%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP660-12 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:23 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 95
% Syntax : Number of formulae : 426 ( 336 unt; 0 typ; 0 def)
% Number of atoms : 524 ( 519 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 179 ( 85 ~; 81 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 276 ( 267 !; 0 ?; 276 :)
% Comments :
%------------------------------------------------------------------------------
tff(x0_type,type,
x0: $i ).
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(x1_type,type,
x1: $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
tff(5,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x0,x1),x1) = x0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
rd(mult(x0,x1),x1) = x0,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i] :
refl(( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
tff(14,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1)))) = mult(x1,rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ld(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1)))) = mult(x1,rd(x1,x1)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1))),
inference(unit_resolution,[status(thm)],[19,7]) ).
tff(21,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
<=> ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
tff(25,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1)),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1)),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
mult(rd(x1,x1),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1)),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
rd(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = x1,
inference(unit_resolution,[status(thm)],[31,7]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1))))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1))))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[33,16]) ).
tff(35,plain,
^ [B: $i,A: $i] :
refl(( ( mult(rd(A,B),B) = A )
<=> ( mult(rd(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(36,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)],[35]) ).
tff(37,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(38,axiom,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
tff(39,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(x1,x1),x1) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
mult(rd(x1,x1),x1) = x1,
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
x1 = mult(rd(x1,x1),x1),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x1,x1),x1) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
rd(mult(x1,x1),x1) = x1,
inference(unit_resolution,[status(thm)],[45,7]) ).
tff(47,plain,
mult(rd(x1,x1),mult(rd(x1,x1),x1)) = mult(rd(x1,x1),x1),
inference(monotonicity,[status(thm)],[43]) ).
tff(48,plain,
mult(rd(x1,x1),x1) = mult(rd(x1,x1),mult(rd(x1,x1),x1)),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
x1 = mult(rd(x1,x1),mult(rd(x1,x1),x1)),
inference(transitivity,[status(thm)],[44,48]) ).
tff(50,plain,
mult(x1,x1) = mult(x1,mult(rd(x1,x1),mult(rd(x1,x1),x1))),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
mult(x1,mult(rd(x1,x1),mult(rd(x1,x1),x1))) = mult(x1,x1),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1) = mult(x1,mult(rd(x1,x1),mult(rd(x1,x1),x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1) = mult(x1,mult(rd(x1,x1),mult(rd(x1,x1),x1))),
inference(unit_resolution,[status(thm)],[52,27]) ).
tff(54,plain,
mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1) = mult(x1,x1),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
rd(mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1),x1) = rd(mult(x1,x1),x1),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1),x1) = mult(mult(x1,rd(x1,x1)),rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
rd(mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1),x1) = mult(mult(x1,rd(x1,x1)),rd(x1,x1)),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
mult(mult(x1,rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1),x1),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
mult(mult(rd(x1,x1),x1),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[43]) ).
tff(60,plain,
mult(mult(mult(rd(x1,x1),x1),rd(x1,x1)),rd(x1,x1)) = mult(mult(x1,rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),x1),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
mult(mult(mult(rd(x1,x1),x1),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[61,27]) ).
tff(63,plain,
mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),x1),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),x1),
inference(transitivity,[status(thm)],[63,60,58,55,46,44]) ).
tff(65,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),x1)),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
ld(rd(x1,x1),mult(rd(x1,x1),x1)) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1))))),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),x1)) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
ld(rd(x1,x1),mult(rd(x1,x1),x1)) = x1,
inference(unit_resolution,[status(thm)],[67,16]) ).
tff(69,plain,
x1 = ld(rd(x1,x1),mult(rd(x1,x1),x1)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x1,mult(x1,x1)) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
ld(x1,mult(x1,x1)) = x1,
inference(unit_resolution,[status(thm)],[70,16]) ).
tff(72,plain,
mult(x1,mult(rd(x1,x1),rd(x1,x1))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1))))),
inference(symmetry,[status(thm)],[34]) ).
tff(73,plain,
mult(x1,mult(rd(x1,x1),rd(x1,x1))) = x1,
inference(transitivity,[status(thm)],[72,65,68]) ).
tff(74,plain,
mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = x1,
inference(transitivity,[status(thm)],[74,72,65,68]) ).
tff(76,plain,
mult(mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),x1) = mult(x1,x1),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),x1) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
mult(mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),x1) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))),
inference(unit_resolution,[status(thm)],[77,27]) ).
tff(79,plain,
mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) = mult(mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),x1),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) = mult(x1,x1),
inference(transitivity,[status(thm)],[79,76]) ).
tff(81,plain,
ld(x1,mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)))) = ld(x1,mult(x1,x1)),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x1,mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
ld(x1,mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),
inference(unit_resolution,[status(thm)],[82,16]) ).
tff(84,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) = ld(x1,mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(rd(x1,x1),rd(x1,x1)),x1),
inference(monotonicity,[status(thm)],[73]) ).
tff(86,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[87,27]) ).
tff(89,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[88,86,84,81,71,69,66,34]) ).
tff(90,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),
inference(unit_resolution,[status(thm)],[91,7]) ).
tff(93,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1) = rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1) = x1,
inference(transitivity,[status(thm)],[93,90,32]) ).
tff(95,plain,
rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),x1) = rd(x1,x1),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),x1) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),x1) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[96,7]) ).
tff(98,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),x1),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = rd(x1,x1),
inference(transitivity,[status(thm)],[98,95]) ).
tff(100,plain,
mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[101,16]) ).
tff(103,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[103,27]) ).
tff(105,plain,
mult(mult(x1,rd(x1,x1)),rd(x1,x1)) = x1,
inference(transitivity,[status(thm)],[58,55,46]) ).
tff(106,plain,
mult(rd(x1,x1),mult(mult(x1,rd(x1,x1)),rd(x1,x1))) = mult(rd(x1,x1),x1),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
mult(rd(x1,x1),mult(mult(x1,rd(x1,x1)),rd(x1,x1))) = x1,
inference(transitivity,[status(thm)],[106,43]) ).
tff(108,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,rd(x1,x1)),rd(x1,x1)))) = mult(rd(x1,x1),x1),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,rd(x1,x1)),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,rd(x1,x1)),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[109,27]) ).
tff(111,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)) = x1,
inference(transitivity,[status(thm)],[110,108,43]) ).
tff(112,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[113,27]) ).
tff(115,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))) = x1,
inference(transitivity,[status(thm)],[115,112,72,65,68]) ).
tff(117,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = x1,
inference(transitivity,[status(thm)],[117,72,65,68]) ).
tff(119,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
mult(x1,mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(transitivity,[status(thm)],[115,112,120,104]) ).
tff(122,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))))) = ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
mult(x1,mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[112]) ).
tff(124,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),
inference(transitivity,[status(thm)],[84,81,71,69,66,34,123,114]) ).
tff(125,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) = ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))))),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),x1),
inference(unit_resolution,[status(thm)],[126,16]) ).
tff(128,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),x1) = ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1)))) = x1,
inference(transitivity,[status(thm)],[63,60,58,55,46]) ).
tff(130,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),x1),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[131,27]) ).
tff(133,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)),
inference(transitivity,[status(thm)],[132,130,128,125,122,102,100]) ).
tff(134,plain,
mult(rd(x1,x1),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))) = mult(rd(x1,x1),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),x1),
inference(monotonicity,[status(thm)],[105]) ).
tff(137,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),rd(x1,x1))) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)),
inference(transitivity,[status(thm)],[136,128,125,122,102,100]) ).
tff(138,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[139,27]) ).
tff(141,plain,
mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1))),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1)),rd(x1,x1)),rd(x1,x1)),
inference(transitivity,[status(thm)],[140,138,135,30]) ).
tff(142,plain,
rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1)),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
rd(mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1)),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
rd(mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),
inference(unit_resolution,[status(thm)],[144,7]) ).
tff(146,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),
inference(unit_resolution,[status(thm)],[146,7]) ).
tff(148,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),rd(x1,x1)),
inference(monotonicity,[status(thm)],[99]) ).
tff(149,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[149,27]) ).
tff(151,plain,
mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),rd(x1,x1)),
inference(transitivity,[status(thm)],[150,148]) ).
tff(152,plain,
rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = rd(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
rd(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)) = rd(x1,x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
rd(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)) = rd(x1,x1),
inference(unit_resolution,[status(thm)],[154,7]) ).
tff(156,plain,
rd(x1,x1) = rd(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
rd(x1,x1) = mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),
inference(transitivity,[status(thm)],[156,153,147]) ).
tff(158,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))))) = mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))))) = mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[158,16]) ).
tff(160,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,plain,
mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[160,27]) ).
tff(162,plain,
mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[43]) ).
tff(163,plain,
mult(x1,mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
x1 = mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[69,66,34,163]) ).
tff(165,plain,
mult(x1,rd(x1,x1)) = mult(mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
mult(mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
mult(mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[167,27]) ).
tff(169,plain,
mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))) = mult(x1,rd(x1,x1)),
inference(transitivity,[status(thm)],[169,166]) ).
tff(171,plain,
mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)),
inference(monotonicity,[status(thm)],[171]) ).
tff(173,plain,
mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[174,16]) ).
tff(176,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),x1) = mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),
inference(transitivity,[status(thm)],[128,125,175]) ).
tff(177,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),rd(x1,x1)) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(x1,rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(x1,rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[178,27]) ).
tff(180,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(x1,rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),rd(x1,x1)),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(x1,rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)))),
inference(transitivity,[status(thm)],[180,177,173,161]) ).
tff(182,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(x1,rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))))),
inference(monotonicity,[status(thm)],[181]) ).
tff(183,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(x1,rd(x1,x1))))) = mult(rd(x1,x1),mult(x1,rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(x1,rd(x1,x1))))) = mult(rd(x1,x1),mult(x1,rd(x1,x1))),
inference(unit_resolution,[status(thm)],[183,16]) ).
tff(185,plain,
mult(rd(x1,x1),mult(x1,rd(x1,x1))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(x1,rd(x1,x1))))),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = mult(x1,rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
rd(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(unit_resolution,[status(thm)],[186,7]) ).
tff(188,plain,
rd(mult(x1,x1),x1) = rd(mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1),x1),
inference(symmetry,[status(thm)],[55]) ).
tff(189,plain,
x1 = rd(mult(x1,x1),x1),
inference(symmetry,[status(thm)],[46]) ).
tff(190,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)) = mult(mult(x1,rd(x1,x1)),rd(x1,x1)),
inference(transitivity,[status(thm)],[110,108,43,189,188,57]) ).
tff(191,plain,
rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),
inference(unit_resolution,[status(thm)],[192,7]) ).
tff(194,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))) = rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)) = mult(mult(x1,rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[170]) ).
tff(196,plain,
mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)) = x1,
inference(transitivity,[status(thm)],[195,58,55,46]) ).
tff(197,plain,
mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[198,27]) ).
tff(200,plain,
mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(x1,rd(x1,x1)),
inference(transitivity,[status(thm)],[200,197]) ).
tff(202,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[203,27]) ).
tff(205,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,rd(x1,x1)),
inference(transitivity,[status(thm)],[204,202,194,191,187]) ).
tff(206,plain,
mult(rd(x1,x1),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(208,plain,
mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[207,27]) ).
tff(209,plain,
mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))),
inference(transitivity,[status(thm)],[208,206,185,182,159]) ).
tff(210,plain,
rd(mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))),
inference(monotonicity,[status(thm)],[209,157]) ).
tff(211,plain,
rd(mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))) = rd(mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
rd(mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[212,7]) ).
tff(214,plain,
mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))) = rd(mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1))),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[215,16]) ).
tff(217,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[116]) ).
tff(218,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(219,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[218,27]) ).
tff(220,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))) = mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),
inference(transitivity,[status(thm)],[220,217,165,168]) ).
tff(222,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(224,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[223,16]) ).
tff(225,plain,
mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1)),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),
inference(transitivity,[status(thm)],[29,134,225,222,216,214,211,145]) ).
tff(227,plain,
rd(mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1)),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[226]) ).
tff(228,plain,
rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),x1)),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(230,plain,
rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[229,7]) ).
tff(231,plain,
mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(233,plain,
rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[232,7]) ).
tff(234,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[204]) ).
tff(235,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),
inference(symmetry,[status(thm)],[202]) ).
tff(236,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[205]) ).
tff(237,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))) = mult(x1,rd(x1,x1)),
inference(transitivity,[status(thm)],[236,194,191,187]) ).
tff(238,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[239,27]) ).
tff(241,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(monotonicity,[status(thm)],[99]) ).
tff(242,plain,
mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[243,240,238,235,234]) ).
tff(245,plain,
rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[99]) ).
tff(248,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[247]) ).
tff(249,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[249,27]) ).
tff(251,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[250,248,235,234]) ).
tff(252,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[253,7]) ).
tff(255,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(257,plain,
rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),rd(x1,x1)),
inference(unit_resolution,[status(thm)],[256,7]) ).
tff(258,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[148]) ).
tff(259,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(260,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[259,27]) ).
tff(261,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[260,258]) ).
tff(262,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[261]) ).
tff(263,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(264,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[263,7]) ).
tff(265,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),rd(x1,x1)),
inference(transitivity,[status(thm)],[265,262,257]) ).
tff(267,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[266]) ).
tff(268,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(269,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[268,16]) ).
tff(270,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(271,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[270,27]) ).
tff(272,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) = x1,
inference(transitivity,[status(thm)],[84,81,71]) ).
tff(273,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[274]) ).
tff(276,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),x1) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)),
inference(transitivity,[status(thm)],[128,125,122,102,100]) ).
tff(277,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) = mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))),
inference(monotonicity,[status(thm)],[99,276]) ).
tff(278,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),
inference(transitivity,[status(thm)],[277,225,222,216]) ).
tff(279,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(281,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[280,27]) ).
tff(282,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(transitivity,[status(thm)],[282,279,275,271]) ).
tff(284,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))))) = ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))),
inference(monotonicity,[status(thm)],[283]) ).
tff(285,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(286,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[285,16]) ).
tff(287,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))))),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),
inference(monotonicity,[status(thm)],[267]) ).
tff(289,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(290,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[289,16]) ).
tff(291,plain,
mult(x1,rd(x1,x1)) = mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[197]) ).
tff(292,plain,
mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),
inference(transitivity,[status(thm)],[169,166,291,199]) ).
tff(293,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(symmetry,[status(thm)],[216]) ).
tff(295,plain,
mult(rd(x1,x1),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[208]) ).
tff(296,plain,
mult(rd(x1,x1),mult(x1,rd(x1,x1))) = mult(rd(x1,x1),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[206]) ).
tff(297,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))) = mult(x1,rd(x1,x1)),
inference(transitivity,[status(thm)],[194,191,187]) ).
tff(298,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1)))) = mult(rd(x1,x1),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(300,plain,
mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[299,27]) ).
tff(301,plain,
mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),
inference(transitivity,[status(thm)],[300,298,296,295]) ).
tff(302,plain,
rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[301]) ).
tff(303,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(304,plain,
rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1),
inference(unit_resolution,[status(thm)],[303,7]) ).
tff(305,plain,
mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1) = rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1) = mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1))),
inference(transitivity,[status(thm)],[305,302,210,213,294,293,290,275,271,288,287,284,269,267,255,252,246,233,231,228,143,20]) ).
tff(307,plain,
ld(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1)) = ld(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(x1,rd(x1,x1)))),
inference(monotonicity,[status(thm)],[306]) ).
tff(308,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1)) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(309,plain,
ld(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1)) = x1,
inference(unit_resolution,[status(thm)],[308,16]) ).
tff(310,plain,
x1 = ld(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),x1)),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
x1 = mult(x1,rd(x1,x1)),
inference(transitivity,[status(thm)],[310,307,18]) ).
tff(312,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(313,plain,
rd(mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),
inference(unit_resolution,[status(thm)],[312,7]) ).
tff(314,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(315,plain,
rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),
inference(unit_resolution,[status(thm)],[314,7]) ).
tff(316,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = rd(x1,x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(317,plain,
rd(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = rd(x1,x1),
inference(unit_resolution,[status(thm)],[316,7]) ).
tff(318,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(319,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[318,7]) ).
tff(320,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),
inference(transitivity,[status(thm)],[255,252,319]) ).
tff(321,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(transitivity,[status(thm)],[287,284,269,267,255,252,246,233]) ).
tff(322,plain,
rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = rd(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(monotonicity,[status(thm)],[321,320]) ).
tff(323,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(324,plain,
rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),rd(x1,x1)),
inference(unit_resolution,[status(thm)],[323,7]) ).
tff(325,plain,
mult(rd(x1,x1),rd(x1,x1)) = rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[324]) ).
tff(326,plain,
mult(rd(x1,x1),rd(x1,x1)) = rd(x1,x1),
inference(transitivity,[status(thm)],[325,322,317]) ).
tff(327,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(x0,x1)) = mult(rd(x1,x1),mult(x0,x1)),
inference(monotonicity,[status(thm)],[326]) ).
tff(328,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x0,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[327]) ).
tff(329,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x0,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(330,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x0,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[329,27]) ).
tff(331,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x0,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
mult(mult(x0,x1),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(x0,x1),rd(x1,x1)),
inference(monotonicity,[status(thm)],[326]) ).
tff(333,plain,
mult(rd(x1,x1),mult(mult(x0,x1),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[332]) ).
tff(334,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(x0,x1),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(335,plain,
mult(mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(x0,x1),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[334,27]) ).
tff(336,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))) = mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),
inference(transitivity,[status(thm)],[331,328]) ).
tff(337,plain,
mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[336,326]) ).
tff(338,plain,
mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[337,335,333]) ).
tff(339,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),
inference(monotonicity,[status(thm)],[338]) ).
tff(340,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(341,plain,
mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[340,27]) ).
tff(342,plain,
mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),
inference(transitivity,[status(thm)],[341,339,331,328]) ).
tff(343,plain,
rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[342]) ).
tff(344,plain,
rd(mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[343]) ).
tff(345,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x0,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(346,plain,
rd(mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x0,x1)),
inference(unit_resolution,[status(thm)],[345,7]) ).
tff(347,plain,
mult(rd(x1,x1),mult(x0,x1)) = rd(mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
mult(x0,mult(mult(x1,rd(x1,x1)),rd(x1,x1))) = mult(x0,x1),
inference(monotonicity,[status(thm)],[105]) ).
tff(349,plain,
mult(rd(x1,x1),mult(x0,mult(mult(x1,rd(x1,x1)),rd(x1,x1)))) = mult(rd(x1,x1),mult(x0,x1)),
inference(monotonicity,[status(thm)],[348]) ).
tff(350,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),mult(x0,mult(mult(x1,rd(x1,x1)),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(351,plain,
mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),mult(x0,mult(mult(x1,rd(x1,x1)),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[350,27]) ).
tff(352,plain,
mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),
inference(transitivity,[status(thm)],[351,349,347,344,315]) ).
tff(353,plain,
rd(mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[352]) ).
tff(354,plain,
rd(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(356,plain,
rd(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[355,7]) ).
tff(357,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))) = rd(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),mult(x0,x1)),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[336]) ).
tff(359,plain,
mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[358,335,333]) ).
tff(360,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),rd(x1,x1))) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),
inference(monotonicity,[status(thm)],[359]) ).
tff(361,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),rd(x1,x1))),
inference(symmetry,[status(thm)],[360]) ).
tff(362,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),rd(x1,x1)))),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),rd(x1,x1)))) = mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),
inference(symmetry,[status(thm)],[362]) ).
tff(364,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(365,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1)))),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[364,27]) ).
tff(366,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))) = mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),
inference(monotonicity,[status(thm)],[326]) ).
tff(367,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),
inference(monotonicity,[status(thm)],[366]) ).
tff(368,plain,
mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(x0,x1),rd(x1,x1))))),rd(x1,x1)),
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1)))) = mult(rd(x1,x1),mult(x0,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(370,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1)))) = mult(rd(x1,x1),mult(x0,x1)),
inference(unit_resolution,[status(thm)],[369,16]) ).
tff(371,plain,
mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)),
inference(monotonicity,[status(thm)],[326]) ).
tff(372,plain,
mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),mult(x0,x1)),
inference(transitivity,[status(thm)],[371,351,349]) ).
tff(373,plain,
mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1))),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(375,plain,
mult(mult(mult(rd(x1,x1),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[374,27]) ).
tff(376,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),
inference(monotonicity,[status(thm)],[326]) ).
tff(377,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)),
inference(monotonicity,[status(thm)],[376]) ).
tff(378,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(379,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[378,27]) ).
tff(380,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)),
inference(symmetry,[status(thm)],[379]) ).
tff(381,plain,
mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),mult(x0,x1)),
inference(transitivity,[status(thm)],[351,349]) ).
tff(382,plain,
mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1))) = mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1))),
inference(monotonicity,[status(thm)],[381]) ).
tff(383,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1))) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1))),
inference(symmetry,[status(thm)],[382]) ).
tff(384,plain,
mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1))),
inference(transitivity,[status(thm)],[373,383]) ).
tff(385,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)))),
inference(monotonicity,[status(thm)],[326,384]) ).
tff(386,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)),
inference(transitivity,[status(thm)],[385,380,377]) ).
tff(387,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[386]) ).
tff(388,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(389,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[388,27]) ).
tff(390,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)),
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))) = mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1))),
inference(transitivity,[status(thm)],[390,387,375,373]) ).
tff(392,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1)))),
inference(monotonicity,[status(thm)],[391]) ).
tff(393,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(394,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[393,16]) ).
tff(395,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))),
inference(symmetry,[status(thm)],[394]) ).
tff(396,plain,
mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)),
inference(monotonicity,[status(thm)],[326]) ).
tff(397,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))),
inference(monotonicity,[status(thm)],[396]) ).
tff(398,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(399,plain,
mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[398,27]) ).
tff(400,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),rd(x1,x1)))),
inference(monotonicity,[status(thm)],[384]) ).
tff(401,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)),
inference(transitivity,[status(thm)],[400,380,377]) ).
tff(402,plain,
mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[401]) ).
tff(403,plain,
mult(mult(mult(rd(x1,x1),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)),
inference(symmetry,[status(thm)],[402]) ).
tff(404,plain,
mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[375]) ).
tff(405,plain,
mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)),
inference(transitivity,[status(thm)],[404,403]) ).
tff(406,plain,
mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[405]) ).
tff(407,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))) = mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(408,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))) = mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)),
inference(unit_resolution,[status(thm)],[407,16]) ).
tff(409,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1)))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))),
inference(symmetry,[status(thm)],[392]) ).
tff(410,plain,
mult(rd(x1,x1),mult(x0,x1)) = ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1)))),
inference(symmetry,[status(thm)],[370]) ).
tff(411,plain,
mult(rd(x1,x1),mult(x0,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))),
inference(transitivity,[status(thm)],[410,409,394]) ).
tff(412,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))),
inference(monotonicity,[status(thm)],[411]) ).
tff(413,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1))) = mult(x0,x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(414,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1))) = mult(x0,x1),
inference(unit_resolution,[status(thm)],[413,16]) ).
tff(415,plain,
mult(x0,x1) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x0,x1))),
inference(symmetry,[status(thm)],[414]) ).
tff(416,plain,
mult(x0,x1) = mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),
inference(transitivity,[status(thm)],[415,412,408,406,399,397,395,392,370,347,344,315,368,365,363,357,354,313]) ).
tff(417,plain,
rd(mult(x0,x1),x1) = rd(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[416,311]) ).
tff(418,plain,
rd(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(x1,rd(x1,x1))) = rd(mult(x0,x1),x1),
inference(symmetry,[status(thm)],[417]) ).
tff(419,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(x1,rd(x1,x1))) = mult(rd(x1,x1),x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(420,plain,
rd(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(x1,rd(x1,x1))) = mult(rd(x1,x1),x0),
inference(unit_resolution,[status(thm)],[419,7]) ).
tff(421,plain,
mult(rd(x1,x1),x0) = rd(mult(mult(rd(x1,x1),x0),mult(x1,rd(x1,x1))),mult(x1,rd(x1,x1))),
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
mult(rd(x1,x1),x0) = x0,
inference(transitivity,[status(thm)],[421,418,9]) ).
tff(423,plain,
( ( mult(rd(x1,x1),x0) != x0 )
<=> ( mult(rd(x1,x1),x0) != x0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(424,axiom,
mult(rd(x1,x1),x0) != x0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(425,plain,
mult(rd(x1,x1),x0) != x0,
inference(modus_ponens,[status(thm)],[424,423]) ).
tff(426,plain,
$false,
inference(unit_resolution,[status(thm)],[425,422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : GRP660-12 : TPTP v9.0.0. Released v8.1.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 16:47:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% See solution above
% 0.20/0.55 % E exiting
%------------------------------------------------------------------------------