%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP660-11 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:23 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 63
% Syntax : Number of formulae : 281 ( 223 unt; 0 typ; 0 def)
% Number of atoms : 347 ( 342 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 115 ( 53 ~; 49 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 199 ( 190 !; 0 ?; 199 :)
% Comments :
%------------------------------------------------------------------------------
tff(x0_type,type,
x0: $i ).
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(x1_type,type,
x1: $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
tff(5,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x0,rd(x1,x1)),rd(x1,x1)) = x0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
rd(mult(x0,rd(x1,x1)),rd(x1,x1)) = x0,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = rd(x1,x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
rd(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = rd(x1,x1),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[12,7]) ).
tff(14,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(15,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)],[14]) ).
tff(16,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(17,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
tff(18,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)],[17,16]) ).
tff(19,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)],[18]) ).
tff(20,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)],[19,15]) ).
tff(21,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x1,x1),x1) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
rd(mult(x1,x1),x1) = x1,
inference(unit_resolution,[status(thm)],[24,7]) ).
tff(26,plain,
^ [B: $i,A: $i] :
refl(( ( mult(rd(A,B),B) = A )
<=> ( mult(rd(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(27,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)],[26]) ).
tff(28,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(29,axiom,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
tff(30,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(x1,x1),x1) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
mult(rd(x1,x1),x1) = x1,
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
mult(rd(x1,x1),mult(rd(x1,x1),x1)) = mult(rd(x1,x1),x1),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
mult(rd(x1,x1),x1) = mult(rd(x1,x1),mult(rd(x1,x1),x1)),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
x1 = mult(rd(x1,x1),x1),
inference(symmetry,[status(thm)],[34]) ).
tff(38,plain,
x1 = mult(rd(x1,x1),mult(rd(x1,x1),x1)),
inference(transitivity,[status(thm)],[37,36]) ).
tff(39,plain,
mult(x1,x1) = mult(x1,mult(rd(x1,x1),mult(rd(x1,x1),x1))),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
mult(x1,mult(rd(x1,x1),mult(rd(x1,x1),x1))) = mult(x1,x1),
inference(symmetry,[status(thm)],[39]) ).
tff(41,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(42,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)],[41,20]) ).
tff(43,plain,
mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1) = mult(x1,x1),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
rd(mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1),x1) = rd(mult(x1,x1),x1),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,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(46,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)],[45,7]) ).
tff(47,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)],[46]) ).
tff(48,plain,
mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[34]) ).
tff(49,plain,
mult(x1,mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
^ [B: $i,A: $i] :
refl(( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(51,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)],[50]) ).
tff(52,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(53,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
tff(54,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,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(58,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)],[57,56]) ).
tff(59,plain,
mult(mult(rd(x1,x1),x1),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[34]) ).
tff(60,plain,
mult(mult(mult(rd(x1,x1),x1),rd(x1,x1)),rd(x1,x1)) = mult(mult(x1,rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),x1),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
mult(mult(mult(rd(x1,x1),x1),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[61,20]) ).
tff(63,plain,
mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),x1),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),x1),
inference(transitivity,[status(thm)],[63,60,47,44,25,37]) ).
tff(65,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),x1)),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
ld(rd(x1,x1),mult(rd(x1,x1),x1)) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(rd(x1,x1),rd(x1,x1))))),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),x1)) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
ld(rd(x1,x1),mult(rd(x1,x1),x1)) = x1,
inference(unit_resolution,[status(thm)],[67,56]) ).
tff(69,plain,
x1 = ld(rd(x1,x1),mult(rd(x1,x1),x1)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
x1 = mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[69,66,58,49]) ).
tff(71,plain,
mult(x1,rd(x1,x1)) = mult(mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
mult(mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
mult(mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)) = mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[73,20]) ).
tff(75,plain,
mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),x1),mult(rd(x1,x1),rd(x1,x1))),rd(x1,x1)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))) = mult(x1,rd(x1,x1)),
inference(transitivity,[status(thm)],[75,72]) ).
tff(77,plain,
mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)) = mult(mult(x1,rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)) = x1,
inference(transitivity,[status(thm)],[77,47,44,25]) ).
tff(79,plain,
mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[80,20]) ).
tff(82,plain,
mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(x1,rd(x1,x1)),
inference(transitivity,[status(thm)],[82,79]) ).
tff(84,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
rd(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = x1,
inference(unit_resolution,[status(thm)],[86,7]) ).
tff(88,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x1,mult(x1,x1)) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
ld(x1,mult(x1,x1)) = x1,
inference(unit_resolution,[status(thm)],[88,56]) ).
tff(90,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)],[58]) ).
tff(91,plain,
mult(x1,mult(rd(x1,x1),rd(x1,x1))) = x1,
inference(transitivity,[status(thm)],[90,65,68]) ).
tff(92,plain,
mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = x1,
inference(transitivity,[status(thm)],[92,90,65,68]) ).
tff(94,plain,
mult(mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),x1) = mult(x1,x1),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),x1) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
mult(mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),x1) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))),
inference(unit_resolution,[status(thm)],[95,20]) ).
tff(97,plain,
mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) = mult(mult(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),x1),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) = mult(x1,x1),
inference(transitivity,[status(thm)],[97,94]) ).
tff(99,plain,
ld(x1,mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)))) = ld(x1,mult(x1,x1)),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x1,mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
ld(x1,mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),
inference(unit_resolution,[status(thm)],[100,56]) ).
tff(102,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) = ld(x1,mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(rd(x1,x1),rd(x1,x1)),x1),
inference(monotonicity,[status(thm)],[91]) ).
tff(104,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[105,20]) ).
tff(107,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[106,104,102,99,89,69,66,58]) ).
tff(108,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(x1,mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),
inference(unit_resolution,[status(thm)],[109,7]) ).
tff(111,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1) = rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1) = x1,
inference(transitivity,[status(thm)],[111,108,87]) ).
tff(113,plain,
rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),x1) = rd(x1,x1),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),x1) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),x1) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[114,7]) ).
tff(116,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),x1),x1),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = rd(x1,x1),
inference(transitivity,[status(thm)],[116,113]) ).
tff(118,plain,
mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[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(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[120,20]) ).
tff(122,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[121,119,85,23]) ).
tff(123,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[124,7]) ).
tff(126,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),
inference(transitivity,[status(thm)],[126,123,13]) ).
tff(128,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[128,7]) ).
tff(130,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(131,plain,
rd(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(unit_resolution,[status(thm)],[130,7]) ).
tff(132,plain,
rd(mult(x1,x1),x1) = rd(mult(mult(mult(x1,rd(x1,x1)),rd(x1,x1)),x1),x1),
inference(symmetry,[status(thm)],[44]) ).
tff(133,plain,
x1 = rd(mult(x1,x1),x1),
inference(symmetry,[status(thm)],[25]) ).
tff(134,plain,
mult(mult(x1,rd(x1,x1)),rd(x1,x1)) = x1,
inference(transitivity,[status(thm)],[47,44,25]) ).
tff(135,plain,
mult(rd(x1,x1),mult(mult(x1,rd(x1,x1)),rd(x1,x1))) = mult(rd(x1,x1),x1),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
mult(rd(x1,x1),mult(mult(x1,rd(x1,x1)),rd(x1,x1))) = x1,
inference(transitivity,[status(thm)],[135,34]) ).
tff(137,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)],[136]) ).
tff(138,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(139,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)],[138,20]) ).
tff(140,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)],[139,137,34,133,132,46]) ).
tff(141,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)],[140]) ).
tff(142,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(143,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)],[142,7]) ).
tff(144,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)],[143]) ).
tff(145,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,rd(x1,x1)),
inference(transitivity,[status(thm)],[22,84,144,141,131]) ).
tff(146,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1)))) = mult(x1,rd(x1,x1)),
inference(transitivity,[status(thm)],[146,144,141,131]) ).
tff(148,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[149,20]) ).
tff(151,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(monotonicity,[status(thm)],[117]) ).
tff(152,plain,
mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[153,150,148,85,23]) ).
tff(155,plain,
rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),rd(x1,x1)),
inference(unit_resolution,[status(thm)],[157,7]) ).
tff(159,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),rd(x1,x1)),
inference(monotonicity,[status(thm)],[117]) ).
tff(160,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[161,20]) ).
tff(163,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(transitivity,[status(thm)],[162,160]) ).
tff(164,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[165,7]) ).
tff(167,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = rd(mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(rd(x1,x1),rd(x1,x1)),
inference(transitivity,[status(thm)],[167,164,158]) ).
tff(169,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(171,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[170,56]) ).
tff(172,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[172,20]) ).
tff(174,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) = x1,
inference(transitivity,[status(thm)],[102,99,89]) ).
tff(175,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[178,56]) ).
tff(180,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)) = x1,
inference(transitivity,[status(thm)],[139,137,34]) ).
tff(181,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(183,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[182,20]) ).
tff(184,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))) = x1,
inference(transitivity,[status(thm)],[184,181,90,65,68]) ).
tff(186,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)) = mult(x1,rd(x1,x1)),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(188,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[187,20]) ).
tff(189,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),rd(x1,x1)),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)))) = mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)))),
inference(transitivity,[status(thm)],[189,186,71,74]) ).
tff(191,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[192,56]) ).
tff(194,plain,
mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))))),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)),
inference(monotonicity,[status(thm)],[117]) ).
tff(196,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[196,56]) ).
tff(198,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[198,20]) ).
tff(200,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[185]) ).
tff(201,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))) = x1,
inference(transitivity,[status(thm)],[200,90,65,68]) ).
tff(202,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(x1,mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
mult(x1,mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),mult(rd(x1,x1),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(transitivity,[status(thm)],[184,181,203,199]) ).
tff(205,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))))) = ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
mult(x1,mult(rd(x1,x1),rd(x1,x1))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(x1,rd(x1,x1))),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[181]) ).
tff(207,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1))))),
inference(transitivity,[status(thm)],[102,99,89,69,66,58,206,183]) ).
tff(208,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) = ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))))),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),x1),
inference(unit_resolution,[status(thm)],[209,56]) ).
tff(211,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),x1) = ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),x1))),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),x1) = mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1)),
inference(transitivity,[status(thm)],[211,208,205,197,195]) ).
tff(213,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) = mult(rd(x1,x1),mult(mult(mult(x1,rd(x1,x1)),mult(rd(x1,x1),mult(rd(x1,x1),rd(x1,x1)))),rd(x1,x1))),
inference(monotonicity,[status(thm)],[117,212]) ).
tff(214,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)) = mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),
inference(transitivity,[status(thm)],[213,194,191,179]) ).
tff(215,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))))),
inference(unit_resolution,[status(thm)],[216,20]) ).
tff(218,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))),mult(mult(rd(x1,x1),rd(x1,x1)),x1)),mult(rd(x1,x1),rd(x1,x1))),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1))))),
inference(transitivity,[status(thm)],[218,215,177,173]) ).
tff(220,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))))) = ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(rd(x1,x1),rd(x1,x1)))))),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,plain,
ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))))) = mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[221,56]) ).
tff(223,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = ld(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))))),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(transitivity,[status(thm)],[223,220,171,169,126,123,156,129]) ).
tff(225,plain,
rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = rd(mult(rd(x1,x1),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1)),mult(x1,mult(mult(rd(x1,x1),rd(x1,x1)),rd(x1,x1))))),
inference(monotonicity,[status(thm)],[224,127]) ).
tff(226,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(227,plain,
rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),rd(x1,x1)),
inference(unit_resolution,[status(thm)],[226,7]) ).
tff(228,plain,
mult(rd(x1,x1),rd(x1,x1)) = rd(mult(mult(rd(x1,x1),rd(x1,x1)),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),mult(mult(mult(rd(x1,x1),rd(x1,x1)),x1),mult(rd(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
mult(rd(x1,x1),rd(x1,x1)) = rd(x1,x1),
inference(transitivity,[status(thm)],[228,225,11]) ).
tff(230,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),x0) = mult(rd(x1,x1),x0),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
mult(rd(x1,x1),x0) = mult(mult(rd(x1,x1),rd(x1,x1)),x0),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
mult(mult(rd(x1,x1),x0),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x0),rd(x1,x1)),
inference(monotonicity,[status(thm)],[231]) ).
tff(233,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),x0),rd(x1,x1)) = mult(mult(rd(x1,x1),x0),rd(x1,x1)),
inference(symmetry,[status(thm)],[232]) ).
tff(234,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)),x0),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(235,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),x0),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[234,20]) ).
tff(236,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),x0),rd(x1,x1)),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))) = mult(mult(rd(x1,x1),x0),rd(x1,x1)),
inference(transitivity,[status(thm)],[236,233]) ).
tff(238,plain,
mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),x0),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
mult(mult(mult(rd(x1,x1),x0),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),x0),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x0,mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,plain,
mult(mult(mult(rd(x1,x1),x0),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x0,mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[240,20]) ).
tff(242,plain,
mult(rd(x1,x1),mult(x0,mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),x0),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
mult(x0,mult(rd(x1,x1),rd(x1,x1))) = mult(x0,rd(x1,x1)),
inference(monotonicity,[status(thm)],[229]) ).
tff(244,plain,
mult(rd(x1,x1),mult(x0,mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(x0,rd(x1,x1))),
inference(monotonicity,[status(thm)],[243]) ).
tff(245,plain,
mult(rd(x1,x1),mult(x0,rd(x1,x1))) = mult(rd(x1,x1),mult(x0,mult(rd(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
mult(rd(x1,x1),mult(x0,rd(x1,x1))) = mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)),
inference(transitivity,[status(thm)],[245,242,239]) ).
tff(247,plain,
mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[249,20]) ).
tff(251,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1))) = mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)),
inference(monotonicity,[status(thm)],[229]) ).
tff(253,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1))),
inference(monotonicity,[status(thm)],[252]) ).
tff(254,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1))) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),mult(rd(x1,x1),rd(x1,x1)))),
inference(symmetry,[status(thm)],[253]) ).
tff(255,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(256,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1))))) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1))),
inference(unit_resolution,[status(thm)],[255,56]) ).
tff(257,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(x0,rd(x1,x1)))) = mult(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),
inference(monotonicity,[status(thm)],[229]) ).
tff(258,plain,
mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(x0,rd(x1,x1)))) = mult(mult(rd(x1,x1),x0),rd(x1,x1)),
inference(transitivity,[status(thm)],[257,236,233]) ).
tff(259,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)) = mult(mult(mult(rd(x1,x1),x0),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(261,plain,
mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)) = mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)))),
inference(unit_resolution,[status(thm)],[260,20]) ).
tff(262,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)))) = mult(mult(mult(rd(x1,x1),rd(x1,x1)),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),rd(x1,x1)),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)))) = mult(rd(x1,x1),mult(x0,rd(x1,x1))),
inference(transitivity,[status(thm)],[262,259,241,244]) ).
tff(264,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1))))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))) = ld(rd(x1,x1),mult(rd(x1,x1),mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1))))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))) = mult(x0,rd(x1,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
ld(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))) = mult(x0,rd(x1,x1)),
inference(unit_resolution,[status(thm)],[266,56]) ).
tff(268,plain,
mult(x0,rd(x1,x1)) = ld(rd(x1,x1),mult(rd(x1,x1),mult(x0,rd(x1,x1)))),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
mult(x0,rd(x1,x1)) = mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)),
inference(transitivity,[status(thm)],[268,265,256,254,251,248]) ).
tff(270,plain,
rd(mult(x0,rd(x1,x1)),rd(x1,x1)) = rd(mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
rd(mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = rd(mult(x0,rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x0,rd(x1,x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(273,plain,
rd(mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)) = mult(rd(x1,x1),mult(x0,rd(x1,x1))),
inference(unit_resolution,[status(thm)],[272,7]) ).
tff(274,plain,
mult(rd(x1,x1),mult(x0,rd(x1,x1))) = rd(mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1)),rd(x1,x1)),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
mult(rd(x1,x1),mult(x0,rd(x1,x1))) = mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1))),
inference(monotonicity,[status(thm)],[269]) ).
tff(276,plain,
mult(rd(x1,x1),mult(mult(rd(x1,x1),mult(x0,rd(x1,x1))),rd(x1,x1))) = mult(rd(x1,x1),mult(x0,rd(x1,x1))),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
mult(x0,rd(x1,x1)) = x0,
inference(transitivity,[status(thm)],[268,265,256,276,274,271,9]) ).
tff(278,plain,
( ( mult(x0,rd(x1,x1)) != x0 )
<=> ( mult(x0,rd(x1,x1)) != x0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(279,axiom,
mult(x0,rd(x1,x1)) != x0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(280,plain,
mult(x0,rd(x1,x1)) != x0,
inference(modus_ponens,[status(thm)],[279,278]) ).
tff(281,plain,
$false,
inference(unit_resolution,[status(thm)],[280,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP660-11 : TPTP v9.0.0. Released v8.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 16:48:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------