%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP660-14 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:08:24 AM UTC 2025
% Result : Unsatisfiable 0.47s 0.63s
% Output : Proof 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 99
% Syntax : Number of formulae : 512 ( 419 unt; 0 typ; 0 def)
% Number of atoms : 615 ( 609 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 184 ( 86 ~; 82 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 5 ( 5 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 : 297 ( 286 !; 0 ?; 297 :)
% Comments :
%------------------------------------------------------------------------------
tff(x0_type,type,
x0: $i ).
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(x1_type,type,
x1: $i ).
tff(rd_type,type,
rd: ( $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/sandbox2/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,mult(ld(x0,x1),mult(x0,x0))),mult(ld(x0,x1),mult(x0,x0))) = x0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
rd(mult(x0,mult(ld(x0,x1),mult(x0,x0))),mult(ld(x0,x1),mult(x0,x0))) = 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/sandbox2/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(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))) = mult(ld(x0,x1),mult(x0,x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))) = mult(ld(x0,x1),mult(x0,x0)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [B: $i,A: $i] :
refl(( ( mult(rd(A,B),B) = A )
<=> ( mult(rd(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(20,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)],[19]) ).
tff(21,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(22,axiom,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
tff(23,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x0,x1),mult(x0,x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x0,x1),mult(x0,x0)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = ld(x1,x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
rd(mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = ld(x1,x1),
inference(unit_resolution,[status(thm)],[28,7]) ).
tff(30,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1))))) = mult(x1,mult(ld(x1,x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1))))) = mult(x1,mult(ld(x1,x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[30,16]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
tff(36,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)],[35,34]) ).
tff(37,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)],[36]) ).
tff(38,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)],[37,33]) ).
tff(39,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),ld(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
mult(mult(mult(rd(x1,x1),x1),ld(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
^ [B: $i,A: $i] :
refl(( ( mult(A,ld(A,B)) = B )
<=> ( mult(A,ld(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
tff(45,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(x1,ld(x1,x1)) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
mult(x1,ld(x1,x1)) = x1,
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(x1,x1),x1) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
mult(rd(x1,x1),x1) = x1,
inference(unit_resolution,[status(thm)],[50,25]) ).
tff(52,plain,
mult(mult(rd(x1,x1),x1),ld(x1,x1)) = mult(x1,ld(x1,x1)),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
mult(mult(rd(x1,x1),x1),ld(x1,x1)) = x1,
inference(transitivity,[status(thm)],[52,49]) ).
tff(54,plain,
mult(mult(mult(rd(x1,x1),x1),ld(x1,x1)),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
mult(x1,rd(x1,x1)) = mult(mult(mult(rd(x1,x1),x1),ld(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x1,x1),x1) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
rd(mult(x1,x1),x1) = x1,
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
mult(rd(x1,x1),mult(rd(x1,x1),x1)) = mult(rd(x1,x1),x1),
inference(monotonicity,[status(thm)],[51]) ).
tff(59,plain,
mult(rd(x1,x1),x1) = mult(rd(x1,x1),mult(rd(x1,x1),x1)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
x1 = mult(rd(x1,x1),x1),
inference(symmetry,[status(thm)],[51]) ).
tff(61,plain,
x1 = mult(rd(x1,x1),mult(rd(x1,x1),x1)),
inference(transitivity,[status(thm)],[60,59]) ).
tff(62,plain,
mult(x1,x1) = mult(x1,mult(rd(x1,x1),mult(rd(x1,x1),x1))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
mult(x1,mult(rd(x1,x1),mult(rd(x1,x1),x1))) = mult(x1,x1),
inference(symmetry,[status(thm)],[62]) ).
tff(64,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(65,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)],[64,38]) ).
tff(66,plain,
mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1) = mult(x1,x1),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,plain,
rd(mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1),x1) = rd(mult(x1,x1),x1),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,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(69,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)],[68,7]) ).
tff(70,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)],[69]) ).
tff(71,plain,
mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),x1),ld(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[40]) ).
tff(72,plain,
mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = mult(x1,rd(x1,x1)),
inference(transitivity,[status(thm)],[71,54]) ).
tff(73,plain,
mult(mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),rd(x1,x1)) = mult(mult(x1,rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
mult(mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),rd(x1,x1)) = x1,
inference(transitivity,[status(thm)],[73,70,67,57]) ).
tff(75,plain,
mult(mult(mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,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(ld(x1,x1),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
mult(mult(mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[76,38]) ).
tff(78,plain,
mult(rd(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
mult(rd(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(transitivity,[status(thm)],[78,75,55,40]) ).
tff(80,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1))))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[81,16]) ).
tff(83,plain,
mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x1,mult(x1,mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
ld(x1,mult(x1,mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),rd(x1,x1)),
inference(unit_resolution,[status(thm)],[84,16]) ).
tff(86,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(87,plain,
ld(rd(x1,x1),mult(rd(x1,x1),x1)) = x1,
inference(unit_resolution,[status(thm)],[86,16]) ).
tff(88,plain,
mult(mult(rd(x1,x1),x1),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[51]) ).
tff(89,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)],[88]) ).
tff(90,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(91,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)],[90,38]) ).
tff(92,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)],[91]) ).
tff(93,plain,
mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),x1),
inference(transitivity,[status(thm)],[92,89,70,67,57,60]) ).
tff(94,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)],[93]) ).
tff(95,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(96,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)],[95,16]) ).
tff(97,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)],[96]) ).
tff(98,plain,
mult(x1,mult(rd(x1,x1),rd(x1,x1))) = x1,
inference(transitivity,[status(thm)],[97,94,87]) ).
tff(99,plain,
ld(x1,mult(x1,mult(rd(x1,x1),rd(x1,x1)))) = ld(x1,x1),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
ld(x1,x1) = ld(x1,mult(x1,mult(rd(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
ld(x1,x1) = mult(rd(x1,x1),rd(x1,x1)),
inference(transitivity,[status(thm)],[100,85]) ).
tff(102,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x1,mult(x1,x1)) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
ld(x1,mult(x1,x1)) = x1,
inference(unit_resolution,[status(thm)],[102,16]) ).
tff(104,plain,
mult(mult(x1,ld(x1,x1)),ld(x1,x1)) = mult(x1,ld(x1,x1)),
inference(monotonicity,[status(thm)],[49]) ).
tff(105,plain,
mult(mult(x1,ld(x1,x1)),ld(x1,x1)) = x1,
inference(transitivity,[status(thm)],[104,49]) ).
tff(106,plain,
mult(mult(mult(x1,ld(x1,x1)),ld(x1,x1)),x1) = mult(x1,x1),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,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,ld(x1,x1)),ld(x1,x1)),x1) = mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
mult(mult(mult(x1,ld(x1,x1)),ld(x1,x1)),x1) = mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1))),
inference(unit_resolution,[status(thm)],[107,38]) ).
tff(109,plain,
mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1))) = mult(mult(mult(x1,ld(x1,x1)),ld(x1,x1)),x1),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1))) = mult(x1,x1),
inference(transitivity,[status(thm)],[109,106]) ).
tff(111,plain,
ld(x1,mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1)))) = ld(x1,mult(x1,x1)),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x1,mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
ld(x1,mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),x1)),
inference(unit_resolution,[status(thm)],[112,16]) ).
tff(114,plain,
mult(ld(x1,x1),mult(ld(x1,x1),x1)) = ld(x1,mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1)))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
mult(rd(x1,x1),rd(x1,x1)) = ld(x1,mult(x1,mult(rd(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[85]) ).
tff(116,plain,
mult(rd(x1,x1),rd(x1,x1)) = ld(x1,x1),
inference(transitivity,[status(thm)],[115,99]) ).
tff(117,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(ld(x1,x1),x1)) = mult(ld(x1,x1),mult(ld(x1,x1),x1)),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(ld(x1,x1),x1)) = x1,
inference(transitivity,[status(thm)],[117,114,111,103]) ).
tff(119,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(ld(x1,x1),x1)),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,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(ld(x1,x1),x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(ld(x1,x1),x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(ld(x1,x1),x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(ld(x1,x1),x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[120,38]) ).
tff(122,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(ld(x1,x1),x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(ld(x1,x1),x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(ld(x1,x1),x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(transitivity,[status(thm)],[122,119,55,40]) ).
tff(124,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(ld(x1,x1),x1),rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1))))),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,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(ld(x1,x1),x1),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(ld(x1,x1),x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(ld(x1,x1),x1),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(ld(x1,x1),x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[125,16]) ).
tff(127,plain,
mult(rd(x1,x1),mult(mult(ld(x1,x1),x1),rd(x1,x1))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(ld(x1,x1),x1),rd(x1,x1))))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(ld(x1,x1),ld(x1,x1)),x1),x1) = mult(ld(x1,x1),ld(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
rd(mult(mult(ld(x1,x1),ld(x1,x1)),x1),x1) = mult(ld(x1,x1),ld(x1,x1)),
inference(unit_resolution,[status(thm)],[128,7]) ).
tff(130,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x1,ld(x1,x1)),ld(x1,x1)) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
rd(mult(x1,ld(x1,x1)),ld(x1,x1)) = x1,
inference(unit_resolution,[status(thm)],[130,7]) ).
tff(132,plain,
x1 = mult(x1,ld(x1,x1)),
inference(symmetry,[status(thm)],[49]) ).
tff(133,plain,
mult(ld(x1,x1),mult(x1,ld(x1,x1))) = mult(ld(x1,x1),x1),
inference(monotonicity,[status(thm)],[49]) ).
tff(134,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(x1,ld(x1,x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),x1)),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(x1,ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(x1,ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[135,38]) ).
tff(137,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)) = mult(x1,ld(x1,x1)),
inference(transitivity,[status(thm)],[136,134,114,111,103,132]) ).
tff(138,plain,
rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)) = rd(mult(x1,ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),ld(x1,x1)),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),ld(x1,x1)),x1),
inference(unit_resolution,[status(thm)],[139,7]) ).
tff(141,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),x1) = rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),x1) = x1,
inference(transitivity,[status(thm)],[141,138,131]) ).
tff(143,plain,
rd(mult(mult(ld(x1,x1),ld(x1,x1)),x1),x1) = rd(x1,x1),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
rd(x1,x1) = rd(mult(mult(ld(x1,x1),ld(x1,x1)),x1),x1),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
rd(x1,x1) = mult(ld(x1,x1),ld(x1,x1)),
inference(transitivity,[status(thm)],[144,129]) ).
tff(146,plain,
mult(mult(ld(x1,x1),x1),rd(x1,x1)) = mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),x1),rd(x1,x1)),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[148,16]) ).
tff(150,plain,
ld(x1,mult(x1,x1)) = ld(x1,mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1)))),
inference(symmetry,[status(thm)],[111]) ).
tff(151,plain,
x1 = ld(x1,mult(x1,x1)),
inference(symmetry,[status(thm)],[103]) ).
tff(152,plain,
mult(ld(x1,x1),mult(ld(x1,x1),x1)) = x1,
inference(transitivity,[status(thm)],[114,111,103]) ).
tff(153,plain,
mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)) = mult(x1,ld(x1,x1)),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)) = x1,
inference(transitivity,[status(thm)],[153,49]) ).
tff(155,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)),ld(x1,x1)) = mult(x1,ld(x1,x1)),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[156,38]) ).
tff(158,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),x1)),
inference(transitivity,[status(thm)],[158,155,49,151,150,113]) ).
tff(160,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),x1))),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),x1))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),x1))) = mult(ld(x1,x1),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),x1))) = mult(ld(x1,x1),x1),
inference(unit_resolution,[status(thm)],[162,16]) ).
tff(164,plain,
mult(ld(x1,x1),x1) = ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),x1))),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
mult(ld(x1,x1),x1) = mult(mult(ld(x1,x1),x1),rd(x1,x1)),
inference(transitivity,[status(thm)],[164,161,149,147]) ).
tff(166,plain,
mult(ld(x1,x1),ld(x1,x1)) = rd(mult(mult(ld(x1,x1),ld(x1,x1)),x1),x1),
inference(symmetry,[status(thm)],[129]) ).
tff(167,plain,
mult(ld(x1,x1),ld(x1,x1)) = rd(x1,x1),
inference(transitivity,[status(thm)],[166,143]) ).
tff(168,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),x1)) = mult(rd(x1,x1),mult(mult(ld(x1,x1),x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[167,165]) ).
tff(169,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),x1)) = mult(x1,mult(ld(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[168,127,124,31]) ).
tff(170,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),x1)),ld(x1,x1)) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[169,101]) ).
tff(171,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[171,38]) ).
tff(173,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
rd(mult(mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)),
inference(unit_resolution,[status(thm)],[174,7]) ).
tff(176,plain,
mult(rd(x1,x1),mult(ld(x1,x1),ld(x1,x1))) = mult(rd(x1,x1),rd(x1,x1)),
inference(monotonicity,[status(thm)],[167]) ).
tff(177,plain,
mult(rd(x1,x1),mult(ld(x1,x1),ld(x1,x1))) = ld(x1,x1),
inference(transitivity,[status(thm)],[176,115,99]) ).
tff(178,plain,
mult(ld(x1,x1),mult(rd(x1,x1),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),ld(x1,x1)),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(rd(x1,x1),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
mult(mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(rd(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[179,38]) ).
tff(181,plain,
mult(mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),ld(x1,x1)),
inference(transitivity,[status(thm)],[180,178]) ).
tff(182,plain,
rd(mult(mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)) = rd(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[181]) ).
tff(183,plain,
rd(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)) = rd(mult(mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)) = ld(x1,x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(185,plain,
rd(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)) = ld(x1,x1),
inference(unit_resolution,[status(thm)],[184,7]) ).
tff(186,plain,
ld(x1,x1) = rd(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
ld(x1,x1) = mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)),
inference(transitivity,[status(thm)],[186,183,175]) ).
tff(188,plain,
mult(mult(ld(x1,x1),x1),ld(x1,x1)) = mult(mult(ld(x1,x1),x1),mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1))),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),ld(x1,x1))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[191,38]) ).
tff(193,plain,
mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),mult(ld(x1,x1),rd(x1,x1))) = mult(x1,mult(ld(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[152]) ).
tff(194,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[193,101]) ).
tff(195,plain,
mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[101]) ).
tff(197,plain,
mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),ld(x1,x1))),
inference(transitivity,[status(thm)],[196,195,192,190]) ).
tff(198,plain,
mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)),
inference(symmetry,[status(thm)],[196]) ).
tff(200,plain,
mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)),
inference(transitivity,[status(thm)],[198,173,170,199]) ).
tff(201,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(203,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[202,38]) ).
tff(204,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(monotonicity,[status(thm)],[167]) ).
tff(205,plain,
mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[204]) ).
tff(206,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(207,plain,
rd(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(unit_resolution,[status(thm)],[206,7]) ).
tff(208,plain,
rd(mult(x1,x1),x1) = rd(mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1),x1),
inference(symmetry,[status(thm)],[67]) ).
tff(209,plain,
x1 = rd(mult(x1,x1),x1),
inference(symmetry,[status(thm)],[57]) ).
tff(210,plain,
mult(mult(x1,rd(x1,x1)),rd(x1,x1)) = x1,
inference(transitivity,[status(thm)],[70,67,57]) ).
tff(211,plain,
mult(rd(x1,x1),mult(mult(x1,rd(x1,x1)),rd(x1,x1))) = mult(rd(x1,x1),x1),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
mult(rd(x1,x1),mult(mult(x1,rd(x1,x1)),rd(x1,x1))) = x1,
inference(transitivity,[status(thm)],[211,51]) ).
tff(213,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)],[212]) ).
tff(214,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(215,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)],[214,38]) ).
tff(216,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)],[215,213,51,209,208,69]) ).
tff(217,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)],[216]) ).
tff(218,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(219,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)],[218,7]) ).
tff(220,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)],[219]) ).
tff(221,plain,
mult(ld(x1,x1),mult(x1,rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[101]) ).
tff(222,plain,
mult(ld(x1,x1),mult(x1,rd(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(transitivity,[status(thm)],[221,220,217,207,55,40,205]) ).
tff(223,plain,
mult(mult(ld(x1,x1),mult(x1,rd(x1,x1))),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),mult(x1,rd(x1,x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(x1,rd(x1,x1))),ld(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(225,plain,
rd(mult(mult(mult(ld(x1,x1),mult(x1,rd(x1,x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(x1,rd(x1,x1))),ld(x1,x1)),
inference(unit_resolution,[status(thm)],[224,7]) ).
tff(226,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(x1,rd(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(x1,rd(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(227,plain,
mult(mult(mult(ld(x1,x1),mult(x1,rd(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(x1,rd(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[226,38]) ).
tff(228,plain,
mult(ld(x1,x1),mult(mult(x1,rd(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),mult(x1,rd(x1,x1))),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
mult(mult(x1,rd(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(x1,rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[167]) ).
tff(230,plain,
mult(mult(x1,rd(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = x1,
inference(transitivity,[status(thm)],[229,70,67,57]) ).
tff(231,plain,
mult(ld(x1,x1),mult(mult(x1,rd(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),x1),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
mult(ld(x1,x1),x1) = mult(ld(x1,x1),mult(mult(x1,rd(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
mult(rd(x1,x1),mult(x1,ld(x1,x1))) = mult(rd(x1,x1),x1),
inference(monotonicity,[status(thm)],[49]) ).
tff(234,plain,
mult(rd(x1,x1),x1) = mult(rd(x1,x1),mult(x1,ld(x1,x1))),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
x1 = mult(rd(x1,x1),mult(x1,ld(x1,x1))),
inference(transitivity,[status(thm)],[60,234]) ).
tff(236,plain,
mult(ld(x1,x1),x1) = mult(ld(x1,x1),mult(rd(x1,x1),mult(x1,ld(x1,x1)))),
inference(monotonicity,[status(thm)],[235]) ).
tff(237,plain,
mult(ld(x1,x1),mult(rd(x1,x1),mult(x1,ld(x1,x1)))) = mult(ld(x1,x1),x1),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)) = mult(ld(x1,x1),mult(rd(x1,x1),mult(x1,ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)) = mult(ld(x1,x1),mult(rd(x1,x1),mult(x1,ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[238,38]) ).
tff(240,plain,
mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),mult(x1,rd(x1,x1))),ld(x1,x1)),ld(x1,x1)),
inference(transitivity,[status(thm)],[239,237,232,228]) ).
tff(241,plain,
rd(mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)) = rd(mult(mult(mult(ld(x1,x1),mult(x1,rd(x1,x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),rd(x1,x1)),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(243,plain,
rd(mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),rd(x1,x1)),x1),
inference(unit_resolution,[status(thm)],[242,7]) ).
tff(244,plain,
mult(mult(ld(x1,x1),rd(x1,x1)),x1) = rd(mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
mult(mult(ld(x1,x1),rd(x1,x1)),x1) = mult(x1,mult(ld(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[244,241,225,223,203,201,198,173,170,83,80,31]) ).
tff(246,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),
inference(symmetry,[status(thm)],[80]) ).
tff(247,plain,
mult(x1,mult(ld(x1,x1),rd(x1,x1))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1))))),
inference(symmetry,[status(thm)],[31]) ).
tff(248,plain,
mult(x1,mult(ld(x1,x1),rd(x1,x1))) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)),
inference(transitivity,[status(thm)],[247,246,82,199]) ).
tff(249,plain,
mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))) = mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
mult(ld(x1,x1),mult(rd(x1,x1),mult(x1,ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)),
inference(symmetry,[status(thm)],[239]) ).
tff(252,plain,
mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)) = mult(ld(x1,x1),x1),
inference(transitivity,[status(thm)],[239,237]) ).
tff(253,plain,
mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1))) = mult(ld(x1,x1),mult(ld(x1,x1),x1)),
inference(monotonicity,[status(thm)],[252]) ).
tff(254,plain,
mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1))) = x1,
inference(transitivity,[status(thm)],[253,114,111,103]) ).
tff(255,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)))) = mult(ld(x1,x1),x1),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(257,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[256,38]) ).
tff(258,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)),
inference(transitivity,[status(thm)],[257,255,236,251]) ).
tff(259,plain,
rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),ld(x1,x1)),ld(x1,x1)) = rd(mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(261,plain,
rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),
inference(unit_resolution,[status(thm)],[260,7]) ).
tff(262,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)) = rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
mult(rd(x1,x1),mult(mult(ld(x1,x1),rd(x1,x1)),x1)) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),
inference(monotonicity,[status(thm)],[145]) ).
tff(264,plain,
mult(rd(x1,x1),mult(mult(ld(x1,x1),rd(x1,x1)),x1)) = mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(transitivity,[status(thm)],[263,262,259,241,225,223,203,201,250]) ).
tff(265,plain,
rd(mult(rd(x1,x1),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)) = rd(mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(monotonicity,[status(thm)],[264,245]) ).
tff(266,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(rd(x1,x1),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)) = rd(x1,x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
rd(mult(rd(x1,x1),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)) = rd(x1,x1),
inference(unit_resolution,[status(thm)],[266,7]) ).
tff(268,plain,
rd(x1,x1) = rd(mult(rd(x1,x1),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),mult(mult(ld(x1,x1),rd(x1,x1)),x1)),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
mult(ld(x1,x1),ld(x1,x1)) = ld(x1,x1),
inference(transitivity,[status(thm)],[166,143,268,265,29]) ).
tff(270,plain,
mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(ld(x0,x1),mult(x0,x0)),
inference(transitivity,[status(thm)],[270,27]) ).
tff(272,plain,
mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),
inference(monotonicity,[status(thm)],[271]) ).
tff(273,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(274,plain,
mult(mult(mult(ld(x1,x1),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[273,38]) ).
tff(275,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))) = mult(ld(x1,x1),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),
inference(monotonicity,[status(thm)],[269]) ).
tff(276,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)) = mult(mult(ld(x1,x1),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[275]) ).
tff(277,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(278,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[277,38]) ).
tff(279,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),
inference(symmetry,[status(thm)],[278]) ).
tff(280,plain,
mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1))) = mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),
inference(monotonicity,[status(thm)],[27]) ).
tff(281,plain,
mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))) = mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1))),
inference(symmetry,[status(thm)],[280]) ).
tff(282,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))) = mult(ld(x1,x1),mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[269,281]) ).
tff(283,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))) = mult(mult(ld(x1,x1),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),
inference(transitivity,[status(thm)],[282,279,276]) ).
tff(284,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[283]) ).
tff(285,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(286,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[285,38]) ).
tff(287,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1)))) = mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),
inference(transitivity,[status(thm)],[287,284,274,272]) ).
tff(289,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1))))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),
inference(monotonicity,[status(thm)],[288]) ).
tff(290,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1))))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(291,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1))))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[290,16]) ).
tff(292,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1))))),
inference(symmetry,[status(thm)],[291]) ).
tff(293,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))) = mult(ld(x1,x1),mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[281]) ).
tff(294,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))) = mult(mult(ld(x1,x1),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),
inference(transitivity,[status(thm)],[293,279,276]) ).
tff(295,plain,
mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[294]) ).
tff(296,plain,
mult(mult(mult(ld(x1,x1),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)),
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[274]) ).
tff(298,plain,
mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))) = mult(ld(x1,x1),mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))),
inference(symmetry,[status(thm)],[272]) ).
tff(299,plain,
mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))) = mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)),
inference(transitivity,[status(thm)],[298,297,296]) ).
tff(300,plain,
mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[299]) ).
tff(301,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1)),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(303,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[302,38]) ).
tff(304,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[269]) ).
tff(306,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1))),
inference(monotonicity,[status(thm)],[305]) ).
tff(307,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),mult(ld(x1,x1),ld(x1,x1)))),
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1))))),
inference(symmetry,[status(thm)],[289]) ).
tff(309,plain,
mult(ld(x0,x1),mult(x0,x0)) = ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0)))),
inference(symmetry,[status(thm)],[18]) ).
tff(310,plain,
mult(ld(x0,x1),mult(x0,x0)) = mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1)),
inference(transitivity,[status(thm)],[309,308,291,307,304,301]) ).
tff(311,plain,
mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1))),
inference(monotonicity,[status(thm)],[310]) ).
tff(312,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(313,plain,
rd(mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),
inference(unit_resolution,[status(thm)],[312,7]) ).
tff(314,plain,
rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)) = rd(mult(mult(ld(x1,x1),mult(ld(x0,x1),mult(x0,x0))),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[310]) ).
tff(315,plain,
rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)) = mult(ld(x0,x1),mult(x0,x0)),
inference(transitivity,[status(thm)],[314,313,311,292,289,18]) ).
tff(316,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(x0,ld(x0,x1)),x0),x0) = mult(x0,mult(ld(x0,x1),mult(x0,x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(317,plain,
mult(mult(mult(x0,ld(x0,x1)),x0),x0) = mult(x0,mult(ld(x0,x1),mult(x0,x0))),
inference(unit_resolution,[status(thm)],[316,38]) ).
tff(318,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(x0,ld(x0,x1)) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(319,plain,
mult(x0,ld(x0,x1)) = x1,
inference(unit_resolution,[status(thm)],[318,47]) ).
tff(320,plain,
mult(mult(x0,ld(x0,x1)),x0) = mult(x1,x0),
inference(monotonicity,[status(thm)],[319]) ).
tff(321,plain,
mult(mult(mult(x0,ld(x0,x1)),x0),x0) = mult(mult(x1,x0),x0),
inference(monotonicity,[status(thm)],[320]) ).
tff(322,plain,
mult(mult(x1,x0),x0) = mult(mult(mult(x0,ld(x0,x1)),x0),x0),
inference(symmetry,[status(thm)],[321]) ).
tff(323,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(x1,x0),x0),ld(x1,x1)),ld(x1,x1)) = mult(mult(x1,x0),x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(324,plain,
rd(mult(mult(mult(x1,x0),x0),ld(x1,x1)),ld(x1,x1)) = mult(mult(x1,x0),x0),
inference(unit_resolution,[status(thm)],[323,7]) ).
tff(325,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[269]) ).
tff(326,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[326]) ).
tff(328,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)),
inference(symmetry,[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(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(330,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[329,38]) ).
tff(331,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(x1,x0),x0),x1),x1) = mult(mult(x1,x0),x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
rd(mult(mult(mult(x1,x0),x0),x1),x1) = mult(mult(x1,x0),x0),
inference(unit_resolution,[status(thm)],[332,7]) ).
tff(334,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(ld(x1,x1),rd(x1,x1))) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(335,plain,
rd(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(ld(x1,x1),rd(x1,x1))) = x1,
inference(unit_resolution,[status(thm)],[334,7]) ).
tff(336,plain,
mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)) = rd(mult(mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[175]) ).
tff(337,plain,
mult(mult(ld(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(ld(x1,x1),rd(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[116]) ).
tff(338,plain,
mult(mult(ld(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = ld(x1,x1),
inference(transitivity,[status(thm)],[337,336,182,185]) ).
tff(339,plain,
mult(rd(x1,x1),mult(mult(ld(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),ld(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(ld(x1,x1),rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(ld(x1,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(ld(x1,x1),rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(ld(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[340,38]) ).
tff(342,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))) = rd(x1,x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(343,plain,
ld(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))) = rd(x1,x1),
inference(unit_resolution,[status(thm)],[342,16]) ).
tff(344,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),ld(x1,x1)),
inference(monotonicity,[status(thm)],[116]) ).
tff(345,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),ld(x1,x1)) = rd(x1,x1),
inference(transitivity,[status(thm)],[344,166,143]) ).
tff(346,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),ld(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),rd(x1,x1)),
inference(monotonicity,[status(thm)],[345]) ).
tff(347,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)),ld(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(348,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),ld(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[347,38]) ).
tff(349,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),ld(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[348]) ).
tff(350,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),rd(x1,x1)),
inference(transitivity,[status(thm)],[349,346]) ).
tff(351,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[350]) ).
tff(352,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))))) = mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(353,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))))) = mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[352,16]) ).
tff(354,plain,
mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))))),
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))) = rd(x1,x1),
inference(transitivity,[status(thm)],[354,351,343]) ).
tff(356,plain,
mult(mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),rd(x1,x1)),
inference(monotonicity,[status(thm)],[355]) ).
tff(357,plain,
mult(rd(x1,x1),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))),rd(x1,x1)),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
ld(x1,x1) = mult(mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))),rd(x1,x1)),
inference(transitivity,[status(thm)],[100,85,357]) ).
tff(359,plain,
mult(ld(x1,x1),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),mult(ld(x1,x1),rd(x1,x1))),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[358]) ).
tff(360,plain,
mult(ld(x1,x1),rd(x1,x1)) = mult(rd(x1,x1),ld(x1,x1)),
inference(transitivity,[status(thm)],[359,341,339]) ).
tff(361,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(362,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[361,16]) ).
tff(363,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))) = mult(ld(x1,x1),mult(x1,rd(x1,x1))),
inference(symmetry,[status(thm)],[221]) ).
tff(364,plain,
rd(mult(mult(x1,rd(x1,x1)),rd(x1,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)],[217]) ).
tff(365,plain,
mult(x1,rd(x1,x1)) = rd(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[207]) ).
tff(366,plain,
mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[152]) ).
tff(367,plain,
mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),rd(x1,x1)) = mult(ld(x1,x1),mult(x1,rd(x1,x1))),
inference(transitivity,[status(thm)],[366,365,364,219,363]) ).
tff(368,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),rd(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(x1,rd(x1,x1))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[367]) ).
tff(369,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),rd(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(370,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),rd(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[369,38]) ).
tff(371,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),rd(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[370]) ).
tff(372,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)))),
inference(transitivity,[status(thm)],[371,368,223,203]) ).
tff(373,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))))),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))))),
inference(symmetry,[status(thm)],[373]) ).
tff(375,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))))) = mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(376,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))))) = mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[375,16]) ).
tff(377,plain,
mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))))),
inference(symmetry,[status(thm)],[376]) ).
tff(378,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))),
inference(symmetry,[status(thm)],[198]) ).
tff(379,plain,
mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[170]) ).
tff(380,plain,
mult(x1,mult(ld(x1,x1),rd(x1,x1))) = mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))),
inference(transitivity,[status(thm)],[247,246,82,379,172,378,377,374,362]) ).
tff(381,plain,
rd(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(ld(x1,x1),rd(x1,x1))) = rd(mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))),mult(rd(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[380,360]) ).
tff(382,plain,
rd(mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))),mult(rd(x1,x1),ld(x1,x1))) = rd(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(ld(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))),mult(rd(x1,x1),ld(x1,x1))) = mult(ld(x1,x1),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(384,plain,
rd(mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))),mult(rd(x1,x1),ld(x1,x1))) = mult(ld(x1,x1),x1),
inference(unit_resolution,[status(thm)],[383,7]) ).
tff(385,plain,
mult(ld(x1,x1),x1) = rd(mult(mult(ld(x1,x1),x1),mult(rd(x1,x1),ld(x1,x1))),mult(rd(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[384]) ).
tff(386,plain,
mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[245,101]) ).
tff(387,plain,
mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(ld(x1,x1),rd(x1,x1)),x1),ld(x1,x1)),
inference(symmetry,[status(thm)],[386]) ).
tff(388,plain,
mult(x1,mult(ld(x1,x1),rd(x1,x1))) = x1,
inference(transitivity,[status(thm)],[247,246,82,387,239,237,385,382,335]) ).
tff(389,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,x0),x0),x1) = mult(x1,mult(x0,mult(x0,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(390,plain,
mult(mult(mult(x1,x0),x0),x1) = mult(x1,mult(x0,mult(x0,x1))),
inference(unit_resolution,[status(thm)],[389,38]) ).
tff(391,plain,
mult(x1,mult(x0,mult(x0,x1))) = mult(mult(mult(x1,x0),x0),x1),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(x1,mult(x0,mult(x0,x1))),ld(x1,x1)),ld(x1,x1)) = mult(x1,mult(x0,mult(x0,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(393,plain,
rd(mult(mult(x1,mult(x0,mult(x0,x1))),ld(x1,x1)),ld(x1,x1)) = mult(x1,mult(x0,mult(x0,x1))),
inference(unit_resolution,[status(thm)],[392,7]) ).
tff(394,plain,
mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(x0,mult(x0,x1))) = mult(x1,mult(x0,mult(x0,x1))),
inference(monotonicity,[status(thm)],[388]) ).
tff(395,plain,
mult(x1,mult(x0,mult(x0,x1))) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(x0,mult(x0,x1))),
inference(symmetry,[status(thm)],[394]) ).
tff(396,plain,
mult(mult(x1,mult(x0,mult(x0,x1))),ld(x1,x1)) = mult(mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(x0,mult(x0,x1))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[395]) ).
tff(397,plain,
mult(mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(x0,mult(x0,x1))),ld(x1,x1)) = mult(mult(x1,mult(x0,mult(x0,x1))),ld(x1,x1)),
inference(symmetry,[status(thm)],[396]) ).
tff(398,plain,
mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = x1,
inference(transitivity,[status(thm)],[249,198,173,170,387,239,237,385,382,335]) ).
tff(399,plain,
mult(mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x0,mult(x0,x1))) = mult(x1,mult(x0,mult(x0,x1))),
inference(monotonicity,[status(thm)],[398]) ).
tff(400,plain,
mult(mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x0,mult(x0,x1))) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(x0,mult(x0,x1))),
inference(transitivity,[status(thm)],[399,395]) ).
tff(401,plain,
mult(mult(mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x0,mult(x0,x1))),ld(x1,x1)) = mult(mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(x0,mult(x0,x1))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[400]) ).
tff(402,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x0,mult(x0,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(mult(x0,mult(x0,x1)),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(403,plain,
mult(mult(mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x0,mult(x0,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(mult(x0,mult(x0,x1)),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[402,38]) ).
tff(404,plain,
mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(mult(x0,mult(x0,x1)),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x0,mult(x0,x1))),ld(x1,x1)),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))) = mult(x0,mult(x0,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(406,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))) = mult(x0,mult(x0,x1)),
inference(unit_resolution,[status(thm)],[405,16]) ).
tff(407,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),ld(x1,x1)) = mult(x0,mult(x0,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(408,plain,
mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),ld(x1,x1)) = mult(x0,mult(x0,x1)),
inference(unit_resolution,[status(thm)],[407,25]) ).
tff(409,plain,
mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[269]) ).
tff(410,plain,
mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(x0,mult(x0,x1)),
inference(transitivity,[status(thm)],[409,408]) ).
tff(411,plain,
mult(ld(x1,x1),mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(x0,mult(x0,x1))),
inference(monotonicity,[status(thm)],[410]) ).
tff(412,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(413,plain,
mult(mult(mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[412,38]) ).
tff(414,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(x0,mult(x0,x1)),ld(x1,x1))) = mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),
inference(monotonicity,[status(thm)],[269]) ).
tff(415,plain,
mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),
inference(symmetry,[status(thm)],[414]) ).
tff(416,plain,
mult(mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[415]) ).
tff(417,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)) = mult(mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),
inference(symmetry,[status(thm)],[416]) ).
tff(418,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(419,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[418,38]) ).
tff(420,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),
inference(symmetry,[status(thm)],[419]) ).
tff(421,plain,
mult(ld(x1,x1),mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),ld(x1,x1))) = mult(ld(x1,x1),mult(x0,mult(x0,x1))),
inference(monotonicity,[status(thm)],[408]) ).
tff(422,plain,
mult(ld(x1,x1),mult(x0,mult(x0,x1))) = mult(ld(x1,x1),mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),ld(x1,x1))),
inference(symmetry,[status(thm)],[421]) ).
tff(423,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[422]) ).
tff(424,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(x0,mult(x0,x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),
inference(monotonicity,[status(thm)],[269]) ).
tff(425,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(x0,mult(x0,x1)))) = mult(mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),
inference(transitivity,[status(thm)],[424,423,420,417]) ).
tff(426,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[425]) ).
tff(427,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(428,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[427,38]) ).
tff(429,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)),
inference(symmetry,[status(thm)],[428]) ).
tff(430,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1)))) = mult(ld(x1,x1),mult(x0,mult(x0,x1))),
inference(transitivity,[status(thm)],[429,426,413,411]) ).
tff(431,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),
inference(monotonicity,[status(thm)],[430]) ).
tff(432,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(433,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[432,16]) ).
tff(434,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))))),
inference(symmetry,[status(thm)],[433]) ).
tff(435,plain,
mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[269]) ).
tff(436,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))),
inference(monotonicity,[status(thm)],[435]) ).
tff(437,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(438,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[437,38]) ).
tff(439,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))) = mult(mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),
inference(transitivity,[status(thm)],[423,420,417]) ).
tff(440,plain,
mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[439]) ).
tff(441,plain,
mult(mult(mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)),
inference(symmetry,[status(thm)],[440]) ).
tff(442,plain,
mult(ld(x1,x1),mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),rd(mult(x0,mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[413]) ).
tff(443,plain,
mult(ld(x1,x1),mult(x0,mult(x0,x1))) = mult(ld(x1,x1),mult(rd(mult(x0,mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))),
inference(symmetry,[status(thm)],[411]) ).
tff(444,plain,
mult(ld(x1,x1),mult(x0,mult(x0,x1))) = mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)),
inference(transitivity,[status(thm)],[443,442,441]) ).
tff(445,plain,
mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1)),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[438]) ).
tff(448,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),mult(ld(x1,x1),ld(x1,x1)))),
inference(symmetry,[status(thm)],[436]) ).
tff(449,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))))),
inference(symmetry,[status(thm)],[431]) ).
tff(450,plain,
mult(x0,mult(x0,x1)) = ld(ld(x1,x1),mult(ld(x1,x1),mult(x0,mult(x0,x1)))),
inference(symmetry,[status(thm)],[406]) ).
tff(451,plain,
mult(x0,mult(x0,x1)) = mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1)),
inference(transitivity,[status(thm)],[450,449,433,448,447,446]) ).
tff(452,plain,
mult(ld(x1,x1),mult(x0,mult(x0,x1))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))),
inference(monotonicity,[status(thm)],[451]) ).
tff(453,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1))) = mult(ld(x1,x1),mult(x0,mult(x0,x1))),
inference(symmetry,[status(thm)],[452]) ).
tff(454,plain,
mult(x0,mult(x0,x1)) = mult(ld(x1,x1),mult(x0,mult(x0,x1))),
inference(transitivity,[status(thm)],[450,449,433,453]) ).
tff(455,plain,
mult(mult(x0,mult(x0,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(x0,mult(x0,x1))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[454]) ).
tff(456,plain,
mult(mult(x0,mult(x0,x1)),ld(x1,x1)) = mult(x0,mult(x0,x1)),
inference(transitivity,[status(thm)],[455,445,438,436,434,431,406]) ).
tff(457,plain,
mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(mult(x0,mult(x0,x1)),ld(x1,x1))) = mult(x1,mult(x0,mult(x0,x1))),
inference(monotonicity,[status(thm)],[388,456]) ).
tff(458,plain,
mult(x1,mult(x0,mult(x0,x1))) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(mult(x0,mult(x0,x1)),ld(x1,x1))),
inference(symmetry,[status(thm)],[457]) ).
tff(459,plain,
mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)) = x1,
inference(transitivity,[status(thm)],[196,387,239,237,385,382,335]) ).
tff(460,plain,
mult(mult(mult(x1,x0),x0),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))) = mult(mult(mult(x1,x0),x0),x1),
inference(monotonicity,[status(thm)],[459]) ).
tff(461,plain,
mult(mult(mult(x1,x0),x0),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1))) = mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(mult(x0,mult(x0,x1)),ld(x1,x1))),
inference(transitivity,[status(thm)],[460,390,458]) ).
tff(462,plain,
mult(ld(x1,x1),mult(mult(mult(x1,x0),x0),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),mult(mult(x0,mult(x0,x1)),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[461]) ).
tff(463,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(mult(x1,x0),x0),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(464,plain,
mult(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(mult(x1,x0),x0),mult(mult(x1,mult(ld(x1,x1),rd(x1,x1))),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[463,38]) ).
tff(465,plain,
mult(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),ld(x1,x1)) = mult(mult(x1,mult(x0,mult(x0,x1))),ld(x1,x1)),
inference(transitivity,[status(thm)],[464,462,404,401,397]) ).
tff(466,plain,
rd(mult(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),ld(x1,x1)),ld(x1,x1)) = rd(mult(mult(x1,mult(x0,mult(x0,x1))),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[465]) ).
tff(467,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(468,plain,
rd(mult(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[467,7]) ).
tff(469,plain,
mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = rd(mult(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[468]) ).
tff(470,plain,
mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = mult(mult(mult(x1,x0),x0),x1),
inference(transitivity,[status(thm)],[469,466,393,391]) ).
tff(471,plain,
rd(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = rd(mult(mult(mult(x1,x0),x0),x1),x1),
inference(monotonicity,[status(thm)],[470,388]) ).
tff(472,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = mult(ld(x1,x1),mult(mult(x1,x0),x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(473,plain,
rd(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x1,mult(ld(x1,x1),rd(x1,x1)))) = mult(ld(x1,x1),mult(mult(x1,x0),x0)),
inference(unit_resolution,[status(thm)],[472,7]) ).
tff(474,plain,
mult(ld(x1,x1),mult(mult(x1,x0),x0)) = rd(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[473]) ).
tff(475,plain,
mult(x0,mult(ld(x0,x1),mult(x0,x0))) = mult(mult(mult(x0,ld(x0,x1)),x0),x0),
inference(symmetry,[status(thm)],[317]) ).
tff(476,plain,
mult(x0,mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1))) = mult(x0,mult(ld(x0,x1),mult(x0,x0))),
inference(monotonicity,[status(thm)],[27]) ).
tff(477,plain,
mult(x0,mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1))) = mult(mult(x1,x0),x0),
inference(transitivity,[status(thm)],[476,475,321]) ).
tff(478,plain,
mult(ld(x1,x1),mult(x0,mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(x1,x0),x0)),
inference(monotonicity,[status(thm)],[477]) ).
tff(479,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(x0,mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(480,plain,
mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(x0,mult(rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[479,38]) ).
tff(481,plain,
mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)) = mult(mult(x1,x0),x0),
inference(transitivity,[status(thm)],[480,478,474,471,333]) ).
tff(482,plain,
mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1))) = mult(ld(x1,x1),mult(mult(x1,x0),x0)),
inference(monotonicity,[status(thm)],[481]) ).
tff(483,plain,
mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1))) = mult(mult(x1,x0),x0),
inference(transitivity,[status(thm)],[482,474,471,333]) ).
tff(484,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(x1,x0),x0)),
inference(monotonicity,[status(thm)],[483]) ).
tff(485,plain,
mult(ld(x1,x1),mult(mult(x1,x0),x0)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)))),
inference(symmetry,[status(thm)],[484]) ).
tff(486,plain,
rd(mult(mult(mult(x1,x0),x0),x1),x1) = rd(mult(mult(ld(x1,x1),mult(mult(x1,x0),x0)),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),mult(x1,mult(ld(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[471]) ).
tff(487,plain,
mult(mult(x1,x0),x0) = rd(mult(mult(mult(x1,x0),x0),x1),x1),
inference(symmetry,[status(thm)],[333]) ).
tff(488,plain,
mult(mult(x1,x0),x0) = mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)),
inference(transitivity,[status(thm)],[487,486,473,485,331,328]) ).
tff(489,plain,
mult(mult(mult(x1,x0),x0),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[488]) ).
tff(490,plain,
mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)),ld(x1,x1)) = mult(mult(mult(x1,x0),x0),ld(x1,x1)),
inference(symmetry,[status(thm)],[489]) ).
tff(491,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(492,plain,
mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[491,38]) ).
tff(493,plain,
mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1)))),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[269]) ).
tff(495,plain,
mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(x1,x0),x0),
inference(transitivity,[status(thm)],[494,480,478,474,471,333]) ).
tff(496,plain,
mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(x1,x0),x0)),
inference(monotonicity,[status(thm)],[495]) ).
tff(497,plain,
mult(ld(x1,x1),mult(mult(x1,x0),x0)) = mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1)))),
inference(symmetry,[status(thm)],[496]) ).
tff(498,plain,
mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)) = mult(mult(mult(x1,x0),x0),ld(x1,x1)),
inference(transitivity,[status(thm)],[480,478,497,493,490]) ).
tff(499,plain,
rd(mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = rd(mult(mult(mult(x1,x0),x0),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[498]) ).
tff(500,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(501,plain,
rd(mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[500,7]) ).
tff(502,plain,
mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))) = rd(mult(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[501]) ).
tff(503,plain,
mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))) = mult(x0,mult(ld(x0,x1),mult(x0,x0))),
inference(transitivity,[status(thm)],[502,499,324,322,317]) ).
tff(504,plain,
rd(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))) = rd(mult(x0,mult(ld(x0,x1),mult(x0,x0))),mult(ld(x0,x1),mult(x0,x0))),
inference(monotonicity,[status(thm)],[503,315]) ).
tff(505,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))) = mult(ld(x1,x1),x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(506,plain,
rd(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))) = mult(ld(x1,x1),x0),
inference(unit_resolution,[status(thm)],[505,7]) ).
tff(507,plain,
mult(ld(x1,x1),x0) = rd(mult(mult(ld(x1,x1),x0),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),rd(mult(ld(x0,x1),mult(x0,x0)),ld(x1,x1))),
inference(symmetry,[status(thm)],[506]) ).
tff(508,plain,
mult(ld(x1,x1),x0) = x0,
inference(transitivity,[status(thm)],[507,504,9]) ).
tff(509,plain,
( ( mult(ld(x1,x1),x0) != x0 )
<=> ( mult(ld(x1,x1),x0) != x0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(510,axiom,
mult(ld(x1,x1),x0) != x0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(511,plain,
mult(ld(x1,x1),x0) != x0,
inference(modus_ponens,[status(thm)],[510,509]) ).
tff(512,plain,
$false,
inference(unit_resolution,[status(thm)],[511,508]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP660-14 : TPTP v9.0.0. Released v8.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:47:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.47/0.63 % SZS status Unsatisfiable
% 0.47/0.63 % SZS output start Proof
% See solution above
% 0.52/0.71 % E exiting
%------------------------------------------------------------------------------