29]) ).
tff(247,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a))) = mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a))) = mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(transitivity,[status(thm)],[247,127,125,71,69,66,20]) ).
tff(249,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a)))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(transitivity,[status(thm)],[250,245,243]) ).
tff(252,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))))),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)) = mult(rd(op_c,mult(a,mult(unit,a))),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(255,plain,
mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)) = mult(rd(op_c,mult(a,mult(unit,a))),unit),
inference(unit_resolution,[status(thm)],[254,46]) ).
tff(256,plain,
mult(unit,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) = mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),
inference(monotonicity,[status(thm)],[255]) ).
tff(257,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) = mult(unit,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),
inference(monotonicity,[status(thm)],[165]) ).
tff(258,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(259,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),
inference(unit_resolution,[status(thm)],[258,60]) ).
tff(260,plain,
mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)),
inference(transitivity,[status(thm)],[149,153]) ).
tff(261,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(monotonicity,[status(thm)],[120,260]) ).
tff(262,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))),
inference(monotonicity,[status(thm)],[261]) ).
tff(263,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(264,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))),
inference(unit_resolution,[status(thm)],[263,60]) ).
tff(265,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))) = mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),
inference(transitivity,[status(thm)],[259,257,256]) ).
tff(266,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)))))) = mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) = mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)))))),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))))),
inference(monotonicity,[status(thm)],[267]) ).
tff(269,plain,
mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = unit,
inference(transitivity,[status(thm)],[149,153,80]) ).
tff(270,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),unit),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),unit) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(rd(op_c,mult(a,mult(unit,a))),unit) = rd(op_c,mult(a,mult(unit,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(273,plain,
mult(rd(op_c,mult(a,mult(unit,a))),unit) = rd(op_c,mult(a,mult(unit,a))),
inference(unit_resolution,[status(thm)],[272,95]) ).
tff(274,plain,
mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)) = rd(op_c,mult(a,mult(unit,a))),
inference(transitivity,[status(thm)],[255,273]) ).
tff(275,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),unit) = mult(rd(op_c,mult(a,mult(unit,a))),unit),
inference(monotonicity,[status(thm)],[274]) ).
tff(276,plain,
mult(rd(op_c,mult(a,mult(unit,a))),unit) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),unit),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(transitivity,[status(thm)],[255,276,271]) ).
tff(278,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) = mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),
inference(symmetry,[status(thm)],[278]) ).
tff(280,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(281,plain,
mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[280,60]) ).
tff(282,plain,
mult(mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(op_c,unit) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(284,plain,
mult(op_c,unit) = op_c,
inference(unit_resolution,[status(thm)],[283,95]) ).
tff(285,plain,
mult(unit,mult(op_c,unit)) = mult(unit,op_c),
inference(monotonicity,[status(thm)],[284]) ).
tff(286,plain,
mult(unit,mult(op_c,unit)) = op_c,
inference(transitivity,[status(thm)],[285,71]) ).
tff(287,plain,
mult(mult(unit,mult(op_c,unit)),a) = mult(op_c,a),
inference(monotonicity,[status(thm)],[286]) ).
tff(288,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(op_c,mult(unit,a))) = mult(mult(unit,mult(op_c,unit)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(289,plain,
mult(unit,mult(op_c,mult(unit,a))) = mult(mult(unit,mult(op_c,unit)),a),
inference(unit_resolution,[status(thm)],[288,60]) ).
tff(290,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(op_c,mult(unit,a))) = mult(op_c,mult(unit,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(291,plain,
mult(unit,mult(op_c,mult(unit,a))) = mult(op_c,mult(unit,a)),
inference(unit_resolution,[status(thm)],[290,46]) ).
tff(292,plain,
mult(mult(unit,mult(op_c,unit)),a) = mult(unit,mult(op_c,mult(unit,a))),
inference(symmetry,[status(thm)],[289]) ).
tff(293,plain,
mult(op_c,a) = mult(mult(unit,mult(op_c,unit)),a),
inference(symmetry,[status(thm)],[287]) ).
tff(294,plain,
mult(a,op_c) = mult(op_c,mult(unit,a)),
inference(transitivity,[status(thm)],[30,293,292,291]) ).
tff(295,plain,
mult(unit,mult(a,op_c)) = mult(unit,mult(op_c,mult(unit,a))),
inference(monotonicity,[status(thm)],[294]) ).
tff(296,plain,
mult(unit,mult(a,op_c)) = mult(op_c,a),
inference(transitivity,[status(thm)],[295,289,287]) ).
tff(297,plain,
mult(a,mult(unit,mult(a,op_c))) = mult(a,mult(op_c,a)),
inference(monotonicity,[status(thm)],[296]) ).
tff(298,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(unit,mult(a,op_c))) = mult(mult(a,mult(unit,a)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(299,plain,
mult(a,mult(unit,mult(a,op_c))) = mult(mult(a,mult(unit,a)),op_c),
inference(unit_resolution,[status(thm)],[298,60]) ).
tff(300,plain,
mult(mult(a,mult(unit,a)),op_c) = mult(a,mult(unit,mult(a,op_c))),
inference(symmetry,[status(thm)],[299]) ).
tff(301,plain,
mult(rd(op_c,mult(a,mult(unit,a))),mult(unit,mult(a,mult(unit,a)))) = mult(rd(op_c,mult(a,mult(unit,a))),mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[173]) ).
tff(302,plain,
mult(rd(op_c,mult(a,mult(unit,a))),mult(unit,mult(a,mult(unit,a)))) = op_c,
inference(transitivity,[status(thm)],[301,39]) ).
tff(303,plain,
mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),mult(unit,mult(a,mult(unit,a))))) = mult(unit,op_c),
inference(monotonicity,[status(thm)],[302]) ).
tff(304,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),mult(unit,mult(a,mult(unit,a))))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(305,plain,
mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),mult(unit,mult(a,mult(unit,a))))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a))),
inference(unit_resolution,[status(thm)],[304,60]) ).
tff(306,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a))) = mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),mult(unit,mult(a,mult(unit,a))))),
inference(symmetry,[status(thm)],[305]) ).
tff(307,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a))) = op_c,
inference(transitivity,[status(thm)],[306,303,71]) ).
tff(308,plain,
mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a)))) = mult(mult(a,mult(unit,a)),op_c),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a)))) = mult(a,mult(op_c,a)),
inference(transitivity,[status(thm)],[308,300,297]) ).
tff(310,plain,
mult(mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[309]) ).
tff(311,plain,
mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(symmetry,[status(thm)],[310]) ).
tff(312,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(op_c,mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(313,plain,
mult(a,mult(op_c,mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[312,60]) ).
tff(314,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))) = mult(a,ld(mult(a,mult(unit,a)),unit)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(315,plain,
mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))) = mult(a,ld(mult(a,mult(unit,a)),unit)),
inference(unit_resolution,[status(thm)],[314,46]) ).
tff(316,plain,
mult(a,ld(mult(a,mult(unit,a)),unit)) = mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(a,ld(mult(a,mult(unit,a)),unit)),
inference(monotonicity,[status(thm)],[161]) ).
tff(318,plain,
mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),
inference(transitivity,[status(thm)],[317,316]) ).
tff(319,plain,
mult(op_c,mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[318]) ).
tff(320,plain,
mult(a,mult(op_c,mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(a,mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),
inference(monotonicity,[status(thm)],[319]) ).
tff(321,plain,
mult(a,mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(a,mult(op_c,mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))),
inference(symmetry,[status(thm)],[320]) ).
tff(322,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))) = op_c,
inference(transitivity,[status(thm)],[127,125,71]) ).
tff(323,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),op_c),
inference(monotonicity,[status(thm)],[322]) ).
tff(324,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),op_c) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)))),
inference(symmetry,[status(thm)],[323]) ).
tff(325,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(326,plain,
mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),op_c),
inference(unit_resolution,[status(thm)],[325,27]) ).
tff(327,plain,
mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)))),
inference(transitivity,[status(thm)],[326,324]) ).
tff(328,plain,
mult(a,mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))))),
inference(monotonicity,[status(thm)],[327]) ).
tff(329,plain,
mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))))) = mult(a,mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),
inference(symmetry,[status(thm)],[328]) ).
tff(330,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))))) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(331,plain,
mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))))) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))),
inference(unit_resolution,[status(thm)],[330,60]) ).
tff(332,plain,
mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))) = mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))))),
inference(symmetry,[status(thm)],[331]) ).
tff(333,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)) = mult(rd(op_c,mult(a,mult(unit,a))),a),
inference(transitivity,[status(thm)],[132,129,11]) ).
tff(334,plain,
mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(monotonicity,[status(thm)],[333]) ).
tff(335,plain,
mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c))),
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
mult(a,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(a,unit),
inference(monotonicity,[status(thm)],[205]) ).
tff(337,plain,
mult(a,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(unit,a),
inference(transitivity,[status(thm)],[336,97,49]) ).
tff(338,plain,
mult(a,mult(a,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(a,mult(unit,a)),
inference(monotonicity,[status(thm)],[337]) ).
tff(339,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(a,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(a,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(340,plain,
mult(a,mult(a,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(a,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[339,60]) ).
tff(341,plain,
mult(mult(a,mult(a,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(a,mult(a,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))),
inference(symmetry,[status(thm)],[340]) ).
tff(342,plain,
mult(a,mult(a,a)) = mult(a,mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[50]) ).
tff(343,plain,
mult(a,mult(a,mult(unit,a))) = mult(a,mult(a,a)),
inference(symmetry,[status(thm)],[342]) ).
tff(344,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)) = mult(mult(a,mult(a,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[343,122]) ).
tff(345,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)) = mult(a,mult(unit,a)),
inference(transitivity,[status(thm)],[344,341,338]) ).
tff(346,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a))) = mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[120,345]) ).
tff(347,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(348,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),a),
inference(unit_resolution,[status(thm)],[347,60]) ).
tff(349,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),a) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a))),
inference(symmetry,[status(thm)],[348]) ).
tff(350,plain,
mult(a,mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[318]) ).
tff(351,plain,
mult(a,mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = unit,
inference(transitivity,[status(thm)],[350,82,80]) ).
tff(352,plain,
mult(a,mult(a,mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(a,unit),
inference(monotonicity,[status(thm)],[351]) ).
tff(353,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(a,mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(a,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(354,plain,
mult(a,mult(a,mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(a,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[353,60]) ).
tff(355,plain,
mult(mult(a,mult(a,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(a,mult(a,mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))),
inference(symmetry,[status(thm)],[354]) ).
tff(356,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(a,mult(a,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[343]) ).
tff(357,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = a,
inference(transitivity,[status(thm)],[356,355,352,97]) ).
tff(358,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(rd(unit,mult(a,mult(unit,a))),a),
inference(monotonicity,[status(thm)],[120,357]) ).
tff(359,plain,
mult(rd(unit,mult(a,mult(unit,a))),a) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
ld(a,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = ld(a,mult(a,mult(rd(unit,mult(a,mult(unit,a))),a))),
inference(symmetry,[status(thm)],[112]) ).
tff(361,plain,
mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))) = ld(a,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),
inference(symmetry,[status(thm)],[84]) ).
tff(362,plain,
mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(transitivity,[status(thm)],[361,360,114,359]) ).
tff(363,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),a),
inference(monotonicity,[status(thm)],[362]) ).
tff(364,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a) = unit,
inference(transitivity,[status(thm)],[363,349,346,99]) ).
tff(365,plain,
mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)) = mult(a,unit),
inference(monotonicity,[status(thm)],[364]) ).
tff(366,plain,
mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)) = a,
inference(transitivity,[status(thm)],[365,97]) ).
tff(367,plain,
mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(monotonicity,[status(thm)],[366]) ).
tff(368,plain,
mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),
inference(transitivity,[status(thm)],[368,335,332,329,321,313,311,282,279]) ).
tff(370,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)))),
inference(monotonicity,[status(thm)],[369]) ).
tff(371,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(op_c,a)) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a)))),
inference(symmetry,[status(thm)],[245]) ).
tff(372,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),
inference(transitivity,[status(thm)],[242,371,249,370,268,264,262,259,257,256]) ).
tff(373,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))))),
inference(symmetry,[status(thm)],[373]) ).
tff(375,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(transitivity,[status(thm)],[374,253,225]) ).
tff(376,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a)))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(a,mult(unit,a)))),
inference(monotonicity,[status(thm)],[375]) ).
tff(377,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a)))) = mult(rd(op_c,mult(a,mult(unit,a))),a),
inference(transitivity,[status(thm)],[376,218,215,132,129,11]) ).
tff(378,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))) = mult(mult(a,mult(a,a)),mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(monotonicity,[status(thm)],[343,377]) ).
tff(379,plain,
mult(mult(a,mult(a,a)),mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(a,mult(a,a)),mult(rd(op_c,mult(a,mult(unit,a))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(381,plain,
mult(a,mult(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(a,mult(a,a)),mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(unit_resolution,[status(thm)],[380,60]) ).
tff(382,plain,
mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)) = op_c,
inference(transitivity,[status(thm)],[226,65,68]) ).
tff(383,plain,
mult(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) = mult(a,op_c),
inference(monotonicity,[status(thm)],[382]) ).
tff(384,plain,
mult(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) = mult(op_c,a),
inference(transitivity,[status(thm)],[383,30]) ).
tff(385,plain,
mult(a,mult(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(a,mult(op_c,a)),
inference(monotonicity,[status(thm)],[384]) ).
tff(386,plain,
mult(a,mult(op_c,a)) = mult(a,mult(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(symmetry,[status(thm)],[385]) ).
tff(387,plain,
mult(a,mult(op_c,a)) = mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))),
inference(transitivity,[status(thm)],[386,381,379]) ).
tff(388,plain,
mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d))) = mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))),mult(a,mult(mult(op_c,op_c),op_d))),
inference(monotonicity,[status(thm)],[387]) ).
tff(389,plain,
mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))),mult(a,mult(mult(op_c,op_c),op_d))) = mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d))),
inference(symmetry,[status(thm)],[388]) ).
tff(390,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(a,mult(mult(op_c,op_c),op_d))))) = mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))),mult(a,mult(mult(op_c,op_c),op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(391,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(a,mult(mult(op_c,op_c),op_d))))) = mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))),mult(a,mult(mult(op_c,op_c),op_d))),
inference(unit_resolution,[status(thm)],[390,60]) ).
tff(392,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d)))))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(393,plain,
ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d)))))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d)))),
inference(unit_resolution,[status(thm)],[392,7]) ).
tff(394,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))))) = mult(mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(op_c,a)))),mult(unit,mult(op_c,op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(395,plain,
mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))))) = mult(mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(op_c,a)))),mult(unit,mult(op_c,op_d))),
inference(unit_resolution,[status(thm)],[394,60]) ).
tff(396,plain,
mult(mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(op_c,a)))),mult(unit,mult(op_c,op_d))) = mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))))),
inference(symmetry,[status(thm)],[395]) ).
tff(397,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(mult(a,mult(op_c,a)),op_c)) = mult(mult(mult(a,mult(op_c,a)),op_c),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(398,plain,
mult(op_c,mult(mult(a,mult(op_c,a)),op_c)) = mult(mult(mult(a,mult(op_c,a)),op_c),op_c),
inference(unit_resolution,[status(thm)],[397,27]) ).
tff(399,plain,
mult(mult(mult(a,mult(op_c,a)),op_c),op_c) = mult(op_c,mult(mult(a,mult(op_c,a)),op_c)),
inference(symmetry,[status(thm)],[398]) ).
tff(400,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),op_c)) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(401,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),op_c)) = op_c,
inference(unit_resolution,[status(thm)],[400,7]) ).
tff(402,plain,
mult(mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))),op_c) = mult(mult(a,mult(unit,a)),op_c),
inference(monotonicity,[status(thm)],[152]) ).
tff(403,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c))) = mult(mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(404,plain,
mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c))) = mult(mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))),op_c),
inference(unit_resolution,[status(thm)],[403,60]) ).
tff(405,plain,
mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c))) = mult(mult(a,mult(unit,a)),op_c),
inference(transitivity,[status(thm)],[404,402]) ).
tff(406,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)))) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),op_c)),
inference(monotonicity,[status(thm)],[405]) ).
tff(407,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(408,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)),
inference(unit_resolution,[status(thm)],[407,7]) ).
tff(409,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)))),
inference(symmetry,[status(thm)],[408]) ).
tff(410,plain,
mult(a,mult(op_c,a)) = mult(a,mult(unit,mult(a,op_c))),
inference(symmetry,[status(thm)],[297]) ).
tff(411,plain,
mult(a,mult(op_c,a)) = mult(mult(a,mult(unit,a)),op_c),
inference(transitivity,[status(thm)],[410,299]) ).
tff(412,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)),
inference(monotonicity,[status(thm)],[120,411]) ).
tff(413,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a))) = op_c,
inference(transitivity,[status(thm)],[412,409,406,401]) ).
tff(414,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a)))) = mult(mult(a,mult(op_c,a)),op_c),
inference(monotonicity,[status(thm)],[413]) ).
tff(415,plain,
mult(mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a)))),op_c) = mult(mult(mult(a,mult(op_c,a)),op_c),op_c),
inference(monotonicity,[status(thm)],[414]) ).
tff(416,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c))) = mult(mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a)))),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(417,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c))) = mult(mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a)))),op_c),
inference(unit_resolution,[status(thm)],[416,60]) ).
tff(418,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(419,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c)),
inference(unit_resolution,[status(thm)],[418,7]) ).
tff(420,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a))) = mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[120]) ).
tff(421,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a))) = unit,
inference(transitivity,[status(thm)],[420,99]) ).
tff(422,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a)))) = mult(mult(a,mult(unit,a)),unit),
inference(monotonicity,[status(thm)],[421]) ).
tff(423,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a)))) = mult(a,mult(unit,a)),
inference(transitivity,[status(thm)],[422,139,136]) ).
tff(424,plain,
mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a)))),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c))) = mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c))),
inference(monotonicity,[status(thm)],[423]) ).
tff(425,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c))))) = mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a)))),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(426,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c))))) = mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a)))),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c))),
inference(unit_resolution,[status(thm)],[425,60]) ).
tff(427,plain,
mult(mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a)))),op_c) = mult(mult(a,mult(op_c,a)),op_c),
inference(monotonicity,[status(thm)],[309]) ).
tff(428,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c))) = mult(mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a)))),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(429,plain,
mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c))) = mult(mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(unit,a)))),op_c),
inference(unit_resolution,[status(thm)],[428,60]) ).
tff(430,plain,
mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c))) = mult(mult(a,mult(op_c,a)),op_c),
inference(transitivity,[status(thm)],[429,427]) ).
tff(431,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c)),
inference(monotonicity,[status(thm)],[430]) ).
tff(432,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c)) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c)))),
inference(symmetry,[status(thm)],[431]) ).
tff(433,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c))) = mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c))))),
inference(monotonicity,[status(thm)],[432]) ).
tff(434,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c))) = mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c))),
inference(transitivity,[status(thm)],[433,426,424]) ).
tff(435,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c)))) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c)))),
inference(monotonicity,[status(thm)],[434]) ).
tff(436,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c)))) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c)))),
inference(symmetry,[status(thm)],[435]) ).
tff(437,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c)))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(438,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c)))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c)),
inference(unit_resolution,[status(thm)],[437,7]) ).
tff(439,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c)) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c)))),
inference(symmetry,[status(thm)],[438]) ).
tff(440,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(op_c,a))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),op_c)),
inference(monotonicity,[status(thm)],[411]) ).
tff(441,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(op_c,a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c)),
inference(transitivity,[status(thm)],[440,439,436,419]) ).
tff(442,plain,
mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(op_c,a)))) = mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),op_c))),
inference(monotonicity,[status(thm)],[441]) ).
tff(443,plain,
mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(op_c,a)))) = mult(op_c,mult(mult(a,mult(op_c,a)),op_c)),
inference(transitivity,[status(thm)],[442,417,415,399]) ).
tff(444,plain,
mult(mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(op_c,a)))),mult(unit,mult(op_c,op_d))) = mult(mult(op_c,mult(mult(a,mult(op_c,a)),op_c)),mult(unit,mult(op_c,op_d))),
inference(monotonicity,[status(thm)],[443]) ).
tff(445,plain,
mult(mult(op_c,mult(mult(a,mult(op_c,a)),op_c)),mult(unit,mult(op_c,op_d))) = mult(mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(op_c,a)))),mult(unit,mult(op_c,op_d))),
inference(symmetry,[status(thm)],[444]) ).
tff(446,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(mult(a,mult(op_c,a)),mult(op_c,mult(unit,mult(op_c,op_d))))) = mult(mult(op_c,mult(mult(a,mult(op_c,a)),op_c)),mult(unit,mult(op_c,op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(447,plain,
mult(op_c,mult(mult(a,mult(op_c,a)),mult(op_c,mult(unit,mult(op_c,op_d))))) = mult(mult(op_c,mult(mult(a,mult(op_c,a)),op_c)),mult(unit,mult(op_c,op_d))),
inference(unit_resolution,[status(thm)],[446,60]) ).
tff(448,plain,
mult(op_c,mult(unit,op_c)) = mult(op_c,op_c),
inference(monotonicity,[status(thm)],[71]) ).
tff(449,plain,
mult(mult(op_c,mult(unit,op_c)),op_d) = mult(mult(op_c,op_c),op_d),
inference(monotonicity,[status(thm)],[448]) ).
tff(450,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(unit,mult(op_c,op_d))) = mult(mult(op_c,mult(unit,op_c)),op_d) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(451,plain,
mult(op_c,mult(unit,mult(op_c,op_d))) = mult(mult(op_c,mult(unit,op_c)),op_d),
inference(unit_resolution,[status(thm)],[450,60]) ).
tff(452,plain,
mult(op_c,mult(unit,mult(op_c,op_d))) = mult(mult(op_c,op_c),op_d),
inference(transitivity,[status(thm)],[451,449]) ).
tff(453,plain,
mult(mult(a,mult(op_c,a)),mult(op_c,mult(unit,mult(op_c,op_d)))) = mult(mult(a,mult(op_c,a)),mult(mult(op_c,op_c),op_d)),
inference(monotonicity,[status(thm)],[452]) ).
tff(454,plain,
mult(op_c,mult(mult(a,mult(op_c,a)),mult(op_c,mult(unit,mult(op_c,op_d))))) = mult(op_c,mult(mult(a,mult(op_c,a)),mult(mult(op_c,op_c),op_d))),
inference(monotonicity,[status(thm)],[453]) ).
tff(455,plain,
mult(op_c,mult(mult(a,mult(op_c,a)),mult(mult(op_c,op_c),op_d))) = mult(op_c,mult(mult(a,mult(op_c,a)),mult(op_c,mult(unit,mult(op_c,op_d))))),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(op_c,mult(a,mult(mult(op_c,op_c),op_d)))) = mult(mult(a,mult(op_c,a)),mult(mult(op_c,op_c),op_d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(457,plain,
mult(a,mult(op_c,mult(a,mult(mult(op_c,op_c),op_d)))) = mult(mult(a,mult(op_c,a)),mult(mult(op_c,op_c),op_d)),
inference(unit_resolution,[status(thm)],[456,60]) ).
tff(458,plain,
mult(op_c,mult(a,mult(op_c,mult(a,mult(mult(op_c,op_c),op_d))))) = mult(op_c,mult(mult(a,mult(op_c,a)),mult(mult(op_c,op_c),op_d))),
inference(monotonicity,[status(thm)],[457]) ).
tff(459,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(a,mult(op_c,mult(a,mult(mult(op_c,op_c),op_d))))) = mult(mult(op_c,mult(a,op_c)),mult(a,mult(mult(op_c,op_c),op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(460,plain,
mult(op_c,mult(a,mult(op_c,mult(a,mult(mult(op_c,op_c),op_d))))) = mult(mult(op_c,mult(a,op_c)),mult(a,mult(mult(op_c,op_c),op_d))),
inference(unit_resolution,[status(thm)],[459,60]) ).
tff(461,plain,
mult(mult(op_c,mult(a,op_c)),mult(a,mult(mult(op_c,op_c),op_d))) = mult(op_c,mult(a,mult(op_c,mult(a,mult(mult(op_c,op_c),op_d))))),
inference(symmetry,[status(thm)],[460]) ).
tff(462,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(op_c,mult(a,op_c)))) = mult(op_c,mult(a,op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(463,plain,
ld(a,mult(a,mult(op_c,mult(a,op_c)))) = mult(op_c,mult(a,op_c)),
inference(unit_resolution,[status(thm)],[462,7]) ).
tff(464,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(op_c,mult(a,op_c))) = mult(mult(a,mult(op_c,a)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(465,plain,
mult(a,mult(op_c,mult(a,op_c))) = mult(mult(a,mult(op_c,a)),op_c),
inference(unit_resolution,[status(thm)],[464,60]) ).
tff(466,plain,
mult(mult(a,mult(op_c,a)),op_c) = mult(a,mult(op_c,mult(a,op_c))),
inference(symmetry,[status(thm)],[465]) ).
tff(467,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,mult(mult(a,mult(op_c,a)),op_c))) = mult(mult(a,mult(op_c,a)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(468,plain,
ld(op_c,mult(op_c,mult(mult(a,mult(op_c,a)),op_c))) = mult(mult(a,mult(op_c,a)),op_c),
inference(unit_resolution,[status(thm)],[467,7]) ).
tff(469,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(a,mult(op_c,a))) = mult(mult(a,mult(op_c,a)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(470,plain,
mult(op_c,mult(a,mult(op_c,a))) = mult(mult(a,mult(op_c,a)),op_c),
inference(unit_resolution,[status(thm)],[469,27]) ).
tff(471,plain,
mult(mult(a,mult(unit,a)),op_c) = mult(a,mult(op_c,a)),
inference(transitivity,[status(thm)],[300,297]) ).
tff(472,plain,
mult(op_c,mult(mult(a,mult(unit,a)),op_c)) = mult(op_c,mult(a,mult(op_c,a))),
inference(monotonicity,[status(thm)],[471]) ).
tff(473,plain,
mult(op_c,mult(mult(a,mult(unit,a)),op_c)) = mult(mult(a,mult(op_c,a)),op_c),
inference(transitivity,[status(thm)],[472,470]) ).
tff(474,plain,
mult(mult(op_c,mult(mult(a,mult(unit,a)),op_c)),op_c) = mult(mult(mult(a,mult(op_c,a)),op_c),op_c),
inference(monotonicity,[status(thm)],[473]) ).
tff(475,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,op_c))) = mult(mult(op_c,mult(mult(a,mult(unit,a)),op_c)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(476,plain,
mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,op_c))) = mult(mult(op_c,mult(mult(a,mult(unit,a)),op_c)),op_c),
inference(unit_resolution,[status(thm)],[475,60]) ).
tff(477,plain,
mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,op_c))) = mult(op_c,mult(mult(a,mult(op_c,a)),op_c)),
inference(transitivity,[status(thm)],[476,474,399]) ).
tff(478,plain,
ld(op_c,mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,op_c)))) = ld(op_c,mult(op_c,mult(mult(a,mult(op_c,a)),op_c))),
inference(monotonicity,[status(thm)],[477]) ).
tff(479,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,op_c)))) = mult(mult(a,mult(unit,a)),mult(op_c,op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(480,plain,
ld(op_c,mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,op_c)))) = mult(mult(a,mult(unit,a)),mult(op_c,op_c)),
inference(unit_resolution,[status(thm)],[479,7]) ).
tff(481,plain,
mult(mult(a,mult(unit,a)),mult(op_c,op_c)) = ld(op_c,mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,op_c)))),
inference(symmetry,[status(thm)],[480]) ).
tff(482,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(unit,mult(a,mult(op_c,op_c)))) = mult(mult(a,mult(unit,a)),mult(op_c,op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(483,plain,
mult(a,mult(unit,mult(a,mult(op_c,op_c)))) = mult(mult(a,mult(unit,a)),mult(op_c,op_c)),
inference(unit_resolution,[status(thm)],[482,60]) ).
tff(484,plain,
mult(mult(unit,mult(op_c,unit)),op_c) = mult(op_c,op_c),
inference(monotonicity,[status(thm)],[286]) ).
tff(485,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(op_c,mult(unit,op_c))) = mult(mult(unit,mult(op_c,unit)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(486,plain,
mult(unit,mult(op_c,mult(unit,op_c))) = mult(mult(unit,mult(op_c,unit)),op_c),
inference(unit_resolution,[status(thm)],[485,60]) ).
tff(487,plain,
mult(op_c,op_c) = mult(op_c,mult(unit,op_c)),
inference(symmetry,[status(thm)],[448]) ).
tff(488,plain,
mult(unit,mult(op_c,op_c)) = mult(unit,mult(op_c,mult(unit,op_c))),
inference(monotonicity,[status(thm)],[487]) ).
tff(489,plain,
mult(unit,mult(op_c,op_c)) = mult(op_c,op_c),
inference(transitivity,[status(thm)],[488,486,484]) ).
tff(490,plain,
mult(a,mult(unit,mult(op_c,op_c))) = mult(a,mult(op_c,op_c)),
inference(monotonicity,[status(thm)],[489]) ).
tff(491,plain,
mult(a,mult(op_c,op_c)) = mult(a,mult(unit,mult(op_c,op_c))),
inference(symmetry,[status(thm)],[490]) ).
tff(492,plain,
mult(unit,mult(a,mult(op_c,op_c))) = mult(unit,mult(a,mult(unit,mult(op_c,op_c)))),
inference(monotonicity,[status(thm)],[491]) ).
tff(493,plain,
mult(unit,mult(a,mult(unit,mult(op_c,op_c)))) = mult(unit,mult(a,mult(op_c,op_c))),
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(a,mult(unit,mult(op_c,op_c)))) = mult(mult(unit,mult(a,unit)),mult(op_c,op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(495,plain,
mult(unit,mult(a,mult(unit,mult(op_c,op_c)))) = mult(mult(unit,mult(a,unit)),mult(op_c,op_c)),
inference(unit_resolution,[status(thm)],[494,60]) ).
tff(496,plain,
mult(mult(unit,mult(a,unit)),mult(op_c,op_c)) = mult(unit,mult(a,mult(unit,mult(op_c,op_c)))),
inference(symmetry,[status(thm)],[495]) ).
tff(497,plain,
mult(mult(unit,mult(a,unit)),mult(op_c,op_c)) = mult(a,mult(op_c,op_c)),
inference(monotonicity,[status(thm)],[169]) ).
tff(498,plain,
mult(a,mult(op_c,op_c)) = mult(mult(unit,mult(a,unit)),mult(op_c,op_c)),
inference(symmetry,[status(thm)],[497]) ).
tff(499,plain,
mult(a,mult(op_c,op_c)) = mult(unit,mult(a,mult(op_c,op_c))),
inference(transitivity,[status(thm)],[498,496,493]) ).
tff(500,plain,
mult(a,mult(a,mult(op_c,op_c))) = mult(a,mult(unit,mult(a,mult(op_c,op_c)))),
inference(monotonicity,[status(thm)],[499]) ).
tff(501,plain,
mult(a,mult(a,mult(op_c,op_c))) = mult(a,mult(op_c,mult(a,op_c))),
inference(transitivity,[status(thm)],[500,483,481,478,468,466]) ).
tff(502,plain,
ld(a,mult(a,mult(a,mult(op_c,op_c)))) = ld(a,mult(a,mult(op_c,mult(a,op_c)))),
inference(monotonicity,[status(thm)],[501]) ).
tff(503,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(a,mult(op_c,op_c)))) = mult(a,mult(op_c,op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(504,plain,
ld(a,mult(a,mult(a,mult(op_c,op_c)))) = mult(a,mult(op_c,op_c)),
inference(unit_resolution,[status(thm)],[503,7]) ).
tff(505,plain,
mult(a,mult(op_c,op_c)) = ld(a,mult(a,mult(a,mult(op_c,op_c)))),
inference(symmetry,[status(thm)],[504]) ).
tff(506,plain,
mult(op_c,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) = mult(op_c,op_c),
inference(monotonicity,[status(thm)],[382]) ).
tff(507,plain,
mult(a,mult(op_c,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(a,mult(op_c,op_c)),
inference(monotonicity,[status(thm)],[506]) ).
tff(508,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(op_c,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(a,mult(op_c,a)),mult(rd(op_c,mult(a,mult(unit,a))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(509,plain,
mult(a,mult(op_c,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(a,mult(op_c,a)),mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(unit_resolution,[status(thm)],[508,60]) ).
tff(510,plain,
mult(mult(a,mult(op_c,a)),mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(a,mult(op_c,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(symmetry,[status(thm)],[509]) ).
tff(511,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)) = op_c,
inference(transitivity,[status(thm)],[409,406,401]) ).
tff(512,plain,
mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c))) = mult(a,op_c),
inference(monotonicity,[status(thm)],[511]) ).
tff(513,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a)))) = mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c))),
inference(monotonicity,[status(thm)],[412]) ).
tff(514,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a)))) = mult(a,op_c),
inference(transitivity,[status(thm)],[513,512]) ).
tff(515,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)),
inference(monotonicity,[status(thm)],[514]) ).
tff(516,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(op_c,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(517,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(op_c,a))),
inference(unit_resolution,[status(thm)],[516,60]) ).
tff(518,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(op_c,a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(op_c,a))))),
inference(symmetry,[status(thm)],[517]) ).
tff(519,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),op_c)) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(op_c,a))),
inference(monotonicity,[status(thm)],[241,471]) ).
tff(520,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(op_c,a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),op_c)),
inference(monotonicity,[status(thm)],[411]) ).
tff(521,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(op_c,a))) = mult(rd(op_c,mult(a,mult(unit,a))),a),
inference(transitivity,[status(thm)],[520,519,518,515,132,129,11]) ).
tff(522,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(op_c,a)))) = mult(mult(a,mult(op_c,a)),mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(monotonicity,[status(thm)],[521]) ).
tff(523,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(op_c,a)))) = mult(op_c,mult(a,op_c)),
inference(transitivity,[status(thm)],[522,510,507,505,502,463]) ).
tff(524,plain,
mult(mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(op_c,a)))),mult(a,mult(mult(op_c,op_c),op_d))) = mult(mult(op_c,mult(a,op_c)),mult(a,mult(mult(op_c,op_c),op_d))),
inference(monotonicity,[status(thm)],[523]) ).
tff(525,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d))))) = mult(mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(op_c,a)))),mult(a,mult(mult(op_c,op_c),op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(526,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d))))) = mult(mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(op_c,a)))),mult(a,mult(mult(op_c,op_c),op_d))),
inference(unit_resolution,[status(thm)],[525,60]) ).
tff(527,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d))))) = mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))))),
inference(transitivity,[status(thm)],[526,524,461,458,455,447,445,396]) ).
tff(528,plain,
ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d)))))) = ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d)))))),
inference(monotonicity,[status(thm)],[527]) ).
tff(529,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(530,plain,
ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d)))),
inference(unit_resolution,[status(thm)],[529,7]) ).
tff(531,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d)))) = ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d)))))),
inference(symmetry,[status(thm)],[530]) ).
tff(532,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(a,mult(mult(op_c,op_c),op_d)))) = mult(a,mult(mult(op_c,op_c),op_d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(533,plain,
ld(a,mult(a,mult(a,mult(mult(op_c,op_c),op_d)))) = mult(a,mult(mult(op_c,op_c),op_d)),
inference(unit_resolution,[status(thm)],[532,7]) ).
tff(534,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(a,mult(mult(op_c,op_c),op_d))) = mult(a,mult(mult(op_c,op_c),op_d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(535,plain,
mult(unit,mult(a,mult(mult(op_c,op_c),op_d))) = mult(a,mult(mult(op_c,op_c),op_d)),
inference(unit_resolution,[status(thm)],[534,46]) ).
tff(536,plain,
mult(a,mult(mult(op_c,op_c),op_d)) = mult(unit,mult(a,mult(mult(op_c,op_c),op_d))),
inference(symmetry,[status(thm)],[535]) ).
tff(537,plain,
mult(a,mult(a,mult(mult(op_c,op_c),op_d))) = mult(a,mult(unit,mult(a,mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[536]) ).
tff(538,plain,
mult(a,mult(unit,mult(a,mult(mult(op_c,op_c),op_d)))) = mult(a,mult(a,mult(mult(op_c,op_c),op_d))),
inference(symmetry,[status(thm)],[537]) ).
tff(539,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(unit,mult(a,mult(mult(op_c,op_c),op_d)))) = mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(540,plain,
mult(a,mult(unit,mult(a,mult(mult(op_c,op_c),op_d)))) = mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)),
inference(unit_resolution,[status(thm)],[539,60]) ).
tff(541,plain,
mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)) = mult(a,mult(unit,mult(a,mult(mult(op_c,op_c),op_d)))),
inference(symmetry,[status(thm)],[540]) ).
tff(542,plain,
mult(mult(a,mult(unit,a)),unit) = mult(a,mult(unit,a)),
inference(transitivity,[status(thm)],[139,136]) ).
tff(543,plain,
mult(unit,mult(mult(a,mult(unit,a)),unit)) = mult(unit,mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[542]) ).
tff(544,plain,
mult(unit,mult(mult(a,mult(unit,a)),unit)) = mult(a,mult(unit,a)),
inference(transitivity,[status(thm)],[543,172,170]) ).
tff(545,plain,
mult(mult(unit,mult(mult(a,mult(unit,a)),unit)),mult(mult(op_c,op_c),op_d)) = mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)),
inference(monotonicity,[status(thm)],[544]) ).
tff(546,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(mult(a,mult(unit,a)),mult(unit,mult(mult(op_c,op_c),op_d)))) = mult(mult(unit,mult(mult(a,mult(unit,a)),unit)),mult(mult(op_c,op_c),op_d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(547,plain,
mult(unit,mult(mult(a,mult(unit,a)),mult(unit,mult(mult(op_c,op_c),op_d)))) = mult(mult(unit,mult(mult(a,mult(unit,a)),unit)),mult(mult(op_c,op_c),op_d)),
inference(unit_resolution,[status(thm)],[546,60]) ).
tff(548,plain,
mult(mult(unit,mult(op_c,unit)),mult(unit,mult(op_c,op_d))) = mult(op_c,mult(unit,mult(op_c,op_d))),
inference(monotonicity,[status(thm)],[286]) ).
tff(549,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(op_c,mult(unit,mult(unit,mult(op_c,op_d))))) = mult(mult(unit,mult(op_c,unit)),mult(unit,mult(op_c,op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(550,plain,
mult(unit,mult(op_c,mult(unit,mult(unit,mult(op_c,op_d))))) = mult(mult(unit,mult(op_c,unit)),mult(unit,mult(op_c,op_d))),
inference(unit_resolution,[status(thm)],[549,60]) ).
tff(551,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(op_c,op_d)) = mult(op_c,op_d) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(552,plain,
mult(unit,mult(op_c,op_d)) = mult(op_c,op_d),
inference(unit_resolution,[status(thm)],[551,46]) ).
tff(553,plain,
mult(unit,mult(unit,mult(op_c,op_d))) = mult(unit,mult(op_c,op_d)),
inference(monotonicity,[status(thm)],[552]) ).
tff(554,plain,
mult(op_c,mult(unit,mult(unit,mult(op_c,op_d)))) = mult(op_c,mult(unit,mult(op_c,op_d))),
inference(monotonicity,[status(thm)],[553]) ).
tff(555,plain,
mult(op_c,mult(unit,mult(op_c,op_d))) = mult(op_c,mult(unit,mult(unit,mult(op_c,op_d)))),
inference(symmetry,[status(thm)],[554]) ).
tff(556,plain,
mult(mult(op_c,mult(unit,op_c)),op_d) = mult(op_c,mult(unit,mult(op_c,op_d))),
inference(symmetry,[status(thm)],[451]) ).
tff(557,plain,
mult(mult(op_c,op_c),op_d) = mult(mult(op_c,mult(unit,op_c)),op_d),
inference(symmetry,[status(thm)],[449]) ).
tff(558,plain,
mult(mult(op_c,op_c),op_d) = mult(op_c,mult(unit,mult(unit,mult(op_c,op_d)))),
inference(transitivity,[status(thm)],[557,556,555]) ).
tff(559,plain,
mult(unit,mult(mult(op_c,op_c),op_d)) = mult(unit,mult(op_c,mult(unit,mult(unit,mult(op_c,op_d))))),
inference(monotonicity,[status(thm)],[558]) ).
tff(560,plain,
mult(unit,mult(mult(op_c,op_c),op_d)) = mult(mult(op_c,op_c),op_d),
inference(transitivity,[status(thm)],[559,550,548,451,449]) ).
tff(561,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(mult(op_c,op_c),op_d))) = mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)),
inference(monotonicity,[status(thm)],[560]) ).
tff(562,plain,
mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)) = mult(mult(a,mult(unit,a)),mult(unit,mult(mult(op_c,op_c),op_d))),
inference(symmetry,[status(thm)],[561]) ).
tff(563,plain,
mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = mult(unit,mult(mult(a,mult(unit,a)),mult(unit,mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[124,562]) ).
tff(564,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(565,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(unit_resolution,[status(thm)],[564,60]) ).
tff(566,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) = mult(a,mult(a,mult(mult(op_c,op_c),op_d))),
inference(transitivity,[status(thm)],[565,563,547,545,541,538]) ).
tff(567,plain,
ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))))) = ld(a,mult(a,mult(a,mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[566]) ).
tff(568,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(569,plain,
ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))),
inference(unit_resolution,[status(thm)],[568,7]) ).
tff(570,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))))),
inference(symmetry,[status(thm)],[569]) ).
tff(571,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = mult(unit,mult(mult(a,mult(unit,a)),mult(unit,mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[165,562]) ).
tff(572,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(573,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(unit_resolution,[status(thm)],[572,60]) ).
tff(574,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) = mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)),
inference(transitivity,[status(thm)],[573,571,547,545]) ).
tff(575,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))))) = mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(monotonicity,[status(thm)],[574]) ).
tff(576,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[575]) ).
tff(577,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(578,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))),
inference(unit_resolution,[status(thm)],[577,60]) ).
tff(579,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))))),
inference(symmetry,[status(thm)],[578]) ).
tff(580,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = mult(mult(op_c,op_c),op_d) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(581,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = mult(mult(op_c,op_c),op_d),
inference(unit_resolution,[status(thm)],[580,7]) ).
tff(582,plain,
mult(mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))),mult(mult(op_c,op_c),op_d)) = mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)),
inference(monotonicity,[status(thm)],[152]) ).
tff(583,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = mult(mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))),mult(mult(op_c,op_c),op_d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(584,plain,
mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = mult(mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))),mult(mult(op_c,op_c),op_d)),
inference(unit_resolution,[status(thm)],[583,60]) ).
tff(585,plain,
mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)),
inference(transitivity,[status(thm)],[584,582]) ).
tff(586,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(monotonicity,[status(thm)],[585]) ).
tff(587,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(588,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(unit_resolution,[status(thm)],[587,7]) ).
tff(589,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))),
inference(symmetry,[status(thm)],[588]) ).
tff(590,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(monotonicity,[status(thm)],[120]) ).
tff(591,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = mult(mult(op_c,op_c),op_d),
inference(transitivity,[status(thm)],[590,589,586,581]) ).
tff(592,plain,
mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(op_c,op_c),op_d)),
inference(monotonicity,[status(thm)],[591]) ).
tff(593,plain,
mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(op_c,op_c),op_d)) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))),
inference(symmetry,[status(thm)],[592]) ).
tff(594,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(op_c,op_c),op_d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(595,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(op_c,op_c),op_d)),
inference(unit_resolution,[status(thm)],[594,60]) ).
tff(596,plain,
mult(unit,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = mult(unit,mult(mult(a,mult(unit,a)),mult(unit,mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[562]) ).
tff(597,plain,
mult(unit,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)),
inference(transitivity,[status(thm)],[596,547,545]) ).
tff(598,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(monotonicity,[status(thm)],[597]) ).
tff(599,plain,
mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))),
inference(symmetry,[status(thm)],[598]) ).
tff(600,plain,
mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))),
inference(transitivity,[status(thm)],[599,595,593]) ).
tff(601,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))),
inference(monotonicity,[status(thm)],[241,600]) ).
tff(602,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = mult(a,mult(mult(op_c,op_c),op_d)),
inference(transitivity,[status(thm)],[601,579,576,570,567,533]) ).
tff(603,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))) = mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d))),
inference(monotonicity,[status(thm)],[602]) ).
tff(604,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[603]) ).
tff(605,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(606,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))),
inference(unit_resolution,[status(thm)],[605,60]) ).
tff(607,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))))),
inference(symmetry,[status(thm)],[606]) ).
tff(608,plain,
mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(op_c,op_c),op_d)) = mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))),
inference(symmetry,[status(thm)],[595]) ).
tff(609,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(symmetry,[status(thm)],[590]) ).
tff(610,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))))),
inference(symmetry,[status(thm)],[586]) ).
tff(611,plain,
mult(mult(op_c,op_c),op_d) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(symmetry,[status(thm)],[581]) ).
tff(612,plain,
mult(mult(op_c,op_c),op_d) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(transitivity,[status(thm)],[611,610,588,609]) ).
tff(613,plain,
mult(a,mult(a,a)) = mult(unit,mult(a,mult(a,mult(unit,a)))),
inference(transitivity,[status(thm)],[342,182,180,177]) ).
tff(614,plain,
mult(a,mult(a,mult(a,a))) = mult(a,mult(unit,mult(a,mult(a,mult(unit,a))))),
inference(monotonicity,[status(thm)],[613]) ).
tff(615,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(a,mult(a,a))) = mult(mult(a,mult(a,a)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(616,plain,
mult(a,mult(a,mult(a,a))) = mult(mult(a,mult(a,a)),a),
inference(unit_resolution,[status(thm)],[615,60]) ).
tff(617,plain,
mult(mult(a,mult(a,a)),a) = mult(a,mult(a,mult(a,a))),
inference(symmetry,[status(thm)],[616]) ).
tff(618,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a))))) = mult(mult(a,mult(a,a)),a),
inference(monotonicity,[status(thm)],[343,212]) ).
tff(619,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a))))) = mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),
inference(transitivity,[status(thm)],[618,617,614,193,198]) ).
tff(620,plain,
mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a))))),mult(mult(op_c,op_c),op_d)) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[619,612]) ).
tff(621,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(op_c,op_c),op_d)))) = mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a))))),mult(mult(op_c,op_c),op_d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(622,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(op_c,op_c),op_d)))) = mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a))))),mult(mult(op_c,op_c),op_d)),
inference(unit_resolution,[status(thm)],[621,60]) ).
tff(623,plain,
mult(a,mult(a,mult(mult(op_c,op_c),op_d))) = mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)),
inference(transitivity,[status(thm)],[537,540]) ).
tff(624,plain,
mult(a,mult(a,mult(a,mult(mult(op_c,op_c),op_d)))) = mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(monotonicity,[status(thm)],[623]) ).
tff(625,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(a,mult(a,mult(mult(op_c,op_c),op_d)))) = mult(mult(a,mult(a,a)),mult(mult(op_c,op_c),op_d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(626,plain,
mult(a,mult(a,mult(a,mult(mult(op_c,op_c),op_d)))) = mult(mult(a,mult(a,a)),mult(mult(op_c,op_c),op_d)),
inference(unit_resolution,[status(thm)],[625,60]) ).
tff(627,plain,
mult(mult(a,mult(a,a)),mult(mult(op_c,op_c),op_d)) = mult(a,mult(a,mult(a,mult(mult(op_c,op_c),op_d)))),
inference(symmetry,[status(thm)],[626]) ).
tff(628,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(op_c,op_c),op_d)) = mult(mult(a,mult(a,a)),mult(mult(op_c,op_c),op_d)),
inference(monotonicity,[status(thm)],[343]) ).
tff(629,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(op_c,op_c),op_d)) = mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(transitivity,[status(thm)],[628,627,624]) ).
tff(630,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(op_c,op_c),op_d))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[629]) ).
tff(631,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(op_c,op_c),op_d))),
inference(symmetry,[status(thm)],[630]) ).
tff(632,plain,
ld(a,mult(a,mult(a,mult(mult(op_c,op_c),op_d)))) = ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))))),
inference(symmetry,[status(thm)],[567]) ).
tff(633,plain,
mult(a,mult(mult(op_c,op_c),op_d)) = ld(a,mult(a,mult(a,mult(mult(op_c,op_c),op_d)))),
inference(symmetry,[status(thm)],[533]) ).
tff(634,plain,
mult(a,mult(mult(op_c,op_c),op_d)) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(op_c,op_c),op_d))),
inference(transitivity,[status(thm)],[633,632,569,631]) ).
tff(635,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(a,mult(mult(op_c,op_c),op_d))) = mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[634]) ).
tff(636,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(a,mult(mult(op_c,op_c),op_d))) = mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d))),
inference(transitivity,[status(thm)],[635,622,620,592,608,598]) ).
tff(637,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(a,mult(unit,a))),mult(a,mult(unit,a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(638,plain,
rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(a,mult(unit,a))),mult(a,mult(unit,a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),
inference(unit_resolution,[status(thm)],[637,18]) ).
tff(639,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(unit,a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[375]) ).
tff(640,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(unit,a))),
inference(symmetry,[status(thm)],[639]) ).
tff(641,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(642,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))),
inference(unit_resolution,[status(thm)],[641,60]) ).
tff(643,plain,
mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a)))) = mult(op_c,unit),
inference(monotonicity,[status(thm)],[421]) ).
tff(644,plain,
mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a)))) = mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(transitivity,[status(thm)],[643,284,69,66,20]) ).
tff(645,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(monotonicity,[status(thm)],[644]) ).
tff(646,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a))))),
inference(symmetry,[status(thm)],[645]) ).
tff(647,plain,
mult(a,op_c) = mult(a,mult(unit,mult(a,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))))),
inference(symmetry,[status(thm)],[231]) ).
tff(648,plain,
mult(op_c,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(op_c,unit),
inference(monotonicity,[status(thm)],[205]) ).
tff(649,plain,
mult(op_c,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = op_c,
inference(transitivity,[status(thm)],[648,284]) ).
tff(650,plain,
mult(a,mult(op_c,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(a,op_c),
inference(monotonicity,[status(thm)],[649]) ).
tff(651,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(op_c,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(652,plain,
mult(a,mult(op_c,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[651,60]) ).
tff(653,plain,
mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(a,mult(op_c,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))),
inference(symmetry,[status(thm)],[652]) ).
tff(654,plain,
mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))) = mult(a,unit),
inference(monotonicity,[status(thm)],[99]) ).
tff(655,plain,
mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))) = a,
inference(transitivity,[status(thm)],[654,97]) ).
tff(656,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))))) = mult(rd(unit,mult(a,mult(unit,a))),a),
inference(monotonicity,[status(thm)],[655]) ).
tff(657,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(658,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))),
inference(unit_resolution,[status(thm)],[657,60]) ).
tff(659,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))) = mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))))),
inference(symmetry,[status(thm)],[658]) ).
tff(660,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))) = mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),
inference(transitivity,[status(thm)],[659,656,115,112,84]) ).
tff(661,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))) = mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[660]) ).
tff(662,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))) = mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(transitivity,[status(thm)],[661,653,650,647,233]) ).
tff(663,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(monotonicity,[status(thm)],[662]) ).
tff(664,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(a,mult(unit,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(665,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(a,mult(unit,a))),
inference(unit_resolution,[status(thm)],[664,60]) ).
tff(666,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(a,mult(unit,a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))))),
inference(symmetry,[status(thm)],[665]) ).
tff(667,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(a,mult(unit,a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(unit,a))),
inference(transitivity,[status(thm)],[666,663,242,371,249,646,642,640]) ).
tff(668,plain,
rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(a,mult(unit,a))),mult(a,mult(unit,a))) = rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(unit,a))),mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[667]) ).
tff(669,plain,
rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(unit,a))),mult(a,mult(unit,a))) = rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(a,mult(unit,a))),mult(a,mult(unit,a))),
inference(symmetry,[status(thm)],[668]) ).
tff(670,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(unit,a))),mult(a,mult(unit,a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(671,plain,
rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(unit,a))),mult(a,mult(unit,a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),
inference(unit_resolution,[status(thm)],[670,18]) ).
tff(672,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) = rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(unit,a))),mult(a,mult(unit,a))),
inference(symmetry,[status(thm)],[671]) ).
tff(673,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),
inference(transitivity,[status(thm)],[672,669,638]) ).
tff(674,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(a,mult(mult(op_c,op_c),op_d)))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))),mult(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[673,636]) ).
tff(675,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(a,mult(mult(op_c,op_c),op_d)))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d)))),
inference(transitivity,[status(thm)],[674,607,604,531,528,393]) ).
tff(676,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(a,mult(mult(op_c,op_c),op_d))))) = mult(mult(a,mult(a,mult(unit,a))),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))))),
inference(monotonicity,[status(thm)],[675]) ).
tff(677,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))))) = mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(a,mult(mult(op_c,op_c),op_d))))),
inference(symmetry,[status(thm)],[676]) ).
tff(678,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(679,plain,
mult(unit,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(unit_resolution,[status(thm)],[678,46]) ).
tff(680,plain,
mult(unit,mult(rd(unit,mult(a,mult(unit,a))),unit)) = mult(unit,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[118]) ).
tff(681,plain,
mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(unit,mult(rd(unit,mult(a,mult(unit,a))),unit)),
inference(monotonicity,[status(thm)],[124,119]) ).
tff(682,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(683,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[682,60]) ).
tff(684,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(monotonicity,[status(thm)],[120,86]) ).
tff(685,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit)) = mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[684]) ).
tff(686,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit)) = mult(a,rd(unit,mult(a,mult(unit,a)))),
inference(transitivity,[status(thm)],[685,239]) ).
tff(687,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit))) = mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),
inference(monotonicity,[status(thm)],[120,686]) ).
tff(688,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(689,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),unit),
inference(unit_resolution,[status(thm)],[688,60]) ).
tff(690,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),unit) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit))),
inference(symmetry,[status(thm)],[689]) ).
tff(691,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),unit) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),unit),
inference(monotonicity,[status(thm)],[241]) ).
tff(692,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),unit),
inference(monotonicity,[status(thm)],[205]) ).
tff(693,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(transitivity,[status(thm)],[692,691,690,687,241]) ).
tff(694,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))),
inference(monotonicity,[status(thm)],[693]) ).
tff(695,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(696,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[695,60]) ).
tff(697,plain,
mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))),
inference(symmetry,[status(thm)],[696]) ).
tff(698,plain,
mult(unit,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),
inference(monotonicity,[status(thm)],[315]) ).
tff(699,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)) = mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)),
inference(transitivity,[status(thm)],[123,82]) ).
tff(700,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(monotonicity,[status(thm)],[120,699]) ).
tff(701,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(702,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),a),
inference(unit_resolution,[status(thm)],[701,60]) ).
tff(703,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),a) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a))),
inference(symmetry,[status(thm)],[702]) ).
tff(704,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),a) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),a),
inference(monotonicity,[status(thm)],[241]) ).
tff(705,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),a) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(transitivity,[status(thm)],[704,703,700]) ).
tff(706,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),a)) = mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[705]) ).
tff(707,plain,
mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),a)),
inference(symmetry,[status(thm)],[706]) ).
tff(708,plain,
mult(a,ld(mult(a,mult(unit,a)),unit)) = mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(symmetry,[status(thm)],[317]) ).
tff(709,plain,
mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))) = mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),a)),
inference(transitivity,[status(thm)],[315,708,707]) ).
tff(710,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[709,698]) ).
tff(711,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(transitivity,[status(thm)],[710,697,694,683,681,680,679]) ).
tff(712,plain,
mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[711]) ).
tff(713,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(714,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(unit_resolution,[status(thm)],[713,60]) ).
tff(715,plain,
mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[711]) ).
tff(716,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(717,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[716,60]) ).
tff(718,plain,
mult(mult(a,mult(a,a)),mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(a,mult(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(symmetry,[status(thm)],[381]) ).
tff(719,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(rd(op_c,mult(a,mult(unit,a))),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(720,plain,
mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(rd(op_c,mult(a,mult(unit,a))),a),
inference(unit_resolution,[status(thm)],[719,46]) ).
tff(721,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(monotonicity,[status(thm)],[165]) ).
tff(722,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(rd(op_c,mult(a,mult(unit,a))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(723,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(unit_resolution,[status(thm)],[722,60]) ).
tff(724,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(rd(op_c,mult(a,mult(unit,a))),a),
inference(transitivity,[status(thm)],[723,721,720]) ).
tff(725,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(mult(a,mult(a,a)),mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(monotonicity,[status(thm)],[343,724]) ).
tff(726,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(mult(a,mult(unit,a)),op_c),
inference(transitivity,[status(thm)],[725,718,385,410,299]) ).
tff(727,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)),
inference(monotonicity,[status(thm)],[120,726]) ).
tff(728,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(729,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(unit_resolution,[status(thm)],[728,60]) ).
tff(730,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))))),
inference(symmetry,[status(thm)],[729]) ).
tff(731,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(732,plain,
ld(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(unit_resolution,[status(thm)],[731,7]) ).
tff(733,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a)),
inference(symmetry,[status(thm)],[246]) ).
tff(734,plain,
ld(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) = ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)))),
inference(symmetry,[status(thm)],[129]) ).
tff(735,plain,
mult(rd(op_c,mult(a,mult(unit,a))),a) = ld(a,mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(symmetry,[status(thm)],[11]) ).
tff(736,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a)),
inference(transitivity,[status(thm)],[723,721,720,735,734,131,733]) ).
tff(737,plain,
ld(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a))))) = ld(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a))),
inference(monotonicity,[status(thm)],[736]) ).
tff(738,plain,
ld(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a))) = ld(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a))))),
inference(symmetry,[status(thm)],[737]) ).
tff(739,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a))) = mult(op_c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(740,plain,
ld(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a))) = mult(op_c,a),
inference(unit_resolution,[status(thm)],[739,7]) ).
tff(741,plain,
mult(op_c,a) = ld(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,a))),
inference(symmetry,[status(thm)],[740]) ).
tff(742,plain,
mult(op_c,a) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(transitivity,[status(thm)],[741,738,732]) ).
tff(743,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,a)) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(monotonicity,[status(thm)],[362,742]) ).
tff(744,plain,
mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(op_c,a),
inference(transitivity,[status(thm)],[653,650,30]) ).
tff(745,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,a)),
inference(monotonicity,[status(thm)],[744]) ).
tff(746,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = op_c,
inference(transitivity,[status(thm)],[745,743,730,727,409,406,401]) ).
tff(747,plain,
mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[746]) ).
tff(748,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(749,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[748,60]) ).
tff(750,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(751,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[750,60]) ).
tff(752,plain,
mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(symmetry,[status(thm)],[751]) ).
tff(753,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(op_c,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(mult(op_c,op_c),op_d),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(754,plain,
mult(op_c,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(mult(op_c,op_c),op_d),a),
inference(unit_resolution,[status(thm)],[753,78]) ).
tff(755,plain,
mult(mult(unit,mult(op_c,unit)),ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))) = mult(op_c,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[286]) ).
tff(756,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(op_c,mult(unit,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(unit,mult(op_c,unit)),ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(757,plain,
mult(unit,mult(op_c,mult(unit,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(unit,mult(op_c,unit)),ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[756,60]) ).
tff(758,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(op_c,mult(unit,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(op_c,mult(unit,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(759,plain,
mult(unit,mult(op_c,mult(unit,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(op_c,mult(unit,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(unit_resolution,[status(thm)],[758,46]) ).
tff(760,plain,
mult(mult(unit,mult(op_c,unit)),ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))) = mult(unit,mult(op_c,mult(unit,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(symmetry,[status(thm)],[757]) ).
tff(761,plain,
mult(op_c,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(unit,mult(op_c,unit)),ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[755]) ).
tff(762,plain,
mult(mult(mult(op_c,op_c),op_d),a) = mult(op_c,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[754]) ).
tff(763,plain,
mult(mult(mult(op_c,op_c),op_d),a) = mult(op_c,mult(unit,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(transitivity,[status(thm)],[762,761,760,759]) ).
tff(764,plain,
mult(unit,mult(mult(mult(op_c,op_c),op_d),a)) = mult(unit,mult(op_c,mult(unit,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[763]) ).
tff(765,plain,
mult(unit,mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(mult(op_c,op_c),op_d),a),
inference(transitivity,[status(thm)],[764,757,755,754]) ).
tff(766,plain,
mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a))) = mult(a,mult(mult(mult(op_c,op_c),op_d),a)),
inference(monotonicity,[status(thm)],[765]) ).
tff(767,plain,
mult(a,mult(mult(mult(op_c,op_c),op_d),a)) = mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[766]) ).
tff(768,plain,
mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(unit,mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[124,767]) ).
tff(769,plain,
mult(unit,mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[768]) ).
tff(770,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(unit,mult(a,unit)),mult(mult(mult(op_c,op_c),op_d),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(771,plain,
mult(unit,mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(unit,mult(a,unit)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(unit_resolution,[status(thm)],[770,60]) ).
tff(772,plain,
mult(mult(unit,mult(a,unit)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(unit,mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[771]) ).
tff(773,plain,
mult(mult(unit,mult(a,unit)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(a,mult(mult(mult(op_c,op_c),op_d),a)),
inference(monotonicity,[status(thm)],[169]) ).
tff(774,plain,
mult(a,mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(unit,mult(a,unit)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(symmetry,[status(thm)],[773]) ).
tff(775,plain,
mult(a,mult(mult(mult(op_c,op_c),op_d),a)) = mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(transitivity,[status(thm)],[774,772,769,752]) ).
tff(776,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))),
inference(monotonicity,[status(thm)],[775]) ).
tff(777,plain,
mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))),
inference(monotonicity,[status(thm)],[776]) ).
tff(778,plain,
mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))) = mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[777]) ).
tff(779,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(op_c,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))))) = mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(780,plain,
mult(a,mult(op_c,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))))) = mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))),
inference(unit_resolution,[status(thm)],[779,60]) ).
tff(781,plain,
mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(a,mult(mult(mult(op_c,op_c),op_d),a)),
inference(monotonicity,[status(thm)],[366]) ).
tff(782,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(mult(op_c,op_c),op_d),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(783,plain,
ld(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(mult(op_c,op_c),op_d),a),
inference(unit_resolution,[status(thm)],[782,7]) ).
tff(784,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(a,mult(mult(mult(op_c,op_c),op_d),a)),
inference(transitivity,[status(thm)],[751,768,771,773]) ).
tff(785,plain,
ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = ld(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[784]) ).
tff(786,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(787,plain,
ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(unit_resolution,[status(thm)],[786,7]) ).
tff(788,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))),
inference(symmetry,[status(thm)],[787]) ).
tff(789,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(mult(op_c,op_c),op_d),a),
inference(transitivity,[status(thm)],[788,785,783]) ).
tff(790,plain,
mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(monotonicity,[status(thm)],[789]) ).
tff(791,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(792,plain,
mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(unit_resolution,[status(thm)],[791,60]) ).
tff(793,plain,
mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))) = mult(a,mult(mult(mult(op_c,op_c),op_d),a)),
inference(transitivity,[status(thm)],[792,790,781]) ).
tff(794,plain,
mult(op_c,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))))) = mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[793]) ).
tff(795,plain,
mult(a,mult(op_c,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))))) = mult(a,mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[794]) ).
tff(796,plain,
mult(a,mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(a,mult(op_c,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))))),
inference(symmetry,[status(thm)],[795]) ).
tff(797,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(798,plain,
mult(a,mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(unit_resolution,[status(thm)],[797,60]) ).
tff(799,plain,
mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(a,mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[798]) ).
tff(800,plain,
mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(transitivity,[status(thm)],[799,796,780,778]) ).
tff(801,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[800]) ).
tff(802,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(transitivity,[status(thm)],[801,749,747]) ).
tff(803,plain,
mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(unit,mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[802]) ).
tff(804,plain,
mult(unit,mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[803]) ).
tff(805,plain,
mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(unit,mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[767]) ).
tff(806,plain,
mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(a,mult(mult(mult(op_c,op_c),op_d),a)),
inference(transitivity,[status(thm)],[805,771,773]) ).
tff(807,plain,
mult(op_c,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[806]) ).
tff(808,plain,
mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(op_c,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[807]) ).
tff(809,plain,
mult(unit,mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(unit,mult(op_c,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[808]) ).
tff(810,plain,
mult(unit,mult(op_c,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(unit,mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[809]) ).
tff(811,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(op_c,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(unit,mult(op_c,unit)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(812,plain,
mult(unit,mult(op_c,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(unit,mult(op_c,unit)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[811,60]) ).
tff(813,plain,
mult(mult(unit,mult(op_c,unit)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(unit,mult(op_c,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(symmetry,[status(thm)],[812]) ).
tff(814,plain,
mult(mult(unit,mult(op_c,unit)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[286]) ).
tff(815,plain,
mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(unit,mult(op_c,unit)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[814]) ).
tff(816,plain,
mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(transitivity,[status(thm)],[815,813,810,804]) ).
tff(817,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[816]) ).
tff(818,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(transitivity,[status(thm)],[817,717,715]) ).
tff(819,plain,
mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[818]) ).
tff(820,plain,
mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(symmetry,[status(thm)],[819]) ).
tff(821,plain,
mult(mult(unit,mult(a,unit)),mult(op_c,a)) = mult(a,mult(op_c,a)),
inference(monotonicity,[status(thm)],[169]) ).
tff(822,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(a,mult(unit,mult(op_c,a)))) = mult(mult(unit,mult(a,unit)),mult(op_c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(823,plain,
mult(unit,mult(a,mult(unit,mult(op_c,a)))) = mult(mult(unit,mult(a,unit)),mult(op_c,a)),
inference(unit_resolution,[status(thm)],[822,60]) ).
tff(824,plain,
mult(op_c,a) = mult(op_c,mult(unit,a)),
inference(transitivity,[status(thm)],[293,292,291]) ).
tff(825,plain,
mult(unit,mult(op_c,a)) = mult(unit,mult(op_c,mult(unit,a))),
inference(monotonicity,[status(thm)],[824]) ).
tff(826,plain,
mult(unit,mult(op_c,a)) = mult(op_c,a),
inference(transitivity,[status(thm)],[825,289,287]) ).
tff(827,plain,
mult(a,mult(unit,mult(op_c,a))) = mult(a,mult(op_c,a)),
inference(monotonicity,[status(thm)],[826]) ).
tff(828,plain,
mult(a,mult(op_c,a)) = mult(a,mult(unit,mult(op_c,a))),
inference(symmetry,[status(thm)],[827]) ).
tff(829,plain,
mult(op_c,mult(a,unit)) = mult(op_c,a),
inference(monotonicity,[status(thm)],[97]) ).
tff(830,plain,
mult(a,mult(op_c,mult(a,unit))) = mult(a,mult(op_c,a)),
inference(monotonicity,[status(thm)],[829]) ).
tff(831,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(op_c,mult(a,unit))) = mult(mult(a,mult(op_c,a)),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(832,plain,
mult(a,mult(op_c,mult(a,unit))) = mult(mult(a,mult(op_c,a)),unit),
inference(unit_resolution,[status(thm)],[831,60]) ).
tff(833,plain,
mult(mult(a,mult(op_c,a)),unit) = mult(a,mult(op_c,mult(a,unit))),
inference(symmetry,[status(thm)],[832]) ).
tff(834,plain,
mult(mult(a,mult(op_c,a)),unit) = mult(a,mult(unit,mult(op_c,a))),
inference(transitivity,[status(thm)],[833,830,828]) ).
tff(835,plain,
mult(unit,mult(mult(a,mult(op_c,a)),unit)) = mult(unit,mult(a,mult(unit,mult(op_c,a)))),
inference(monotonicity,[status(thm)],[834]) ).
tff(836,plain,
mult(unit,mult(mult(a,mult(op_c,a)),unit)) = mult(a,mult(op_c,a)),
inference(transitivity,[status(thm)],[835,823,821]) ).
tff(837,plain,
mult(mult(unit,mult(mult(a,mult(op_c,a)),unit)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(monotonicity,[status(thm)],[836]) ).
tff(838,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(mult(a,mult(op_c,a)),mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(unit,mult(mult(a,mult(op_c,a)),unit)),mult(mult(mult(op_c,op_c),op_d),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(839,plain,
mult(unit,mult(mult(a,mult(op_c,a)),mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(unit,mult(mult(a,mult(op_c,a)),unit)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(unit_resolution,[status(thm)],[838,60]) ).
tff(840,plain,
mult(mult(a,mult(op_c,a)),mult(unit,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(monotonicity,[status(thm)],[765]) ).
tff(841,plain,
mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(a,mult(op_c,a)),mult(unit,mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[840]) ).
tff(842,plain,
mult(unit,mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(unit,mult(mult(a,mult(op_c,a)),mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[841]) ).
tff(843,plain,
mult(unit,mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(transitivity,[status(thm)],[842,839,837]) ).
tff(844,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[843]) ).
tff(845,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[844]) ).
tff(846,plain,
mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[845]) ).
tff(847,plain,
mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[846]) ).
tff(848,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit)),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(849,plain,
mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit)),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[848,60]) ).
tff(850,plain,
mult(mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit)),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))))),
inference(symmetry,[status(thm)],[849]) ).
tff(851,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit) = mult(rd(unit,mult(a,mult(unit,a))),unit),
inference(transitivity,[status(thm)],[684,119]) ).
tff(852,plain,
mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit)) = mult(unit,mult(rd(unit,mult(a,mult(unit,a))),unit)),
inference(monotonicity,[status(thm)],[851]) ).
tff(853,plain,
mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit)) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(transitivity,[status(thm)],[852,680,679]) ).
tff(854,plain,
mult(mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit)),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[853]) ).
tff(855,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(unit,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit)),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[854]) ).
tff(856,plain,
mult(unit,mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[805]) ).
tff(857,plain,
mult(a,mult(mult(mult(op_c,op_c),op_d),a)) = mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(transitivity,[status(thm)],[774,772,856]) ).
tff(858,plain,
mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(a,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[857]) ).
tff(859,plain,
mult(a,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[858]) ).
tff(860,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(861,plain,
mult(a,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(unit_resolution,[status(thm)],[860,60]) ).
tff(862,plain,
mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(a,mult(unit,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[861]) ).
tff(863,plain,
mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(transitivity,[status(thm)],[862,859]) ).
tff(864,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[863]) ).
tff(865,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(mult(op_c,op_c),op_d),a),
inference(transitivity,[status(thm)],[864,788,785,783]) ).
tff(866,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(monotonicity,[status(thm)],[865]) ).
tff(867,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[866]) ).
tff(868,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(869,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[868,60]) ).
tff(870,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))),
inference(symmetry,[status(thm)],[869]) ).
tff(871,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))),mult(a,mult(unit,a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(872,plain,
rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))),mult(a,mult(unit,a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(unit_resolution,[status(thm)],[871,18]) ).
tff(873,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a)))) = mult(mult(a,mult(op_c,a)),unit),
inference(monotonicity,[status(thm)],[421]) ).
tff(874,plain,
mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a)))) = mult(mult(a,mult(unit,a)),op_c),
inference(transitivity,[status(thm)],[873,833,830,410,299]) ).
tff(875,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)),
inference(monotonicity,[status(thm)],[120,874]) ).
tff(876,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(877,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))),
inference(unit_resolution,[status(thm)],[876,60]) ).
tff(878,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,a))))),
inference(symmetry,[status(thm)],[877]) ).
tff(879,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))) = op_c,
inference(transitivity,[status(thm)],[878,875,409,406,401]) ).
tff(880,plain,
rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))),mult(a,mult(unit,a))) = rd(op_c,mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[879]) ).
tff(881,plain,
rd(op_c,mult(a,mult(unit,a))) = rd(mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,a))),mult(a,mult(unit,a))),
inference(symmetry,[status(thm)],[880]) ).
tff(882,plain,
mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(transitivity,[status(thm)],[255,273,881,872]) ).
tff(883,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[882]) ).
tff(884,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(transitivity,[status(thm)],[883,870,867,855,850,847,820]) ).
tff(885,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))),
inference(monotonicity,[status(thm)],[884]) ).
tff(886,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(887,plain,
ld(a,mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[886,7]) ).
tff(888,plain,
mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(transitivity,[status(thm)],[858,861]) ).
tff(889,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[888]) ).
tff(890,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[889]) ).
tff(891,plain,
mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[890]) ).
tff(892,plain,
mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[891]) ).
tff(893,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(894,plain,
mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[893,60]) ).
tff(895,plain,
mult(mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(symmetry,[status(thm)],[894]) ).
tff(896,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),a) = mult(rd(op_c,mult(a,mult(unit,a))),a),
inference(monotonicity,[status(thm)],[274]) ).
tff(897,plain,
mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),a)) = mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(monotonicity,[status(thm)],[896]) ).
tff(898,plain,
mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),a)) = op_c,
inference(transitivity,[status(thm)],[897,226,65,68]) ).
tff(899,plain,
mult(mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[898]) ).
tff(900,plain,
mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[899]) ).
tff(901,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(a,mult(mult(mult(op_c,op_c),op_d),a)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(902,plain,
mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(a,mult(mult(mult(op_c,op_c),op_d),a)),op_c),
inference(unit_resolution,[status(thm)],[901,27]) ).
tff(903,plain,
mult(mult(a,mult(mult(mult(op_c,op_c),op_d),a)),op_c) = mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[902]) ).
tff(904,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(mult(op_c,op_c),op_d),mult(a,op_c))) = mult(mult(a,mult(mult(mult(op_c,op_c),op_d),a)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(905,plain,
mult(a,mult(mult(mult(op_c,op_c),op_d),mult(a,op_c))) = mult(mult(a,mult(mult(mult(op_c,op_c),op_d),a)),op_c),
inference(unit_resolution,[status(thm)],[904,60]) ).
tff(906,plain,
mult(a,mult(mult(mult(op_c,op_c),op_d),mult(a,op_c))) = mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(transitivity,[status(thm)],[905,903,900,895,892]) ).
tff(907,plain,
ld(a,mult(a,mult(mult(mult(op_c,op_c),op_d),mult(a,op_c)))) = ld(a,mult(a,mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[906]) ).
tff(908,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(mult(mult(op_c,op_c),op_d),mult(a,op_c)))) = mult(mult(mult(op_c,op_c),op_d),mult(a,op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(909,plain,
ld(a,mult(a,mult(mult(mult(op_c,op_c),op_d),mult(a,op_c)))) = mult(mult(mult(op_c,op_c),op_d),mult(a,op_c)),
inference(unit_resolution,[status(thm)],[908,7]) ).
tff(910,plain,
mult(mult(mult(op_c,op_c),op_d),mult(a,op_c)) = ld(a,mult(a,mult(mult(mult(op_c,op_c),op_d),mult(a,op_c)))),
inference(symmetry,[status(thm)],[909]) ).
tff(911,plain,
mult(op_c,op_d) = mult(unit,mult(op_c,op_d)),
inference(symmetry,[status(thm)],[552]) ).
tff(912,plain,
^ [A: $i] :
refl(
( ( mult(op_d,A) = mult(A,op_d) )
<=> ( mult(op_d,A) = mult(A,op_d) ) )),
inference(bind,[status(th)],]) ).
tff(913,plain,
( ! [A: $i] : ( mult(op_d,A) = mult(A,op_d) )
<=> ! [A: $i] : ( mult(op_d,A) = mult(A,op_d) ) ),
inference(quant_intro,[status(thm)],[912]) ).
tff(914,plain,
( ! [A: $i] : ( mult(op_d,A) = mult(A,op_d) )
<=> ! [A: $i] : ( mult(op_d,A) = mult(A,op_d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(915,axiom,
! [A: $i] : ( mult(op_d,A) = mult(A,op_d) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
tff(916,plain,
! [A: $i] : ( mult(op_d,A) = mult(A,op_d) ),
inference(modus_ponens,[status(thm)],[915,914]) ).
tff(917,plain,
! [A: $i] : ( mult(op_d,A) = mult(A,op_d) ),
inference(skolemize,[status(sab)],[916]) ).
tff(918,plain,
! [A: $i] : ( mult(op_d,A) = mult(A,op_d) ),
inference(modus_ponens,[status(thm)],[917,913]) ).
tff(919,plain,
( ~ ! [A: $i] : ( mult(op_d,A) = mult(A,op_d) )
| ( mult(op_d,op_c) = mult(op_c,op_d) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(920,plain,
mult(op_d,op_c) = mult(op_c,op_d),
inference(unit_resolution,[status(thm)],[919,918]) ).
tff(921,plain,
mult(op_d,op_c) = mult(unit,mult(op_c,op_d)),
inference(transitivity,[status(thm)],[920,911]) ).
tff(922,plain,
mult(op_c,mult(op_d,op_c)) = mult(op_c,mult(unit,mult(op_c,op_d))),
inference(monotonicity,[status(thm)],[921]) ).
tff(923,plain,
mult(op_c,mult(op_d,op_c)) = mult(mult(op_c,op_c),op_d),
inference(transitivity,[status(thm)],[922,451,449]) ).
tff(924,plain,
mult(mult(op_c,mult(op_d,op_c)),mult(op_c,a)) = mult(mult(mult(op_c,op_c),op_d),mult(a,op_c)),
inference(monotonicity,[status(thm)],[923,29]) ).
tff(925,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(op_d,mult(op_c,mult(op_c,a)))) = mult(mult(op_c,mult(op_d,op_c)),mult(op_c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(926,plain,
mult(op_c,mult(op_d,mult(op_c,mult(op_c,a)))) = mult(mult(op_c,mult(op_d,op_c)),mult(op_c,a)),
inference(unit_resolution,[status(thm)],[925,60]) ).
tff(927,plain,
mult(op_c,mult(op_c,a)) = mult(op_c,mult(a,op_c)),
inference(monotonicity,[status(thm)],[29]) ).
tff(928,plain,
mult(op_d,mult(op_c,mult(op_c,a))) = mult(op_d,mult(op_c,mult(a,op_c))),
inference(monotonicity,[status(thm)],[927]) ).
tff(929,plain,
mult(op_d,mult(op_c,mult(a,op_c))) = mult(op_d,mult(op_c,mult(op_c,a))),
inference(symmetry,[status(thm)],[928]) ).
tff(930,plain,
( ~ ! [A: $i] : ( mult(op_d,A) = mult(A,op_d) )
| ( mult(op_d,mult(op_c,mult(a,op_c))) = mult(mult(op_c,mult(a,op_c)),op_d) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(931,plain,
mult(op_d,mult(op_c,mult(a,op_c))) = mult(mult(op_c,mult(a,op_c)),op_d),
inference(unit_resolution,[status(thm)],[930,918]) ).
tff(932,plain,
mult(mult(op_c,mult(a,op_c)),op_d) = mult(op_d,mult(op_c,mult(a,op_c))),
inference(symmetry,[status(thm)],[931]) ).
tff(933,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(a,mult(op_c,op_d))) = mult(mult(op_c,mult(a,op_c)),op_d) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(934,plain,
mult(op_c,mult(a,mult(op_c,op_d))) = mult(mult(op_c,mult(a,op_c)),op_d),
inference(unit_resolution,[status(thm)],[933,60]) ).
tff(935,plain,
mult(a,mult(op_c,op_d)) = mult(a,mult(unit,mult(op_c,op_d))),
inference(monotonicity,[status(thm)],[911]) ).
tff(936,plain,
mult(op_c,mult(a,mult(op_c,op_d))) = mult(op_c,mult(a,mult(unit,mult(op_c,op_d)))),
inference(monotonicity,[status(thm)],[935]) ).
tff(937,plain,
mult(op_c,mult(a,mult(unit,mult(op_c,op_d)))) = mult(op_c,mult(a,mult(op_c,op_d))),
inference(symmetry,[status(thm)],[936]) ).
tff(938,plain,
mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,mult(op_c,op_d)))) = mult(op_c,mult(a,mult(unit,mult(op_c,op_d)))),
inference(monotonicity,[status(thm)],[746]) ).
tff(939,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d)))))) = mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,mult(op_c,op_d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(940,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d)))))) = mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(unit,mult(op_c,op_d)))),
inference(unit_resolution,[status(thm)],[939,60]) ).
tff(941,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(op_c,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d))))))) = mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(942,plain,
mult(a,mult(op_c,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d))))))) = mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d))))),
inference(unit_resolution,[status(thm)],[941,60]) ).
tff(943,plain,
mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(unit,mult(op_c,op_d))) = mult(a,mult(unit,mult(op_c,op_d))),
inference(monotonicity,[status(thm)],[366]) ).
tff(944,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d))))) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(unit,mult(op_c,op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(945,plain,
mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d))))) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(unit,mult(op_c,op_d))),
inference(unit_resolution,[status(thm)],[944,60]) ).
tff(946,plain,
mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d))))) = mult(a,mult(unit,mult(op_c,op_d))),
inference(transitivity,[status(thm)],[945,943]) ).
tff(947,plain,
mult(op_c,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d)))))) = mult(op_c,mult(a,mult(unit,mult(op_c,op_d)))),
inference(monotonicity,[status(thm)],[946]) ).
tff(948,plain,
mult(a,mult(op_c,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d))))))) = mult(a,mult(op_c,mult(a,mult(unit,mult(op_c,op_d))))),
inference(monotonicity,[status(thm)],[947]) ).
tff(949,plain,
mult(a,mult(op_c,mult(a,mult(unit,mult(op_c,op_d))))) = mult(a,mult(op_c,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d))))))),
inference(symmetry,[status(thm)],[948]) ).
tff(950,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(op_c,mult(a,mult(unit,mult(op_c,op_d))))) = mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(951,plain,
mult(a,mult(op_c,mult(a,mult(unit,mult(op_c,op_d))))) = mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))),
inference(unit_resolution,[status(thm)],[950,60]) ).
tff(952,plain,
mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))) = mult(a,mult(op_c,mult(a,mult(unit,mult(op_c,op_d))))),
inference(symmetry,[status(thm)],[951]) ).
tff(953,plain,
mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))) = mult(mult(a,mult(op_c,a)),mult(op_c,op_d)),
inference(monotonicity,[status(thm)],[552]) ).
tff(954,plain,
mult(mult(a,mult(op_c,a)),mult(op_c,op_d)) = mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))),
inference(symmetry,[status(thm)],[953]) ).
tff(955,plain,
mult(mult(a,mult(op_c,a)),mult(op_c,op_d)) = mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d))))),
inference(transitivity,[status(thm)],[954,952,949,942]) ).
tff(956,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(unit,mult(op_c,op_d)))))),
inference(monotonicity,[status(thm)],[955]) ).
tff(957,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d))) = mult(op_d,mult(op_c,mult(op_c,a))),
inference(transitivity,[status(thm)],[956,940,938,937,934,932,929]) ).
tff(958,plain,
mult(op_c,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d)))) = mult(op_c,mult(op_d,mult(op_c,mult(op_c,a)))),
inference(monotonicity,[status(thm)],[957]) ).
tff(959,plain,
mult(op_c,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d)))) = mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(transitivity,[status(thm)],[958,926,924,910,907,887]) ).
tff(960,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d))))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[959]) ).
tff(961,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d))))) = mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(962,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d))))) = mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d))),
inference(unit_resolution,[status(thm)],[961,60]) ).
tff(963,plain,
mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d))))),
inference(symmetry,[status(thm)],[962]) ).
tff(964,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(op_c,mult(a,mult(unit,a))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(965,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(unit_resolution,[status(thm)],[964,60]) ).
tff(966,plain,
mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(symmetry,[status(thm)],[965]) ).
tff(967,plain,
mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(monotonicity,[status(thm)],[124]) ).
tff(968,plain,
mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(symmetry,[status(thm)],[967]) ).
tff(969,plain,
mult(rd(op_c,mult(a,mult(unit,a))),a) = mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),a)),
inference(symmetry,[status(thm)],[720]) ).
tff(970,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,mult(op_c,a))) = mult(op_c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(971,plain,
ld(op_c,mult(op_c,mult(op_c,a))) = mult(op_c,a),
inference(unit_resolution,[status(thm)],[970,7]) ).
tff(972,plain,
mult(op_c,mult(a,op_c)) = mult(op_c,mult(op_c,a)),
inference(symmetry,[status(thm)],[927]) ).
tff(973,plain,
mult(op_c,mult(unit,mult(op_c,unit))) = mult(op_c,op_c),
inference(monotonicity,[status(thm)],[286]) ).
tff(974,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(unit,mult(op_c,unit))) = mult(mult(op_c,mult(unit,op_c)),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(975,plain,
mult(op_c,mult(unit,mult(op_c,unit))) = mult(mult(op_c,mult(unit,op_c)),unit),
inference(unit_resolution,[status(thm)],[974,60]) ).
tff(976,plain,
mult(mult(op_c,mult(unit,op_c)),unit) = mult(op_c,mult(unit,mult(op_c,unit))),
inference(symmetry,[status(thm)],[975]) ).
tff(977,plain,
mult(mult(op_c,op_c),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(mult(op_c,mult(unit,op_c)),unit),
inference(monotonicity,[status(thm)],[487,205]) ).
tff(978,plain,
mult(mult(op_c,op_c),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(op_c,op_c),
inference(transitivity,[status(thm)],[977,976,973]) ).
tff(979,plain,
mult(a,mult(mult(op_c,op_c),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(a,mult(op_c,op_c)),
inference(monotonicity,[status(thm)],[978]) ).
tff(980,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(op_c,op_c),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(mult(op_c,op_c),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(981,plain,
mult(a,mult(mult(op_c,op_c),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(mult(op_c,op_c),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[980,60]) ).
tff(982,plain,
mult(mult(a,mult(mult(op_c,op_c),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(a,mult(mult(op_c,op_c),mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))),
inference(symmetry,[status(thm)],[981]) ).
tff(983,plain,
mult(unit,mult(op_c,a)) = mult(a,op_c),
inference(transitivity,[status(thm)],[825,289,287,29]) ).
tff(984,plain,
mult(op_c,mult(unit,mult(op_c,a))) = mult(op_c,mult(a,op_c)),
inference(monotonicity,[status(thm)],[983]) ).
tff(985,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(unit,mult(op_c,a))) = mult(mult(op_c,mult(unit,op_c)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(986,plain,
mult(op_c,mult(unit,mult(op_c,a))) = mult(mult(op_c,mult(unit,op_c)),a),
inference(unit_resolution,[status(thm)],[985,60]) ).
tff(987,plain,
mult(mult(op_c,mult(unit,op_c)),a) = mult(op_c,mult(unit,mult(op_c,a))),
inference(symmetry,[status(thm)],[986]) ).
tff(988,plain,
mult(mult(op_c,op_c),a) = mult(mult(op_c,mult(unit,op_c)),a),
inference(monotonicity,[status(thm)],[487]) ).
tff(989,plain,
mult(mult(op_c,op_c),a) = mult(op_c,mult(a,op_c)),
inference(transitivity,[status(thm)],[988,987,984]) ).
tff(990,plain,
mult(a,mult(mult(op_c,op_c),a)) = mult(a,mult(op_c,mult(a,op_c))),
inference(monotonicity,[status(thm)],[989]) ).
tff(991,plain,
mult(a,mult(op_c,mult(a,op_c))) = mult(a,mult(mult(op_c,op_c),a)),
inference(symmetry,[status(thm)],[990]) ).
tff(992,plain,
mult(op_c,mult(mult(a,mult(unit,a)),op_c)) = mult(a,mult(mult(op_c,op_c),a)),
inference(transitivity,[status(thm)],[472,470,466,991]) ).
tff(993,plain,
mult(mult(op_c,mult(mult(a,mult(unit,a)),op_c)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(mult(a,mult(mult(op_c,op_c),a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[992]) ).
tff(994,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(op_c,mult(mult(a,mult(unit,a)),op_c)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(995,plain,
mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(op_c,mult(mult(a,mult(unit,a)),op_c)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[994,60]) ).
tff(996,plain,
mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(op_c,mult(op_c,a)),
inference(transitivity,[status(thm)],[995,993,982,979,505,502,463,972]) ).
tff(997,plain,
ld(op_c,mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))))) = ld(op_c,mult(op_c,mult(op_c,a))),
inference(monotonicity,[status(thm)],[996]) ).
tff(998,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))))) = mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(999,plain,
ld(op_c,mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))))) = mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),
inference(unit_resolution,[status(thm)],[998,7]) ).
tff(1000,plain,
mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = ld(op_c,mult(op_c,mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))))),
inference(symmetry,[status(thm)],[999]) ).
tff(1001,plain,
mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(a,op_c),
inference(transitivity,[status(thm)],[1000,997,971,29]) ).
tff(1002,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,op_c)),
inference(monotonicity,[status(thm)],[1001]) ).
tff(1003,plain,
mult(unit,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(unit,unit),
inference(monotonicity,[status(thm)],[205]) ).
tff(1004,plain,
mult(unit,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = unit,
inference(transitivity,[status(thm)],[1003,141]) ).
tff(1005,plain,
mult(a,mult(unit,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(a,unit),
inference(monotonicity,[status(thm)],[1004]) ).
tff(1006,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(unit,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(unit,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1007,plain,
mult(a,mult(unit,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(a,mult(unit,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[1006,60]) ).
tff(1008,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(a,mult(unit,mult(a,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))),
inference(symmetry,[status(thm)],[1007]) ).
tff(1009,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))) = mult(mult(a,mult(unit,a)),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[660]) ).
tff(1010,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))) = a,
inference(transitivity,[status(thm)],[1009,1008,1005,97]) ).
tff(1011,plain,
mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[1010]) ).
tff(1012,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1013,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[1012,60]) ).
tff(1014,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),unit),
inference(monotonicity,[status(thm)],[269]) ).
tff(1015,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),unit) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(symmetry,[status(thm)],[1014]) ).
tff(1016,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),unit) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),unit),
inference(symmetry,[status(thm)],[691]) ).
tff(1017,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),unit))),
inference(symmetry,[status(thm)],[687]) ).
tff(1018,plain,
mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))) = mult(a,rd(unit,mult(a,mult(unit,a)))),
inference(transitivity,[status(thm)],[315,708,239]) ).
tff(1019,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),
inference(monotonicity,[status(thm)],[120,1018]) ).
tff(1020,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(transitivity,[status(thm)],[1019,1017,689,1016,1015]) ).
tff(1021,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))))),
inference(monotonicity,[status(thm)],[1020]) ).
tff(1022,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(symmetry,[status(thm)],[1019]) ).
tff(1023,plain,
mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a)))))) = mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),
inference(monotonicity,[status(thm)],[1022]) ).
tff(1024,plain,
mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a)))))) = mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),
inference(transitivity,[status(thm)],[1023,1021,1013,1011,317,316]) ).
tff(1025,plain,
mult(op_c,mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))))) = mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[1024]) ).
tff(1026,plain,
mult(mult(a,mult(unit,a)),mult(op_c,mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a)))))))) = mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),
inference(monotonicity,[status(thm)],[1025]) ).
tff(1027,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(op_c,mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a)))))))) = mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1028,plain,
mult(mult(a,mult(unit,a)),mult(op_c,mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a)))))))) = mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a)))))),
inference(unit_resolution,[status(thm)],[1027,60]) ).
tff(1029,plain,
mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a)))))) = mult(mult(a,mult(unit,a)),mult(op_c,mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a)))))))),
inference(symmetry,[status(thm)],[1028]) ).
tff(1030,plain,
mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a)))))),
inference(monotonicity,[status(thm)],[1019]) ).
tff(1031,plain,
mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),
inference(transitivity,[status(thm)],[1030,1029,1026]) ).
tff(1032,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))),
inference(monotonicity,[status(thm)],[1031]) ).
tff(1033,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1034,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(unit_resolution,[status(thm)],[1033,60]) ).
tff(1035,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))))),
inference(symmetry,[status(thm)],[1034]) ).
tff(1036,plain,
mult(op_c,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))) = mult(op_c,unit),
inference(monotonicity,[status(thm)],[80]) ).
tff(1037,plain,
mult(op_c,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))) = op_c,
inference(transitivity,[status(thm)],[1036,284]) ).
tff(1038,plain,
mult(mult(a,mult(unit,a)),mult(op_c,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(a,mult(unit,a)),op_c),
inference(monotonicity,[status(thm)],[1037]) ).
tff(1039,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(op_c,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1040,plain,
mult(mult(a,mult(unit,a)),mult(op_c,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)),
inference(unit_resolution,[status(thm)],[1039,60]) ).
tff(1041,plain,
mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)) = mult(mult(a,mult(unit,a)),mult(op_c,mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(symmetry,[status(thm)],[1040]) ).
tff(1042,plain,
mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),ld(mult(a,mult(unit,a)),unit)),
inference(monotonicity,[status(thm)],[161]) ).
tff(1043,plain,
mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))) = mult(mult(a,mult(unit,a)),op_c),
inference(transitivity,[status(thm)],[1042,1041,1038]) ).
tff(1044,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)),
inference(monotonicity,[status(thm)],[120,1043]) ).
tff(1045,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(symmetry,[status(thm)],[1044]) ).
tff(1046,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),op_c)) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),op_c)))),
inference(symmetry,[status(thm)],[406]) ).
tff(1047,plain,
op_c = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),op_c)),
inference(symmetry,[status(thm)],[401]) ).
tff(1048,plain,
op_c = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),
inference(transitivity,[status(thm)],[1047,1046,408,1045]) ).
tff(1049,plain,
mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(op_c,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[1048]) ).
tff(1050,plain,
mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit)))) = mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(transitivity,[status(thm)],[1049,1035,1032,1002,132,129,11,969,968,966]) ).
tff(1051,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))),
inference(monotonicity,[status(thm)],[1050]) ).
tff(1052,plain,
mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),
inference(symmetry,[status(thm)],[1051]) ).
tff(1053,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1054,plain,
ld(a,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))))) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))),
inference(unit_resolution,[status(thm)],[1053,7]) ).
tff(1055,plain,
mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) = mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(monotonicity,[status(thm)],[366]) ).
tff(1056,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))))) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1057,plain,
mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))))) = mult(mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(unit_resolution,[status(thm)],[1056,60]) ).
tff(1058,plain,
mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))))) = mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a)))),
inference(transitivity,[status(thm)],[1057,1055]) ).
tff(1059,plain,
ld(a,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))))) = ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))),
inference(monotonicity,[status(thm)],[1058]) ).
tff(1060,plain,
ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))) = ld(a,mult(a,mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))))),
inference(symmetry,[status(thm)],[1059]) ).
tff(1061,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1062,plain,
ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(unit_resolution,[status(thm)],[1061,7]) ).
tff(1063,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))) = ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))))),
inference(symmetry,[status(thm)],[1062]) ).
tff(1064,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(op_c,mult(a,mult(unit,a))),a))),
inference(symmetry,[status(thm)],[370]) ).
tff(1065,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)))),
inference(symmetry,[status(thm)],[268]) ).
tff(1066,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))))),
inference(symmetry,[status(thm)],[264]) ).
tff(1067,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))),
inference(symmetry,[status(thm)],[262]) ).
tff(1068,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))))),
inference(symmetry,[status(thm)],[259]) ).
tff(1069,plain,
mult(unit,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),
inference(symmetry,[status(thm)],[257]) ).
tff(1070,plain,
mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)) = mult(unit,mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),
inference(symmetry,[status(thm)],[256]) ).
tff(1071,plain,
mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)) = mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),
inference(transitivity,[status(thm)],[1070,1069,1068,1067,1066,1065,1064,1063,1060,1054,1052]) ).
tff(1072,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d)))) = mult(mult(mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(unit,mult(a,ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(op_c,a)),mult(op_c,op_d))),
inference(monotonicity,[status(thm)],[1071,953]) ).
tff(1073,plain,
mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(transitivity,[status(thm)],[1072,963,960,885,714,712]) ).
tff(1074,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))))) = mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[1073]) ).
tff(1075,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(a,mult(a,mult(unit,a))),mult(mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit)),mult(mult(a,mult(op_c,a)),mult(unit,mult(op_c,op_d))))),
inference(symmetry,[status(thm)],[1074]) ).
tff(1076,plain,
mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a))))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[619]) ).
tff(1077,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a))))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1078,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(unit,a))))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(unit_resolution,[status(thm)],[1077,60]) ).
tff(1079,plain,
mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(unit,mult(op_c,mult(unit,ld(op_c,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[124,763]) ).
tff(1080,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(mult(op_c,op_c),op_d),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1081,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),a)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(unit_resolution,[status(thm)],[1080,60]) ).
tff(1082,plain,
mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(mult(op_c,op_c),op_d),a),
inference(transitivity,[status(thm)],[1081,1079,757,755,754]) ).
tff(1083,plain,
mult(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(a,mult(mult(mult(op_c,op_c),op_d),a)),
inference(monotonicity,[status(thm)],[1082]) ).
tff(1084,plain,
mult(a,mult(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[1083]) ).
tff(1085,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(a,mult(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(a,mult(a,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1086,plain,
mult(a,mult(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(a,mult(a,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(unit_resolution,[status(thm)],[1085,60]) ).
tff(1087,plain,
mult(mult(a,mult(a,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(a,mult(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))),
inference(symmetry,[status(thm)],[1086]) ).
tff(1088,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(a,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[343]) ).
tff(1089,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(transitivity,[status(thm)],[1088,1087,1084,858,861]) ).
tff(1090,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[1089]) ).
tff(1091,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(symmetry,[status(thm)],[1090]) ).
tff(1092,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[864]) ).
tff(1093,plain,
ld(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = ld(a,mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))),
inference(symmetry,[status(thm)],[785]) ).
tff(1094,plain,
mult(mult(mult(op_c,op_c),op_d),a) = ld(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[783]) ).
tff(1095,plain,
mult(mult(mult(op_c,op_c),op_d),a) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(transitivity,[status(thm)],[1094,1093,787,1092,1091]) ).
tff(1096,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))),
inference(monotonicity,[status(thm)],[1095]) ).
tff(1097,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(transitivity,[status(thm)],[1096,1078,1076]) ).
tff(1098,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[1097]) ).
tff(1099,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[1098]) ).
tff(1100,plain,
mult(unit,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))) = mult(unit,unit),
inference(monotonicity,[status(thm)],[99]) ).
tff(1101,plain,
mult(unit,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a)))) = mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)),
inference(transitivity,[status(thm)],[1100,141,86]) ).
tff(1102,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(unit,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(monotonicity,[status(thm)],[1101]) ).
tff(1103,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(rd(unit,mult(a,mult(unit,a))),mult(unit,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1104,plain,
mult(rd(unit,mult(a,mult(unit,a))),mult(unit,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))),
inference(unit_resolution,[status(thm)],[1103,60]) ).
tff(1105,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))) = mult(rd(unit,mult(a,mult(unit,a))),mult(unit,mult(rd(unit,mult(a,mult(unit,a))),mult(a,mult(unit,a))))),
inference(symmetry,[status(thm)],[1104]) ).
tff(1106,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a))) = mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),
inference(transitivity,[status(thm)],[1105,1102]) ).
tff(1107,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))) = mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit)))),
inference(monotonicity,[status(thm)],[1106]) ).
tff(1108,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))) = unit,
inference(transitivity,[status(thm)],[1107,149,153,80]) ).
tff(1109,plain,
mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(unit,mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[1108,767]) ).
tff(1110,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1111,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[1110,60]) ).
tff(1112,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a))),
inference(transitivity,[status(thm)],[1111,1109,771,773,767]) ).
tff(1113,plain,
mult(unit,mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(unit,mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[1112]) ).
tff(1114,plain,
mult(unit,mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(a,mult(mult(mult(op_c,op_c),op_d),a)),
inference(transitivity,[status(thm)],[1113,771,773]) ).
tff(1115,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))) = mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[1114]) ).
tff(1116,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1117,plain,
mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(unit_resolution,[status(thm)],[1116,60]) ).
tff(1118,plain,
mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(a,mult(unit,a)),mult(unit,mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))),
inference(symmetry,[status(thm)],[1117]) ).
tff(1119,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1120,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(unit_resolution,[status(thm)],[1119,7]) ).
tff(1121,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))),mult(mult(mult(op_c,op_c),op_d),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1122,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))),mult(mult(mult(op_c,op_c),op_d),a)),
inference(unit_resolution,[status(thm)],[1121,60]) ).
tff(1123,plain,
mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))),mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[1122]) ).
tff(1124,plain,
mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))),mult(mult(mult(op_c,op_c),op_d),a)) = mult(a,mult(mult(mult(op_c,op_c),op_d),a)),
inference(monotonicity,[status(thm)],[1010]) ).
tff(1125,plain,
mult(a,mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(a,mult(unit,a)))),mult(mult(mult(op_c,op_c),op_d),a)),
inference(symmetry,[status(thm)],[1124]) ).
tff(1126,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(transitivity,[status(thm)],[1111,1109,771,773,1125,1123]) ).
tff(1127,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[1126]) ).
tff(1128,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))),
inference(symmetry,[status(thm)],[1127]) ).
tff(1129,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1130,plain,
ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[1129,7]) ).
tff(1131,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) = ld(mult(a,mult(unit,a)),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))))),
inference(symmetry,[status(thm)],[1130]) ).
tff(1132,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[241,863]) ).
tff(1133,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(a,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[1132]) ).
tff(1134,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1135,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(unit_resolution,[status(thm)],[1134,60]) ).
tff(1136,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[784]) ).
tff(1137,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))),
inference(symmetry,[status(thm)],[1136]) ).
tff(1138,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(transitivity,[status(thm)],[1137,1135,1133,1131,1128,1120]) ).
tff(1139,plain,
mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(unit,rd(unit,mult(a,mult(unit,a))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[1138]) ).
tff(1140,plain,
mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(transitivity,[status(thm)],[1139,1118,1115]) ).
tff(1141,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[375,1140]) ).
tff(1142,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(symmetry,[status(thm)],[1141]) ).
tff(1143,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1144,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(unit_resolution,[status(thm)],[1143,60]) ).
tff(1145,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(unit,mult(a,mult(unit,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[165,767]) ).
tff(1146,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1147,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(unit_resolution,[status(thm)],[1146,60]) ).
tff(1148,plain,
mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(monotonicity,[status(thm)],[261]) ).
tff(1149,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1150,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(unit_resolution,[status(thm)],[1149,60]) ).
tff(1151,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(a,mult(mult(mult(op_c,op_c),op_d),a)),
inference(transitivity,[status(thm)],[1147,1145,771,773]) ).
tff(1152,plain,
mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[1151]) ).
tff(1153,plain,
mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))),
inference(symmetry,[status(thm)],[1152]) ).
tff(1154,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(mult(a,mult(unit,a)),mult(unit,mult(a,mult(unit,a)))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))))),
inference(monotonicity,[status(thm)],[1153]) ).
tff(1155,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(a,mult(mult(mult(op_c,op_c),op_d),a)),
inference(transitivity,[status(thm)],[1154,1150,1148,1147,1145,771,773]) ).
tff(1156,plain,
mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))),
inference(monotonicity,[status(thm)],[1155]) ).
tff(1157,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[1156]) ).
tff(1158,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(mult(a,mult(unit,a)),mult(a,mult(mult(mult(op_c,op_c),op_d),a)))))),
inference(symmetry,[status(thm)],[1157]) ).
tff(1159,plain,
mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(op_c,op_c),op_d),a))),
inference(transitivity,[status(thm)],[1158,1144,1142,1099]) ).
tff(1160,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))) = mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(monotonicity,[status(thm)],[1159]) ).
tff(1161,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(a,mult(a,mult(unit,a))),mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(op_c,mult(a,mult(mult(mult(op_c,op_c),op_d),a))))),
inference(symmetry,[status(thm)],[1160]) ).
tff(1162,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))),mult(mult(mult(op_c,op_c),op_d),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1163,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(op_c,op_c),op_d),a)))) = mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))),mult(mult(mult(op_c,op_c),op_d),a)),
inference(unit_resolution,[status(thm)],[1162,60]) ).
tff(1164,plain,
mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))),mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(op_c,op_c),op_d),a)))),
inference(symmetry,[status(thm)],[1163]) ).
tff(1165,plain,
mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))) = mult(a,mult(op_c,a)),
inference(transitivity,[status(thm)],[378,718,385]) ).
tff(1166,plain,
mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))),mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)),
inference(monotonicity,[status(thm)],[1165]) ).
tff(1167,plain,
mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(mult(a,mult(a,mult(unit,a))),mult(mult(mult(rd(unit,mult(a,mult(unit,a))),mult(mult(a,mult(unit,a)),ld(mult(a,mult(unit,a)),unit))),mult(unit,mult(rd(op_c,mult(a,mult(unit,a))),unit))),mult(a,mult(a,mult(unit,a))))),mult(mult(mult(op_c,op_c),op_d),a)),
inference(symmetry,[status(thm)],[1166]) ).
tff(1168,plain,
mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a)) = mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d))),
inference(transitivity,[status(thm)],[1167,1164,1161,1075,677,391,389]) ).
tff(1169,plain,
ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(a,mult(mult(op_c,op_c),op_d)))),
inference(monotonicity,[status(thm)],[1168]) ).
tff(1170,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(mult(op_c,op_c),op_d),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1171,plain,
ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))) = mult(mult(mult(op_c,op_c),op_d),a),
inference(unit_resolution,[status(thm)],[1170,7]) ).
tff(1172,plain,
mult(mult(mult(op_c,op_c),op_d),a) = ld(mult(a,mult(op_c,a)),mult(mult(a,mult(op_c,a)),mult(mult(mult(op_c,op_c),op_d),a))),
inference(symmetry,[status(thm)],[1171]) ).
tff(1173,plain,
mult(mult(mult(op_c,op_c),op_d),a) = mult(a,mult(mult(op_c,op_c),op_d)),
inference(transitivity,[status(thm)],[1172,1169,9]) ).
tff(1174,plain,
( ( mult(mult(mult(op_c,op_c),op_d),a) != mult(a,mult(mult(op_c,op_c),op_d)) )
<=> ( mult(mult(mult(op_c,op_c),op_d),a) != mult(a,mult(mult(op_c,op_c),op_d)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1175,axiom,
mult(mult(mult(op_c,op_c),op_d),a) != mult(a,mult(mult(op_c,op_c),op_d)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(1176,plain,
mult(mult(mult(op_c,op_c),op_d),a) != mult(a,mult(mult(op_c,op_c),op_d)),
inference(modus_ponens,[status(thm)],[1175,1174]) ).
tff(1177,plain,
$false,
inference(unit_resolution,[status(thm)],[1176,1173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP681-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 20:10:01 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 100.38/64.50 % SZS status Unsatisfiable
% 100.38/64.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------