TSTP Solution File: GRP765-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP765-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:29:46 EDT 2022
% Result : Unsatisfiable 130.05s 83.38s
% Output : Proof 130.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 307
% Syntax : Number of formulae : 1475 (1181 unt; 9 typ; 0 def)
% Number of atoms : 1775 (1762 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 561 ( 264 ~; 260 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 739 ( 719 !; 0 ?; 739 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i ) > $i ).
tff(x1_type,type,
x1: $i ).
tff(x0_type,type,
x0: $i ).
tff(eta_type,type,
eta: $i > $i ).
tff(i_type,type,
i: $i > $i ).
tff(difference_type,type,
difference: ( $i * $i ) > $i ).
tff(quotient_type,type,
quotient: ( $i * $i ) > $i ).
tff(one_type,type,
one: $i ).
tff(j_type,type,
j: $i > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( product(A,difference(A,B)) = B )
<=> ( product(A,difference(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
<=> ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
<=> ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
tff(5,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(product(eta(x0),x0),difference(product(eta(x0),x0),product(eta(x0),product(x0,x1)))) = product(eta(x0),product(x0,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
product(product(eta(x0),x0),difference(product(eta(x0),x0),product(eta(x0),product(x0,x1)))) = product(eta(x0),product(x0,x1)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(eta(x0),x0),product(eta(x0),product(x0,x1))) = quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
difference(product(eta(x0),x0),product(eta(x0),product(x0,x1))) = quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)) = difference(product(eta(x0),x0),product(eta(x0),product(x0,x1))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [B: $i,A: $i] :
refl(
( ( difference(A,product(A,B)) = B )
<=> ( difference(A,product(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
<=> ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
<=> ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
tff(24,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(difference(x0,one),product(difference(x0,one),product(eta(x0),x0))) = product(eta(x0),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
difference(difference(x0,one),product(difference(x0,one),product(eta(x0),x0))) = product(eta(x0),x0),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
^ [B: $i,A: $i] :
refl(
( ( product(quotient(A,B),B) = A )
<=> ( product(quotient(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
tff(33,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(one,x0),x0) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
product(quotient(one,x0),x0) = one,
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
^ [A: $i] :
refl(
( ( j(A) = quotient(one,A) )
<=> ( j(A) = quotient(one,A) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [A: $i] : ( j(A) = quotient(one,A) )
<=> ! [A: $i] : ( j(A) = quotient(one,A) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [A: $i] : ( j(A) = quotient(one,A) )
<=> ! [A: $i] : ( j(A) = quotient(one,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
! [A: $i] : ( j(A) = quotient(one,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
tff(42,plain,
! [A: $i] : ( j(A) = quotient(one,A) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [A: $i] : ( j(A) = quotient(one,A) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [A: $i] : ( j(A) = quotient(one,A) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
| ( j(x0) = quotient(one,x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
j(x0) = quotient(one,x0),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
product(j(x0),x0) = product(quotient(one,x0),x0),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(x0,product(x0,j(x0))) = j(x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
difference(x0,product(x0,j(x0))) = j(x0),
inference(unit_resolution,[status(thm)],[48,26]) ).
tff(50,plain,
^ [A: $i] :
refl(
( ( product(i(A),A) = product(A,j(A)) )
<=> ( product(i(A),A) = product(A,j(A)) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
<=> ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
<=> ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
tff(54,plain,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
| ( product(i(x0),x0) = product(x0,j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
product(i(x0),x0) = product(x0,j(x0)),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
^ [A: $i] :
refl(
( ( eta(A) = product(i(A),A) )
<=> ( eta(A) = product(i(A),A) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [A: $i] : ( eta(A) = product(i(A),A) )
<=> ! [A: $i] : ( eta(A) = product(i(A),A) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [A: $i] : ( eta(A) = product(i(A),A) )
<=> ! [A: $i] : ( eta(A) = product(i(A),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
! [A: $i] : ( eta(A) = product(i(A),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
tff(63,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ~ ! [A: $i] : ( eta(A) = product(i(A),A) )
| ( eta(x0) = product(i(x0),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
eta(x0) = product(i(x0),x0),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
^ [A: $i] :
refl(
( ( product(one,A) = A )
<=> ( product(one,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [A: $i] : ( product(one,A) = A )
<=> ! [A: $i] : ( product(one,A) = A ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [A: $i] : ( product(one,A) = A )
<=> ! [A: $i] : ( product(one,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
! [A: $i] : ( product(one,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
tff(72,plain,
! [A: $i] : ( product(one,A) = A ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [A: $i] : ( product(one,A) = A ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [A: $i] : ( product(one,A) = A ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,eta(x0)) = eta(x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
product(one,eta(x0)) = eta(x0),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
product(i(x0),x0) = eta(x0),
inference(symmetry,[status(thm)],[67]) ).
tff(78,plain,
^ [A: $i] :
refl(
( ( i(A) = difference(A,one) )
<=> ( i(A) = difference(A,one) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [A: $i] : ( i(A) = difference(A,one) )
<=> ! [A: $i] : ( i(A) = difference(A,one) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [A: $i] : ( i(A) = difference(A,one) )
<=> ! [A: $i] : ( i(A) = difference(A,one) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
! [A: $i] : ( i(A) = difference(A,one) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
tff(82,plain,
! [A: $i] : ( i(A) = difference(A,one) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [A: $i] : ( i(A) = difference(A,one) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [A: $i] : ( i(A) = difference(A,one) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ~ ! [A: $i] : ( i(A) = difference(A,one) )
| ( i(x0) = difference(x0,one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
i(x0) = difference(x0,one),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
difference(x0,one) = i(x0),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
product(difference(x0,one),x0) = product(i(x0),x0),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
product(difference(x0,one),x0) = eta(x0),
inference(transitivity,[status(thm)],[88,77]) ).
tff(90,plain,
product(one,product(difference(x0,one),x0)) = product(one,eta(x0)),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
product(i(x0),x0) = product(difference(x0,one),x0),
inference(symmetry,[status(thm)],[88]) ).
tff(92,plain,
eta(x0) = product(difference(x0,one),x0),
inference(transitivity,[status(thm)],[67,91]) ).
tff(93,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(x0,difference(x0,one)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
product(x0,difference(x0,one)) = one,
inference(unit_resolution,[status(thm)],[93,7]) ).
tff(95,plain,
product(product(x0,difference(x0,one)),eta(x0)) = product(one,product(difference(x0,one),x0)),
inference(monotonicity,[status(thm)],[94,92]) ).
tff(96,plain,
product(product(x0,difference(x0,one)),eta(x0)) = product(x0,j(x0)),
inference(transitivity,[status(thm)],[95,90,76,67,58]) ).
tff(97,plain,
difference(x0,product(product(x0,difference(x0,one)),eta(x0))) = difference(x0,product(x0,j(x0))),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,axiom,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
tff(102,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,difference(x0,one)),eta(x0))) = quotient(product(difference(x0,one),product(eta(x0),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
difference(x0,product(product(x0,difference(x0,one)),eta(x0))) = quotient(product(difference(x0,one),product(eta(x0),x0)),x0),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
quotient(product(difference(x0,one),product(eta(x0),x0)),x0) = difference(x0,product(product(x0,difference(x0,one)),eta(x0))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
product(product(difference(x0,one),x0),x0) = product(eta(x0),x0),
inference(monotonicity,[status(thm)],[89]) ).
tff(109,plain,
product(eta(x0),x0) = product(product(difference(x0,one),x0),x0),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
difference(difference(x0,one),product(eta(x0),x0)) = difference(difference(x0,one),product(product(difference(x0,one),x0),x0)),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
difference(difference(x0,one),product(product(difference(x0,one),x0),x0)) = difference(difference(x0,one),product(eta(x0),x0)),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),x0),x0)) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
difference(difference(x0,one),product(product(difference(x0,one),x0),x0)) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[112,104]) ).
tff(114,plain,
quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),x0),x0)),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(eta(x0),x0)),
inference(transitivity,[status(thm)],[114,111]) ).
tff(116,plain,
product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(difference(x0,one),difference(difference(x0,one),product(eta(x0),x0))),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
product(difference(x0,one),difference(difference(x0,one),product(eta(x0),x0))) = product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(difference(x0,one),difference(difference(x0,one),product(eta(x0),x0))) = product(eta(x0),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
product(difference(x0,one),difference(difference(x0,one),product(eta(x0),x0))) = product(eta(x0),x0),
inference(unit_resolution,[status(thm)],[118,7]) ).
tff(120,plain,
product(eta(x0),x0) = product(difference(x0,one),difference(difference(x0,one),product(eta(x0),x0))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
product(eta(x0),x0) = product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(transitivity,[status(thm)],[120,117]) ).
tff(122,plain,
product(difference(x0,one),product(eta(x0),x0)) = product(difference(x0,one),product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
product(difference(x0,one),product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(difference(x0,one),product(eta(x0),x0)),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),x0) = quotient(product(difference(x0,one),product(eta(x0),x0)),x0),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),x0) = j(x0),
inference(transitivity,[status(thm)],[124,107,97,49]) ).
tff(126,plain,
product(quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),x0),x0) = product(j(x0),x0),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),x0),x0) = product(difference(x0,one),product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
product(quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),x0),x0) = product(difference(x0,one),product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),
inference(unit_resolution,[status(thm)],[127,35]) ).
tff(129,plain,
product(difference(x0,one),product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),x0),x0),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
product(difference(x0,one),product(eta(x0),x0)) = one,
inference(transitivity,[status(thm)],[122,129,126,47,37]) ).
tff(131,plain,
difference(difference(x0,one),product(difference(x0,one),product(eta(x0),x0))) = difference(i(x0),one),
inference(monotonicity,[status(thm)],[87,130]) ).
tff(132,plain,
difference(i(x0),one) = difference(difference(x0,one),product(difference(x0,one),product(eta(x0),x0))),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [A: $i] : ( i(A) = difference(A,one) )
| ( i(i(x0)) = difference(i(x0),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
i(i(x0)) = difference(i(x0),one),
inference(unit_resolution,[status(thm)],[133,84]) ).
tff(135,plain,
i(i(x0)) = product(eta(x0),x0),
inference(transitivity,[status(thm)],[134,132,28]) ).
tff(136,plain,
product(i(i(x0)),quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0))) = product(product(eta(x0),x0),difference(product(eta(x0),x0),product(eta(x0),product(x0,x1)))),
inference(monotonicity,[status(thm)],[135,19]) ).
tff(137,plain,
^ [B: $i,A: $i] :
refl(
( ( quotient(product(A,B),B) = A )
<=> ( quotient(product(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(138,plain,
( ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[137]) ).
tff(139,plain,
( ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,axiom,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
tff(141,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(skolemize,[status(sab)],[141]) ).
tff(143,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[142,138]) ).
tff(144,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),difference(x0,one)) = quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
quotient(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),difference(x0,one)) = quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),
inference(unit_resolution,[status(thm)],[144,143]) ).
tff(146,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(x0,product(x0,product(x1,difference(x0,one)))) = product(x1,difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
difference(x0,product(x0,product(x1,difference(x0,one)))) = product(x1,difference(x0,one)),
inference(unit_resolution,[status(thm)],[146,26]) ).
tff(148,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(x0,product(x1,difference(x0,one))))) = product(x0,product(x1,difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(x0,product(x1,difference(x0,one))))) = product(x0,product(x1,difference(x0,one))),
inference(unit_resolution,[status(thm)],[148,7]) ).
tff(150,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(x0,i(i(x0))),i(i(x0))) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
product(quotient(x0,i(i(x0))),i(i(x0))) = x0,
inference(unit_resolution,[status(thm)],[150,35]) ).
tff(152,plain,
one = product(x0,difference(x0,one)),
inference(symmetry,[status(thm)],[94]) ).
tff(153,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(difference(x0,one),difference(difference(x0,one),one)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
product(difference(x0,one),difference(difference(x0,one),one)) = one,
inference(unit_resolution,[status(thm)],[153,7]) ).
tff(155,plain,
difference(difference(x0,one),one) = difference(i(x0),one),
inference(monotonicity,[status(thm)],[87]) ).
tff(156,plain,
difference(i(x0),one) = difference(difference(x0,one),one),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
i(i(x0)) = difference(difference(x0,one),one),
inference(transitivity,[status(thm)],[134,156]) ).
tff(158,plain,
product(difference(x0,one),i(i(x0))) = product(difference(x0,one),difference(difference(x0,one),one)),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
product(difference(x0,one),i(i(x0))) = product(x0,difference(x0,one)),
inference(transitivity,[status(thm)],[158,154,152]) ).
tff(160,plain,
product(x0,product(difference(x0,one),i(i(x0)))) = product(x0,product(x0,difference(x0,one))),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
product(x0,product(x0,difference(x0,one))) = product(x0,product(difference(x0,one),i(i(x0)))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
product(x0,product(x0,difference(x0,one))) = product(x0,one),
inference(monotonicity,[status(thm)],[94]) ).
tff(163,plain,
product(x0,one) = product(x0,product(x0,difference(x0,one))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
^ [A: $i] :
refl(
( ( product(A,one) = A )
<=> ( product(A,one) = A ) )),
inference(bind,[status(th)],]) ).
tff(165,plain,
( ! [A: $i] : ( product(A,one) = A )
<=> ! [A: $i] : ( product(A,one) = A ) ),
inference(quant_intro,[status(thm)],[164]) ).
tff(166,plain,
( ! [A: $i] : ( product(A,one) = A )
<=> ! [A: $i] : ( product(A,one) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(167,axiom,
! [A: $i] : ( product(A,one) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
tff(168,plain,
! [A: $i] : ( product(A,one) = A ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [A: $i] : ( product(A,one) = A ),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [A: $i] : ( product(A,one) = A ),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(x0,one) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(172,plain,
product(x0,one) = x0,
inference(unit_resolution,[status(thm)],[171,170]) ).
tff(173,plain,
x0 = product(x0,one),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
x0 = product(x0,product(difference(x0,one),i(i(x0)))),
inference(transitivity,[status(thm)],[173,163,161]) ).
tff(175,plain,
quotient(x0,i(i(x0))) = quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))) = quotient(x0,i(i(x0))),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))) = product(quotient(x0,i(i(x0))),i(i(x0))),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))) = x0,
inference(transitivity,[status(thm)],[177,151]) ).
tff(179,plain,
product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))),product(x1,difference(x0,one))) = product(x0,product(x1,difference(x0,one))),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
product(x0,product(x1,difference(x0,one))) = product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))),product(x1,difference(x0,one))),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(x0,product(x1,difference(x0,one)))) = difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))),product(x1,difference(x0,one)))),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))),product(x1,difference(x0,one)))) = difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(x0,product(x1,difference(x0,one)))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(x0,product(product(x1,difference(x0,one)),x0)),x0),x0) = product(x0,product(product(x1,difference(x0,one)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
product(quotient(product(x0,product(product(x1,difference(x0,one)),x0)),x0),x0) = product(x0,product(product(x1,difference(x0,one)),x0)),
inference(unit_resolution,[status(thm)],[183,35]) ).
tff(185,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,x0),product(x1,difference(x0,one)))) = quotient(product(x0,product(product(x1,difference(x0,one)),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
difference(x0,product(product(x0,x0),product(x1,difference(x0,one)))) = quotient(product(x0,product(product(x1,difference(x0,one)),x0)),x0),
inference(unit_resolution,[status(thm)],[185,104]) ).
tff(187,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(product(x0,x0),product(x1,difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(product(x0,x0),product(x1,difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
product(quotient(product(product(x0,x0),product(x1,difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(product(x0,x0),product(x1,difference(x0,one))),
inference(unit_resolution,[status(thm)],[187,35]) ).
tff(189,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(x0,x1))) = quotient(product(i(i(x0)),product(product(x0,x1),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(190,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(x0,x1))) = quotient(product(i(i(x0)),product(product(x0,x1),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[189,104]) ).
tff(191,plain,
product(difference(x0,one),i(i(x0))) = one,
inference(transitivity,[status(thm)],[158,154]) ).
tff(192,plain,
product(product(difference(x0,one),i(i(x0))),product(x0,x1)) = product(one,product(x0,x1)),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
product(one,product(x0,x1)) = product(product(difference(x0,one),i(i(x0))),product(x0,x1)),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,product(x0,x1)) = product(x0,x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(195,plain,
product(one,product(x0,x1)) = product(x0,x1),
inference(unit_resolution,[status(thm)],[194,74]) ).
tff(196,plain,
product(x0,x1) = product(one,product(x0,x1)),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,x0) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(198,plain,
product(one,x0) = x0,
inference(unit_resolution,[status(thm)],[197,74]) ).
tff(199,plain,
product(j(x0),x0) = one,
inference(transitivity,[status(thm)],[47,37]) ).
tff(200,plain,
product(product(j(x0),x0),x0) = product(one,x0),
inference(monotonicity,[status(thm)],[199]) ).
tff(201,plain,
product(quotient(one,x0),x0) = product(j(x0),x0),
inference(symmetry,[status(thm)],[47]) ).
tff(202,plain,
one = product(quotient(one,x0),x0),
inference(symmetry,[status(thm)],[37]) ).
tff(203,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(x0,product(x0,one)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
difference(x0,product(x0,one)) = one,
inference(unit_resolution,[status(thm)],[203,26]) ).
tff(205,plain,
product(x0,difference(x0,one)) = product(j(x0),x0),
inference(transitivity,[status(thm)],[94,202,201]) ).
tff(206,plain,
product(product(x0,difference(x0,one)),x0) = product(product(j(x0),x0),x0),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
product(product(x0,difference(x0,one)),x0) = product(x0,one),
inference(transitivity,[status(thm)],[206,200,198,173]) ).
tff(208,plain,
difference(x0,product(product(x0,difference(x0,one)),x0)) = difference(x0,product(x0,one)),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,difference(x0,one)),x0)) = quotient(product(difference(x0,one),product(x0,x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(210,plain,
difference(x0,product(product(x0,difference(x0,one)),x0)) = quotient(product(difference(x0,one),product(x0,x0)),x0),
inference(unit_resolution,[status(thm)],[209,104]) ).
tff(211,plain,
quotient(product(difference(x0,one),product(x0,x0)),x0) = difference(x0,product(product(x0,difference(x0,one)),x0)),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
quotient(product(difference(x0,one),product(x0,x0)),x0) = product(j(x0),x0),
inference(transitivity,[status(thm)],[211,208,204,202,201]) ).
tff(213,plain,
product(quotient(product(difference(x0,one),product(x0,x0)),x0),x0) = product(product(j(x0),x0),x0),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(difference(x0,one),product(x0,x0)),x0),x0) = product(difference(x0,one),product(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(215,plain,
product(quotient(product(difference(x0,one),product(x0,x0)),x0),x0) = product(difference(x0,one),product(x0,x0)),
inference(unit_resolution,[status(thm)],[214,35]) ).
tff(216,plain,
product(difference(x0,one),product(x0,x0)) = product(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
product(difference(x0,one),product(x0,x0)) = x0,
inference(transitivity,[status(thm)],[216,213,200,198]) ).
tff(218,plain,
product(product(difference(x0,one),product(x0,x0)),x1) = product(x0,x1),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
product(product(difference(x0,one),product(x0,x0)),x1) = product(product(difference(x0,one),i(i(x0))),product(x0,x1)),
inference(transitivity,[status(thm)],[218,196,193]) ).
tff(220,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(x0,x0)),x1)) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(x0,x1))),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),product(x0,x0)),x1)) = quotient(product(product(x0,x0),product(x1,difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(222,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(x0,x0)),x1)) = quotient(product(product(x0,x0),product(x1,difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[221,104]) ).
tff(223,plain,
quotient(product(product(x0,x0),product(x1,difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),product(x0,x0)),x1)),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
quotient(product(product(x0,x0),product(x1,difference(x0,one))),difference(x0,one)) = quotient(product(i(i(x0)),product(product(x0,x1),difference(x0,one))),difference(x0,one)),
inference(transitivity,[status(thm)],[223,220,190]) ).
tff(225,plain,
product(quotient(product(product(x0,x0),product(x1,difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(quotient(product(i(i(x0)),product(product(x0,x1),difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
product(quotient(product(i(i(x0)),product(product(x0,x1),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(quotient(product(product(x0,x0),product(x1,difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(i(i(x0)),product(product(x0,x1),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(product(x0,x1),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
product(quotient(product(i(i(x0)),product(product(x0,x1),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(product(x0,x1),difference(x0,one))),
inference(unit_resolution,[status(thm)],[227,35]) ).
tff(229,plain,
product(i(i(x0)),product(product(x0,x1),difference(x0,one))) = product(quotient(product(i(i(x0)),product(product(x0,x1),difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[228]) ).
tff(230,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,i(i(x0))) = i(i(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(231,plain,
product(one,i(i(x0))) = i(i(x0)),
inference(unit_resolution,[status(thm)],[230,74]) ).
tff(232,plain,
product(product(x0,difference(x0,one)),i(i(x0))) = product(one,i(i(x0))),
inference(monotonicity,[status(thm)],[94]) ).
tff(233,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(x0,difference(x0,product(product(x0,difference(x0,one)),i(i(x0))))) = product(product(x0,difference(x0,one)),i(i(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(234,plain,
product(x0,difference(x0,product(product(x0,difference(x0,one)),i(i(x0))))) = product(product(x0,difference(x0,one)),i(i(x0))),
inference(unit_resolution,[status(thm)],[233,7]) ).
tff(235,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,difference(x0,one)),i(i(x0)))) = quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(236,plain,
difference(x0,product(product(x0,difference(x0,one)),i(i(x0)))) = quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),
inference(unit_resolution,[status(thm)],[235,104]) ).
tff(237,plain,
quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0) = difference(x0,product(product(x0,difference(x0,one)),i(i(x0)))),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
product(x0,quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0)) = product(x0,difference(x0,product(product(x0,difference(x0,one)),i(i(x0))))),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
product(x0,quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0)) = i(i(x0)),
inference(transitivity,[status(thm)],[238,234,232,231]) ).
tff(240,plain,
product(product(x0,quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0)),product(product(x0,x1),difference(x0,one))) = product(i(i(x0)),product(product(x0,x1),difference(x0,one))),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
product(product(x0,quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0)),product(product(x0,x1),difference(x0,one))) = product(product(x0,x0),product(x1,difference(x0,one))),
inference(transitivity,[status(thm)],[240,229,226,188]) ).
tff(242,plain,
difference(x0,product(product(x0,quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0)),product(product(x0,x1),difference(x0,one)))) = difference(x0,product(product(x0,x0),product(x1,difference(x0,one)))),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0)),product(product(x0,x1),difference(x0,one)))) = quotient(product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(244,plain,
difference(x0,product(product(x0,quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0)),product(product(x0,x1),difference(x0,one)))) = quotient(product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),x0),
inference(unit_resolution,[status(thm)],[243,104]) ).
tff(245,plain,
quotient(product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),x0) = difference(x0,product(product(x0,quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0)),product(product(x0,x1),difference(x0,one)))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
quotient(product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),x0) = quotient(product(x0,product(product(x1,difference(x0,one)),x0)),x0),
inference(transitivity,[status(thm)],[245,242,186]) ).
tff(247,plain,
product(quotient(product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),x0),x0) = product(quotient(product(x0,product(product(x1,difference(x0,one)),x0)),x0),x0),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),x0),x0) = product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(249,plain,
product(quotient(product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),x0),x0) = product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),
inference(unit_resolution,[status(thm)],[248,35]) ).
tff(250,plain,
product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)) = product(quotient(product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),x0),x0),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0) = quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(252,plain,
product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0) = quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[251,35]) ).
tff(253,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(one,difference(one,x0)) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(254,plain,
product(one,difference(one,x0)) = x0,
inference(unit_resolution,[status(thm)],[253,7]) ).
tff(255,plain,
difference(one,x0) = difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),i(i(x0))))),
inference(monotonicity,[status(thm)],[152,174]) ).
tff(256,plain,
difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),i(i(x0))))) = difference(one,x0),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),i(i(x0))))) = quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(258,plain,
difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),i(i(x0))))) = quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[257,16]) ).
tff(259,plain,
quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0) = difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),i(i(x0))))),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0) = difference(one,x0),
inference(transitivity,[status(thm)],[259,256]) ).
tff(261,plain,
product(one,quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0)) = product(one,difference(one,x0)),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0)) = quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
product(one,quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0)) = quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[262,74]) ).
tff(264,plain,
quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0) = product(one,quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0) = x0,
inference(transitivity,[status(thm)],[264,261,254]) ).
tff(266,plain,
product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0) = product(x0,x0),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
product(x0,x0) = product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
product(x0,x0) = quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),
inference(transitivity,[status(thm)],[267,252]) ).
tff(269,plain,
product(product(x0,x0),difference(x0,one)) = product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[268]) ).
tff(270,plain,
product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(product(x0,x0),difference(x0,one)),
inference(symmetry,[status(thm)],[269]) ).
tff(271,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(x0,difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(272,plain,
product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(x0,difference(x0,one))),
inference(unit_resolution,[status(thm)],[271,35]) ).
tff(273,plain,
product(i(i(x0)),product(x0,difference(x0,one))) = product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[272]) ).
tff(274,plain,
product(i(i(x0)),product(x0,difference(x0,one))) = product(i(i(x0)),one),
inference(monotonicity,[status(thm)],[94]) ).
tff(275,plain,
product(i(i(x0)),one) = product(i(i(x0)),product(x0,difference(x0,one))),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(i(i(x0)),one) = i(i(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(277,plain,
product(i(i(x0)),one) = i(i(x0)),
inference(unit_resolution,[status(thm)],[276,170]) ).
tff(278,plain,
i(i(x0)) = product(i(i(x0)),one),
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
product(product(x0,difference(x0,one)),i(i(x0))) = product(product(x0,x0),difference(x0,one)),
inference(transitivity,[status(thm)],[232,231,278,275,273,270]) ).
tff(280,plain,
difference(x0,product(product(x0,difference(x0,one)),i(i(x0)))) = difference(x0,product(product(x0,x0),difference(x0,one))),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
difference(x0,product(product(x0,x0),difference(x0,one))) = difference(x0,product(product(x0,difference(x0,one)),i(i(x0)))),
inference(symmetry,[status(thm)],[280]) ).
tff(282,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,x0),difference(x0,one))) = quotient(product(x0,product(difference(x0,one),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(283,plain,
difference(x0,product(product(x0,x0),difference(x0,one))) = quotient(product(x0,product(difference(x0,one),x0)),x0),
inference(unit_resolution,[status(thm)],[282,104]) ).
tff(284,plain,
quotient(product(x0,product(difference(x0,one),x0)),x0) = difference(x0,product(product(x0,x0),difference(x0,one))),
inference(symmetry,[status(thm)],[283]) ).
tff(285,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(product(x0,product(difference(x0,one),x0)),x0),difference(x0,one)),difference(x0,one)) = quotient(product(x0,product(difference(x0,one),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(286,plain,
product(quotient(quotient(product(x0,product(difference(x0,one),x0)),x0),difference(x0,one)),difference(x0,one)) = quotient(product(x0,product(difference(x0,one),x0)),x0),
inference(unit_resolution,[status(thm)],[285,35]) ).
tff(287,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) = quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(288,plain,
product(one,quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) = quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[287,74]) ).
tff(289,plain,
product(difference(x0,one),x0) = product(x0,j(x0)),
inference(transitivity,[status(thm)],[88,58]) ).
tff(290,plain,
product(x0,product(difference(x0,one),x0)) = product(x0,product(x0,j(x0))),
inference(monotonicity,[status(thm)],[289]) ).
tff(291,plain,
product(x0,product(x0,j(x0))) = product(x0,product(difference(x0,one),x0)),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
difference(one,product(x0,product(x0,j(x0)))) = difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),x0))),
inference(monotonicity,[status(thm)],[152,291]) ).
tff(293,plain,
difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),x0))) = difference(one,product(x0,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),x0))) = quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(295,plain,
difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),x0))) = quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[294,16]) ).
tff(296,plain,
quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0) = difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),x0))),
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0) = difference(one,product(x0,product(x0,j(x0)))),
inference(transitivity,[status(thm)],[296,293]) ).
tff(298,plain,
product(one,quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) = product(one,difference(one,product(x0,product(x0,j(x0))))),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
product(one,difference(one,product(x0,product(x0,j(x0))))) = product(one,quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(symmetry,[status(thm)],[298]) ).
tff(300,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(one,difference(one,product(x0,product(x0,j(x0))))) = product(x0,product(x0,j(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(301,plain,
product(one,difference(one,product(x0,product(x0,j(x0))))) = product(x0,product(x0,j(x0))),
inference(unit_resolution,[status(thm)],[300,7]) ).
tff(302,plain,
product(x0,product(x0,j(x0))) = product(one,difference(one,product(x0,product(x0,j(x0))))),
inference(symmetry,[status(thm)],[301]) ).
tff(303,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(x0,product(difference(x0,one),difference(x0,one))),product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0))))) = product(x0,product(x0,j(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(304,plain,
difference(product(x0,product(difference(x0,one),difference(x0,one))),product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0))))) = product(x0,product(x0,j(x0))),
inference(unit_resolution,[status(thm)],[303,26]) ).
tff(305,plain,
product(x0,product(x0,j(x0))) = quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),
inference(transitivity,[status(thm)],[302,299,288]) ).
tff(306,plain,
product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0)))) = product(product(x0,product(difference(x0,one),difference(x0,one))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(monotonicity,[status(thm)],[305]) ).
tff(307,plain,
product(product(x0,product(difference(x0,one),difference(x0,one))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) = product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(x0,difference(x0,product(product(x0,product(difference(x0,one),difference(x0,one))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)))) = product(product(x0,product(difference(x0,one),difference(x0,one))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(309,plain,
product(x0,difference(x0,product(product(x0,product(difference(x0,one),difference(x0,one))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)))) = product(product(x0,product(difference(x0,one),difference(x0,one))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(unit_resolution,[status(thm)],[308,7]) ).
tff(310,plain,
quotient(one,x0) = j(x0),
inference(symmetry,[status(thm)],[46]) ).
tff(311,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(i(i(x0)),difference(x0,one)),difference(x0,one)) = i(i(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(312,plain,
quotient(product(i(i(x0)),difference(x0,one)),difference(x0,one)) = i(i(x0)),
inference(unit_resolution,[status(thm)],[311,143]) ).
tff(313,plain,
product(i(i(x0)),difference(x0,one)) = product(i(i(x0)),i(x0)),
inference(monotonicity,[status(thm)],[87]) ).
tff(314,plain,
product(i(i(x0)),i(x0)) = product(i(i(x0)),difference(x0,one)),
inference(symmetry,[status(thm)],[313]) ).
tff(315,plain,
( ~ ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
| ( product(i(i(x0)),i(x0)) = product(i(x0),j(i(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(316,plain,
product(i(i(x0)),i(x0)) = product(i(x0),j(i(x0))),
inference(unit_resolution,[status(thm)],[315,56]) ).
tff(317,plain,
product(i(x0),j(i(x0))) = product(i(i(x0)),i(x0)),
inference(symmetry,[status(thm)],[316]) ).
tff(318,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(x0,difference(x0,one)),difference(x0,one)) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(319,plain,
quotient(product(x0,difference(x0,one)),difference(x0,one)) = x0,
inference(unit_resolution,[status(thm)],[318,143]) ).
tff(320,plain,
quotient(one,difference(x0,one)) = quotient(product(x0,difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[152]) ).
tff(321,plain,
( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
| ( j(difference(x0,one)) = quotient(one,difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(322,plain,
j(difference(x0,one)) = quotient(one,difference(x0,one)),
inference(unit_resolution,[status(thm)],[321,44]) ).
tff(323,plain,
j(i(x0)) = j(difference(x0,one)),
inference(monotonicity,[status(thm)],[86]) ).
tff(324,plain,
j(i(x0)) = x0,
inference(transitivity,[status(thm)],[323,322,320,319]) ).
tff(325,plain,
product(i(x0),j(i(x0))) = product(i(x0),x0),
inference(monotonicity,[status(thm)],[324]) ).
tff(326,plain,
product(i(x0),x0) = product(i(x0),j(i(x0))),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(x0,product(x0,difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(328,plain,
product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(x0,product(x0,difference(x0,one))),
inference(unit_resolution,[status(thm)],[327,35]) ).
tff(329,plain,
product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)) = x0,
inference(transitivity,[status(thm)],[328,162,172]) ).
tff(330,plain,
product(difference(x0,one),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = product(i(x0),x0),
inference(monotonicity,[status(thm)],[87,329]) ).
tff(331,plain,
product(difference(x0,one),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = product(i(i(x0)),difference(x0,one)),
inference(transitivity,[status(thm)],[330,326,317,314]) ).
tff(332,plain,
quotient(product(difference(x0,one),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) = quotient(product(i(i(x0)),difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[331]) ).
tff(333,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(difference(x0,one),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(334,plain,
difference(difference(x0,one),product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(difference(x0,one),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[333,104]) ).
tff(335,plain,
difference(difference(x0,one),product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = difference(difference(x0,one),one),
inference(transitivity,[status(thm)],[334,332,312,134,156]) ).
tff(336,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(difference(x0,one),difference(difference(x0,one),one)),
inference(monotonicity,[status(thm)],[335]) ).
tff(337,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(338,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(unit_resolution,[status(thm)],[337,7]) ).
tff(339,plain,
product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))),
inference(symmetry,[status(thm)],[338]) ).
tff(340,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(341,plain,
product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[340,35]) ).
tff(342,plain,
product(product(difference(x0,one),difference(x0,one)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)) = product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(monotonicity,[status(thm)],[341]) ).
tff(343,plain,
product(product(difference(x0,one),difference(x0,one)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)) = one,
inference(transitivity,[status(thm)],[342,339,336,154]) ).
tff(344,plain,
quotient(product(product(difference(x0,one),difference(x0,one)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0) = quotient(one,x0),
inference(monotonicity,[status(thm)],[343]) ).
tff(345,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,product(difference(x0,one),difference(x0,one))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0))) = quotient(product(product(difference(x0,one),difference(x0,one)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(346,plain,
difference(x0,product(product(x0,product(difference(x0,one),difference(x0,one))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0))) = quotient(product(product(difference(x0,one),difference(x0,one)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),
inference(unit_resolution,[status(thm)],[345,104]) ).
tff(347,plain,
difference(x0,product(product(x0,product(difference(x0,one),difference(x0,one))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0))) = j(x0),
inference(transitivity,[status(thm)],[346,344,310]) ).
tff(348,plain,
product(x0,difference(x0,product(product(x0,product(difference(x0,one),difference(x0,one))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)))) = product(x0,j(x0)),
inference(monotonicity,[status(thm)],[347]) ).
tff(349,plain,
product(x0,j(x0)) = product(x0,difference(x0,product(product(x0,product(difference(x0,one),difference(x0,one))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)))),
inference(symmetry,[status(thm)],[348]) ).
tff(350,plain,
product(product(j(x0),x0),eta(x0)) = product(one,product(difference(x0,one),x0)),
inference(monotonicity,[status(thm)],[199,92]) ).
tff(351,plain,
product(product(j(x0),x0),eta(x0)) = product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0)))),
inference(transitivity,[status(thm)],[350,90,76,67,58,349,309,307]) ).
tff(352,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(j(x0),product(x0,x0)),product(j(x0),product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)))) = quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(353,plain,
difference(product(j(x0),product(x0,x0)),product(j(x0),product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)))) = quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),j(x0)),
inference(unit_resolution,[status(thm)],[352,16]) ).
tff(354,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),j(x0)) = quotient(product(x0,product(j(x0),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(355,plain,
product(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),j(x0)) = quotient(product(x0,product(j(x0),x0)),x0),
inference(unit_resolution,[status(thm)],[354,35]) ).
tff(356,plain,
quotient(product(x0,product(j(x0),x0)),x0) = product(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),j(x0)),
inference(symmetry,[status(thm)],[355]) ).
tff(357,plain,
x0 = product(one,x0),
inference(symmetry,[status(thm)],[198]) ).
tff(358,plain,
product(j(x0),x0) = product(x0,difference(x0,one)),
inference(transitivity,[status(thm)],[47,37,152]) ).
tff(359,plain,
product(x0,product(j(x0),x0)) = product(x0,product(x0,difference(x0,one))),
inference(monotonicity,[status(thm)],[358]) ).
tff(360,plain,
product(x0,product(j(x0),x0)) = product(one,x0),
inference(transitivity,[status(thm)],[359,162,172,357]) ).
tff(361,plain,
quotient(product(x0,product(j(x0),x0)),x0) = quotient(product(one,x0),x0),
inference(monotonicity,[status(thm)],[360]) ).
tff(362,plain,
quotient(product(one,x0),x0) = quotient(product(x0,product(j(x0),x0)),x0),
inference(symmetry,[status(thm)],[361]) ).
tff(363,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(one,x0),x0) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(364,plain,
quotient(product(one,x0),x0) = one,
inference(unit_resolution,[status(thm)],[363,143]) ).
tff(365,plain,
one = quotient(product(one,x0),x0),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(product(x0,x0),difference(product(x0,x0),x0)) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(367,plain,
product(product(x0,x0),difference(product(x0,x0),x0)) = x0,
inference(unit_resolution,[status(thm)],[366,7]) ).
tff(368,plain,
x0 = product(x0,product(x0,difference(x0,one))),
inference(transitivity,[status(thm)],[173,163]) ).
tff(369,plain,
difference(product(x0,x0),x0) = difference(product(x0,x0),product(x0,product(x0,difference(x0,one)))),
inference(monotonicity,[status(thm)],[368]) ).
tff(370,plain,
difference(product(x0,x0),product(x0,product(x0,difference(x0,one)))) = difference(product(x0,x0),x0),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(x0,x0),product(x0,product(x0,difference(x0,one)))) = quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(372,plain,
difference(product(x0,x0),product(x0,product(x0,difference(x0,one)))) = quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),
inference(unit_resolution,[status(thm)],[371,16]) ).
tff(373,plain,
quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0) = difference(product(x0,x0),product(x0,product(x0,difference(x0,one)))),
inference(symmetry,[status(thm)],[372]) ).
tff(374,plain,
quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0) = difference(product(x0,x0),x0),
inference(transitivity,[status(thm)],[373,370]) ).
tff(375,plain,
product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)) = product(product(x0,x0),difference(product(x0,x0),x0)),
inference(monotonicity,[status(thm)],[374]) ).
tff(376,plain,
product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)) = x0,
inference(transitivity,[status(thm)],[375,367]) ).
tff(377,plain,
product(j(x0),product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0))) = product(j(x0),x0),
inference(monotonicity,[status(thm)],[376]) ).
tff(378,plain,
product(j(x0),product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0))) = product(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),j(x0)),
inference(transitivity,[status(thm)],[377,47,37,365,362,356]) ).
tff(379,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0))) = quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(380,plain,
product(one,quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0))) = quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),
inference(unit_resolution,[status(thm)],[379,74]) ).
tff(381,plain,
one = product(j(x0),x0),
inference(transitivity,[status(thm)],[202,201]) ).
tff(382,plain,
difference(one,product(j(x0),product(x0,x0))) = difference(product(j(x0),x0),product(j(x0),product(x0,x0))),
inference(monotonicity,[status(thm)],[381]) ).
tff(383,plain,
difference(product(j(x0),x0),product(j(x0),product(x0,x0))) = difference(one,product(j(x0),product(x0,x0))),
inference(symmetry,[status(thm)],[382]) ).
tff(384,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(j(x0),x0),product(j(x0),product(x0,x0))) = quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(385,plain,
difference(product(j(x0),x0),product(j(x0),product(x0,x0))) = quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),
inference(unit_resolution,[status(thm)],[384,16]) ).
tff(386,plain,
quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)) = difference(product(j(x0),x0),product(j(x0),product(x0,x0))),
inference(symmetry,[status(thm)],[385]) ).
tff(387,plain,
quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)) = difference(one,product(j(x0),product(x0,x0))),
inference(transitivity,[status(thm)],[386,383]) ).
tff(388,plain,
product(one,quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0))) = product(one,difference(one,product(j(x0),product(x0,x0)))),
inference(monotonicity,[status(thm)],[387]) ).
tff(389,plain,
product(one,difference(one,product(j(x0),product(x0,x0)))) = product(one,quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0))),
inference(symmetry,[status(thm)],[388]) ).
tff(390,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(one,difference(one,product(j(x0),product(x0,x0)))) = product(j(x0),product(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(391,plain,
product(one,difference(one,product(j(x0),product(x0,x0)))) = product(j(x0),product(x0,x0)),
inference(unit_resolution,[status(thm)],[390,7]) ).
tff(392,plain,
product(j(x0),product(x0,x0)) = product(one,difference(one,product(j(x0),product(x0,x0)))),
inference(symmetry,[status(thm)],[391]) ).
tff(393,plain,
product(j(x0),product(x0,x0)) = quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),
inference(transitivity,[status(thm)],[392,389,380]) ).
tff(394,plain,
difference(product(j(x0),product(x0,x0)),product(j(x0),product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)))) = difference(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),product(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),j(x0))),
inference(monotonicity,[status(thm)],[393,378]) ).
tff(395,plain,
difference(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),product(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),j(x0))) = difference(product(j(x0),product(x0,x0)),product(j(x0),product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)))),
inference(symmetry,[status(thm)],[394]) ).
tff(396,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),product(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),j(x0))) = j(x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(397,plain,
difference(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),product(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),j(x0))) = j(x0),
inference(unit_resolution,[status(thm)],[396,26]) ).
tff(398,plain,
j(x0) = difference(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),product(quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),j(x0))),
inference(symmetry,[status(thm)],[397]) ).
tff(399,plain,
j(x0) = quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),j(x0)),
inference(transitivity,[status(thm)],[398,395,353]) ).
tff(400,plain,
product(j(x0),j(x0)) = product(quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),j(x0)),j(x0)),
inference(monotonicity,[status(thm)],[399]) ).
tff(401,plain,
product(quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),j(x0)),j(x0)) = product(j(x0),j(x0)),
inference(symmetry,[status(thm)],[400]) ).
tff(402,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),j(x0)),j(x0)) = quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(403,plain,
product(quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),j(x0)),j(x0)) = quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),
inference(unit_resolution,[status(thm)],[402,35]) ).
tff(404,plain,
quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)) = product(quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),j(x0)),j(x0)),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),difference(x0,one)),difference(x0,one)) = quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(406,plain,
product(quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),difference(x0,one)),difference(x0,one)) = quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),
inference(unit_resolution,[status(thm)],[405,35]) ).
tff(407,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),difference(x0,one))) = quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(408,plain,
difference(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),difference(x0,one))) = quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),
inference(unit_resolution,[status(thm)],[407,104]) ).
tff(409,plain,
product(product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)),j(x0)) = product(x0,j(x0)),
inference(monotonicity,[status(thm)],[376]) ).
tff(410,plain,
product(x0,j(x0)) = product(product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)),j(x0)),
inference(symmetry,[status(thm)],[409]) ).
tff(411,plain,
product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)) = i(i(x0)),
inference(transitivity,[status(thm)],[272,274,277]) ).
tff(412,plain,
product(product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),i(x0)),
inference(monotonicity,[status(thm)],[411,87]) ).
tff(413,plain,
product(product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),difference(x0,one)) = product(product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)),j(x0)),
inference(transitivity,[status(thm)],[412,316,325,58,410]) ).
tff(414,plain,
quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)) = product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0),
inference(symmetry,[status(thm)],[252]) ).
tff(415,plain,
quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)) = product(x0,x0),
inference(transitivity,[status(thm)],[414,266]) ).
tff(416,plain,
difference(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),difference(x0,one))) = difference(product(x0,x0),product(product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)),j(x0))),
inference(monotonicity,[status(thm)],[415,413]) ).
tff(417,plain,
difference(product(x0,x0),product(product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)),j(x0))) = difference(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),difference(x0,one))),
inference(symmetry,[status(thm)],[416]) ).
tff(418,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(product(x0,x0),product(product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)),j(x0))) = quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(419,plain,
difference(product(x0,x0),product(product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)),j(x0))) = quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),
inference(unit_resolution,[status(thm)],[418,104]) ).
tff(420,plain,
quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)) = difference(product(x0,x0),product(product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)),j(x0))),
inference(symmetry,[status(thm)],[419]) ).
tff(421,plain,
quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)) = quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),
inference(transitivity,[status(thm)],[420,417,408]) ).
tff(422,plain,
quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),difference(x0,one)) = quotient(quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),difference(x0,one)),
inference(monotonicity,[status(thm)],[421]) ).
tff(423,plain,
quotient(quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),difference(x0,one)) = quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),difference(x0,one)),
inference(symmetry,[status(thm)],[422]) ).
tff(424,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)))) = quotient(quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(425,plain,
difference(product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)))) = quotient(quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[424,16]) ).
tff(426,plain,
product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)) = difference(difference(x0,one),one),
inference(transitivity,[status(thm)],[272,274,277,134,156]) ).
tff(427,plain,
product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = product(difference(x0,one),difference(difference(x0,one),one)),
inference(monotonicity,[status(thm)],[426]) ).
tff(428,plain,
product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = one,
inference(transitivity,[status(thm)],[427,154]) ).
tff(429,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(difference(x0,one),difference(difference(x0,one),product(product(j(x0),x0),x0))) = product(product(j(x0),x0),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(430,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(j(x0),x0),x0))) = product(product(j(x0),x0),x0),
inference(unit_resolution,[status(thm)],[429,7]) ).
tff(431,plain,
product(difference(x0,one),i(i(x0))) = product(j(x0),x0),
inference(transitivity,[status(thm)],[158,154,202,201]) ).
tff(432,plain,
product(product(difference(x0,one),i(i(x0))),x0) = product(product(j(x0),x0),x0),
inference(monotonicity,[status(thm)],[431]) ).
tff(433,plain,
product(product(j(x0),x0),x0) = product(product(difference(x0,one),i(i(x0))),x0),
inference(symmetry,[status(thm)],[432]) ).
tff(434,plain,
difference(difference(x0,one),product(product(j(x0),x0),x0)) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),x0)),
inference(monotonicity,[status(thm)],[433]) ).
tff(435,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),x0)) = difference(difference(x0,one),product(product(j(x0),x0),x0)),
inference(symmetry,[status(thm)],[434]) ).
tff(436,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),x0)) = quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(437,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),x0)) = quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[436,104]) ).
tff(438,plain,
quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),x0)),
inference(symmetry,[status(thm)],[437]) ).
tff(439,plain,
product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0) = difference(difference(x0,one),product(product(j(x0),x0),x0)),
inference(transitivity,[status(thm)],[252,438,435]) ).
tff(440,plain,
product(difference(x0,one),product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0)) = product(difference(x0,one),difference(difference(x0,one),product(product(j(x0),x0),x0))),
inference(monotonicity,[status(thm)],[439]) ).
tff(441,plain,
product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))) = product(difference(x0,one),product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),
inference(monotonicity,[status(thm)],[414]) ).
tff(442,plain,
product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))) = x0,
inference(transitivity,[status(thm)],[441,440,430,200,198]) ).
tff(443,plain,
difference(product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)))) = difference(x0,one),
inference(monotonicity,[status(thm)],[442,428]) ).
tff(444,plain,
difference(x0,one) = difference(product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)))),
inference(symmetry,[status(thm)],[443]) ).
tff(445,plain,
difference(x0,one) = quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),difference(x0,one)),
inference(transitivity,[status(thm)],[444,425,423]) ).
tff(446,plain,
product(difference(x0,one),difference(x0,one)) = product(quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[445]) ).
tff(447,plain,
product(difference(x0,one),difference(x0,one)) = product(j(x0),j(x0)),
inference(transitivity,[status(thm)],[446,406,404,401]) ).
tff(448,plain,
product(x0,product(difference(x0,one),difference(x0,one))) = product(x0,product(j(x0),j(x0))),
inference(monotonicity,[status(thm)],[447]) ).
tff(449,plain,
product(x0,product(j(x0),j(x0))) = product(x0,product(difference(x0,one),difference(x0,one))),
inference(symmetry,[status(thm)],[448]) ).
tff(450,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(x0,product(j(x0),j(x0))),j(x0)),j(x0)) = product(x0,product(j(x0),j(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(451,plain,
product(quotient(product(x0,product(j(x0),j(x0))),j(x0)),j(x0)) = product(x0,product(j(x0),j(x0))),
inference(unit_resolution,[status(thm)],[450,35]) ).
tff(452,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(j(x0),product(j(x0),one)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(453,plain,
difference(j(x0),product(j(x0),one)) = one,
inference(unit_resolution,[status(thm)],[452,26]) ).
tff(454,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(j(x0),one) = j(x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(455,plain,
product(j(x0),one) = j(x0),
inference(unit_resolution,[status(thm)],[454,170]) ).
tff(456,plain,
j(x0) = product(j(x0),one),
inference(symmetry,[status(thm)],[455]) ).
tff(457,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,j(x0)) = j(x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(458,plain,
product(one,j(x0)) = j(x0),
inference(unit_resolution,[status(thm)],[457,74]) ).
tff(459,plain,
product(product(j(x0),x0),j(x0)) = product(one,j(x0)),
inference(monotonicity,[status(thm)],[199]) ).
tff(460,plain,
product(product(j(x0),x0),j(x0)) = product(j(x0),one),
inference(transitivity,[status(thm)],[459,458,456]) ).
tff(461,plain,
difference(j(x0),product(product(j(x0),x0),j(x0))) = difference(j(x0),product(j(x0),one)),
inference(monotonicity,[status(thm)],[460]) ).
tff(462,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(j(x0),product(product(j(x0),x0),j(x0))) = quotient(product(x0,product(j(x0),j(x0))),j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(463,plain,
difference(j(x0),product(product(j(x0),x0),j(x0))) = quotient(product(x0,product(j(x0),j(x0))),j(x0)),
inference(unit_resolution,[status(thm)],[462,104]) ).
tff(464,plain,
quotient(product(x0,product(j(x0),j(x0))),j(x0)) = difference(j(x0),product(product(j(x0),x0),j(x0))),
inference(symmetry,[status(thm)],[463]) ).
tff(465,plain,
quotient(product(x0,product(j(x0),j(x0))),j(x0)) = one,
inference(transitivity,[status(thm)],[464,461,453]) ).
tff(466,plain,
product(quotient(product(x0,product(j(x0),j(x0))),j(x0)),j(x0)) = product(one,j(x0)),
inference(monotonicity,[status(thm)],[465]) ).
tff(467,plain,
product(one,j(x0)) = product(quotient(product(x0,product(j(x0),j(x0))),j(x0)),j(x0)),
inference(symmetry,[status(thm)],[466]) ).
tff(468,plain,
j(x0) = product(one,j(x0)),
inference(symmetry,[status(thm)],[458]) ).
tff(469,plain,
j(x0) = product(x0,product(difference(x0,one),difference(x0,one))),
inference(transitivity,[status(thm)],[468,467,451,449]) ).
tff(470,plain,
difference(j(x0),product(product(j(x0),x0),eta(x0))) = difference(product(x0,product(difference(x0,one),difference(x0,one))),product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0))))),
inference(monotonicity,[status(thm)],[469,351]) ).
tff(471,plain,
product(one,product(difference(x0,one),x0)) = product(product(j(x0),x0),eta(x0)),
inference(symmetry,[status(thm)],[350]) ).
tff(472,plain,
product(one,eta(x0)) = product(one,product(difference(x0,one),x0)),
inference(symmetry,[status(thm)],[90]) ).
tff(473,plain,
eta(x0) = product(one,eta(x0)),
inference(symmetry,[status(thm)],[76]) ).
tff(474,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(eta(x0),product(x0,x0)),product(x0,x0)) = eta(x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(475,plain,
product(quotient(eta(x0),product(x0,x0)),product(x0,x0)) = eta(x0),
inference(unit_resolution,[status(thm)],[474,35]) ).
tff(476,plain,
product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))) = product(i(x0),x0),
inference(monotonicity,[status(thm)],[87,442]) ).
tff(477,plain,
product(i(x0),x0) = product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),
inference(symmetry,[status(thm)],[476]) ).
tff(478,plain,
eta(x0) = product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),
inference(transitivity,[status(thm)],[67,477]) ).
tff(479,plain,
quotient(eta(x0),product(x0,x0)) = quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),
inference(monotonicity,[status(thm)],[478,268]) ).
tff(480,plain,
quotient(product(difference(x0,one),product(difference(x0,one),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))) = quotient(eta(x0),product(x0,x0)),
inference(symmetry,[status(thm)],[479]) ).
tff(481,plain,
quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)) = quotient(eta(x0),product(x0,x0)),
inference(transitivity,[status(thm)],[420,417,408,480]) ).
tff(482,plain,
product(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),product(x0,x0)) = product(quotient(eta(x0),product(x0,x0)),product(x0,x0)),
inference(monotonicity,[status(thm)],[481]) ).
tff(483,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),product(x0,x0)) = product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(484,plain,
product(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),product(x0,x0)) = product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),
inference(unit_resolution,[status(thm)],[483,35]) ).
tff(485,plain,
product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))) = product(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),product(x0,x0)),
inference(symmetry,[status(thm)],[484]) ).
tff(486,plain,
quotient(product(difference(x0,one),product(x0,x0)),x0) = one,
inference(transitivity,[status(thm)],[211,208,204]) ).
tff(487,plain,
quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0) = quotient(one,x0),
inference(monotonicity,[status(thm)],[486]) ).
tff(488,plain,
quotient(one,x0) = quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),
inference(symmetry,[status(thm)],[487]) ).
tff(489,plain,
j(x0) = quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),
inference(transitivity,[status(thm)],[46,488]) ).
tff(490,plain,
product(j(x0),product(j(x0),product(x0,x0))) = product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),
inference(monotonicity,[status(thm)],[489]) ).
tff(491,plain,
product(j(x0),product(j(x0),product(x0,x0))) = product(product(j(x0),x0),eta(x0)),
inference(transitivity,[status(thm)],[490,485,482,475,473,472,471]) ).
tff(492,plain,
difference(j(x0),product(j(x0),product(j(x0),product(x0,x0)))) = difference(j(x0),product(product(j(x0),x0),eta(x0))),
inference(monotonicity,[status(thm)],[491]) ).
tff(493,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(j(x0),product(j(x0),product(j(x0),product(x0,x0)))) = product(j(x0),product(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(494,plain,
difference(j(x0),product(j(x0),product(j(x0),product(x0,x0)))) = product(j(x0),product(x0,x0)),
inference(unit_resolution,[status(thm)],[493,26]) ).
tff(495,plain,
product(j(x0),product(x0,x0)) = difference(j(x0),product(j(x0),product(j(x0),product(x0,x0)))),
inference(symmetry,[status(thm)],[494]) ).
tff(496,plain,
quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)) = product(one,quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0))),
inference(symmetry,[status(thm)],[380]) ).
tff(497,plain,
product(x0,product(j(x0),j(x0))) = product(quotient(product(x0,product(j(x0),j(x0))),j(x0)),j(x0)),
inference(symmetry,[status(thm)],[451]) ).
tff(498,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))) = product(x0,product(difference(x0,one),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(499,plain,
quotient(product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))) = product(x0,product(difference(x0,one),difference(x0,one))),
inference(unit_resolution,[status(thm)],[498,143]) ).
tff(500,plain,
quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0) = product(one,quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(symmetry,[status(thm)],[288]) ).
tff(501,plain,
quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0) = product(x0,product(x0,j(x0))),
inference(transitivity,[status(thm)],[500,298,301]) ).
tff(502,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(eta(x0),x0),x0) = eta(x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(503,plain,
quotient(product(eta(x0),x0),x0) = eta(x0),
inference(unit_resolution,[status(thm)],[502,143]) ).
tff(504,plain,
product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0) = difference(difference(x0,one),product(eta(x0),x0)),
inference(transitivity,[status(thm)],[341,114,111]) ).
tff(505,plain,
product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)) = product(difference(x0,one),difference(difference(x0,one),product(eta(x0),x0))),
inference(monotonicity,[status(thm)],[504]) ).
tff(506,plain,
product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)) = product(eta(x0),x0),
inference(transitivity,[status(thm)],[505,119]) ).
tff(507,plain,
quotient(product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0) = quotient(product(eta(x0),x0),x0),
inference(monotonicity,[status(thm)],[506]) ).
tff(508,plain,
quotient(product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0) = product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0)))),
inference(transitivity,[status(thm)],[507,503,67,58,349,309,307]) ).
tff(509,plain,
quotient(quotient(product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) = quotient(product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))),
inference(monotonicity,[status(thm)],[508,501]) ).
tff(510,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,difference(x0,one)))) = quotient(quotient(product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(511,plain,
difference(product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,difference(x0,one)))) = quotient(quotient(product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(unit_resolution,[status(thm)],[510,16]) ).
tff(512,plain,
product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,difference(x0,one))) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),one),
inference(monotonicity,[status(thm)],[94]) ).
tff(513,plain,
product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),one) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,difference(x0,one))),
inference(symmetry,[status(thm)],[512]) ).
tff(514,plain,
product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),one) = product(product(x0,product(x0,j(x0))),one),
inference(monotonicity,[status(thm)],[501]) ).
tff(515,plain,
product(product(x0,product(x0,j(x0))),one) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),one),
inference(symmetry,[status(thm)],[514]) ).
tff(516,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(product(x0,product(x0,j(x0))),one) = product(x0,product(x0,j(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(517,plain,
product(product(x0,product(x0,j(x0))),one) = product(x0,product(x0,j(x0))),
inference(unit_resolution,[status(thm)],[516,170]) ).
tff(518,plain,
product(x0,product(x0,j(x0))) = product(product(x0,product(x0,j(x0))),one),
inference(symmetry,[status(thm)],[517]) ).
tff(519,plain,
eta(x0) = product(x0,j(x0)),
inference(transitivity,[status(thm)],[67,58]) ).
tff(520,plain,
product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),eta(x0)) = product(x0,product(x0,j(x0))),
inference(monotonicity,[status(thm)],[329,519]) ).
tff(521,plain,
product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),eta(x0)) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,difference(x0,one))),
inference(transitivity,[status(thm)],[520,518,515,513]) ).
tff(522,plain,
quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0),
inference(symmetry,[status(thm)],[341]) ).
tff(523,plain,
difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),eta(x0))) = difference(product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,difference(x0,one)))),
inference(monotonicity,[status(thm)],[522,521]) ).
tff(524,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),eta(x0))) = quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(525,plain,
difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),eta(x0))) = quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(unit_resolution,[status(thm)],[524,104]) ).
tff(526,plain,
quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),eta(x0))),
inference(symmetry,[status(thm)],[525]) ).
tff(527,plain,
quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = j(x0),
inference(transitivity,[status(thm)],[526,523,511,509,499,448,497,466,458]) ).
tff(528,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(x0,product(x0,j(x0))),product(product(x0,product(x0,j(x0))),one)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(529,plain,
difference(product(x0,product(x0,j(x0))),product(product(x0,product(x0,j(x0))),one)) = one,
inference(unit_resolution,[status(thm)],[528,26]) ).
tff(530,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(x0,product(x0,j(x0))))) = product(x0,product(x0,j(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(531,plain,
product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(x0,product(x0,j(x0))))) = product(x0,product(x0,j(x0))),
inference(unit_resolution,[status(thm)],[530,7]) ).
tff(532,plain,
product(x0,product(x0,j(x0))) = product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),eta(x0)),
inference(symmetry,[status(thm)],[520]) ).
tff(533,plain,
difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(x0,product(x0,j(x0)))) = difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),eta(x0))),
inference(monotonicity,[status(thm)],[532]) ).
tff(534,plain,
difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),eta(x0))) = difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(x0,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[533]) ).
tff(535,plain,
quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(x0,product(x0,j(x0)))),
inference(transitivity,[status(thm)],[526,534]) ).
tff(536,plain,
product(product(x0,product(x0,j(x0))),x0) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0),
inference(monotonicity,[status(thm)],[305]) ).
tff(537,plain,
product(product(x0,product(x0,j(x0))),x0) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),
inference(transitivity,[status(thm)],[536,341]) ).
tff(538,plain,
product(product(product(x0,product(x0,j(x0))),x0),quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(x0,product(x0,j(x0))))),
inference(monotonicity,[status(thm)],[537,535]) ).
tff(539,plain,
product(product(product(x0,product(x0,j(x0))),x0),quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(product(x0,product(x0,j(x0))),one),
inference(transitivity,[status(thm)],[538,531,518]) ).
tff(540,plain,
difference(product(x0,product(x0,j(x0))),product(product(product(x0,product(x0,j(x0))),x0),quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = difference(product(x0,product(x0,j(x0))),product(product(x0,product(x0,j(x0))),one)),
inference(monotonicity,[status(thm)],[539]) ).
tff(541,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(product(x0,product(x0,j(x0))),product(product(product(x0,product(x0,j(x0))),x0),quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = quotient(product(x0,product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(542,plain,
difference(product(x0,product(x0,j(x0))),product(product(product(x0,product(x0,j(x0))),x0),quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = quotient(product(x0,product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))),
inference(unit_resolution,[status(thm)],[541,104]) ).
tff(543,plain,
quotient(product(x0,product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))) = difference(product(x0,product(x0,j(x0))),product(product(product(x0,product(x0,j(x0))),x0),quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))),
inference(symmetry,[status(thm)],[542]) ).
tff(544,plain,
quotient(product(x0,product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))) = quotient(product(x0,product(j(x0),x0)),x0),
inference(transitivity,[status(thm)],[543,540,529,365,362]) ).
tff(545,plain,
quotient(quotient(product(x0,product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))),quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(quotient(product(x0,product(j(x0),x0)),x0),j(x0)),
inference(monotonicity,[status(thm)],[544,527]) ).
tff(546,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0)))),product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(x0,product(x0,j(x0))),x0))) = quotient(quotient(product(x0,product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))),quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(547,plain,
difference(product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0)))),product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(x0,product(x0,j(x0))),x0))) = quotient(quotient(product(x0,product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))),quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),
inference(unit_resolution,[status(thm)],[546,16]) ).
tff(548,plain,
product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(x0,product(x0,j(x0))),x0)) = product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(monotonicity,[status(thm)],[537]) ).
tff(549,plain,
product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(x0,product(x0,j(x0))),x0)),
inference(symmetry,[status(thm)],[548]) ).
tff(550,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(551,plain,
product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),
inference(unit_resolution,[status(thm)],[550,35]) ).
tff(552,plain,
product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(symmetry,[status(thm)],[551]) ).
tff(553,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(difference(x0,one),difference(difference(x0,one),product(x0,x0))) = product(x0,x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(554,plain,
product(difference(x0,one),difference(difference(x0,one),product(x0,x0))) = product(x0,x0),
inference(unit_resolution,[status(thm)],[553,7]) ).
tff(555,plain,
product(product(difference(x0,one),i(i(x0))),product(x0,x0)) = product(one,product(x0,x0)),
inference(monotonicity,[status(thm)],[191]) ).
tff(556,plain,
product(one,product(x0,x0)) = product(product(difference(x0,one),i(i(x0))),product(x0,x0)),
inference(symmetry,[status(thm)],[555]) ).
tff(557,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,product(x0,x0)) = product(x0,x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(558,plain,
product(one,product(x0,x0)) = product(x0,x0),
inference(unit_resolution,[status(thm)],[557,74]) ).
tff(559,plain,
product(x0,x0) = product(one,product(x0,x0)),
inference(symmetry,[status(thm)],[558]) ).
tff(560,plain,
product(x0,x0) = product(product(difference(x0,one),i(i(x0))),product(x0,x0)),
inference(transitivity,[status(thm)],[559,556]) ).
tff(561,plain,
difference(difference(x0,one),product(x0,x0)) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(x0,x0))),
inference(monotonicity,[status(thm)],[560]) ).
tff(562,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(x0,x0))) = difference(difference(x0,one),product(x0,x0)),
inference(symmetry,[status(thm)],[561]) ).
tff(563,plain,
product(product(difference(x0,one),i(i(x0))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))) = product(one,product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),
inference(monotonicity,[status(thm)],[191,414]) ).
tff(564,plain,
product(one,product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0)) = product(product(difference(x0,one),i(i(x0))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),
inference(symmetry,[status(thm)],[563]) ).
tff(565,plain,
product(one,product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0)) = product(one,product(x0,x0)),
inference(monotonicity,[status(thm)],[266]) ).
tff(566,plain,
product(one,product(x0,x0)) = product(one,product(quotient(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),
inference(symmetry,[status(thm)],[565]) ).
tff(567,plain,
product(product(difference(x0,one),i(i(x0))),product(x0,x0)) = product(product(difference(x0,one),i(i(x0))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),
inference(transitivity,[status(thm)],[555,566,564]) ).
tff(568,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(x0,x0))) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),
inference(monotonicity,[status(thm)],[567]) ).
tff(569,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(x0,x0))),
inference(symmetry,[status(thm)],[568]) ).
tff(570,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(i(i(x0)),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(571,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(i(i(x0)),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[570,104]) ).
tff(572,plain,
quotient(product(i(i(x0)),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)))),
inference(symmetry,[status(thm)],[571]) ).
tff(573,plain,
product(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = product(x0,x0),
inference(monotonicity,[status(thm)],[329]) ).
tff(574,plain,
product(x0,x0) = product(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),
inference(symmetry,[status(thm)],[573]) ).
tff(575,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(one,i(i(x0))),i(i(x0))) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(576,plain,
quotient(product(one,i(i(x0))),i(i(x0))) = one,
inference(unit_resolution,[status(thm)],[575,143]) ).
tff(577,plain,
i(i(x0)) = product(one,i(i(x0))),
inference(symmetry,[status(thm)],[231]) ).
tff(578,plain,
product(i(i(x0)),product(difference(x0,one),i(i(x0)))) = product(i(i(x0)),product(x0,difference(x0,one))),
inference(monotonicity,[status(thm)],[159]) ).
tff(579,plain,
product(i(i(x0)),product(difference(x0,one),i(i(x0)))) = product(one,i(i(x0))),
inference(transitivity,[status(thm)],[578,274,277,577]) ).
tff(580,plain,
quotient(product(i(i(x0)),product(difference(x0,one),i(i(x0)))),i(i(x0))) = quotient(product(one,i(i(x0))),i(i(x0))),
inference(monotonicity,[status(thm)],[579]) ).
tff(581,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(i(i(x0)),product(product(i(i(x0)),i(i(x0))),difference(x0,one))) = quotient(product(i(i(x0)),product(difference(x0,one),i(i(x0)))),i(i(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(582,plain,
difference(i(i(x0)),product(product(i(i(x0)),i(i(x0))),difference(x0,one))) = quotient(product(i(i(x0)),product(difference(x0,one),i(i(x0)))),i(i(x0))),
inference(unit_resolution,[status(thm)],[581,104]) ).
tff(583,plain,
difference(i(i(x0)),product(product(i(i(x0)),i(i(x0))),difference(x0,one))) = product(x0,difference(x0,one)),
inference(transitivity,[status(thm)],[582,580,576,152]) ).
tff(584,plain,
product(i(i(x0)),difference(i(i(x0)),product(product(i(i(x0)),i(i(x0))),difference(x0,one)))) = product(i(i(x0)),product(x0,difference(x0,one))),
inference(monotonicity,[status(thm)],[583]) ).
tff(585,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(i(i(x0)),difference(i(i(x0)),product(product(i(i(x0)),i(i(x0))),difference(x0,one)))) = product(product(i(i(x0)),i(i(x0))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(586,plain,
product(i(i(x0)),difference(i(i(x0)),product(product(i(i(x0)),i(i(x0))),difference(x0,one)))) = product(product(i(i(x0)),i(i(x0))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[585,7]) ).
tff(587,plain,
product(product(i(i(x0)),i(i(x0))),difference(x0,one)) = product(i(i(x0)),difference(i(i(x0)),product(product(i(i(x0)),i(i(x0))),difference(x0,one)))),
inference(symmetry,[status(thm)],[586]) ).
tff(588,plain,
product(product(i(i(x0)),i(i(x0))),difference(x0,one)) = product(i(i(x0)),product(x0,difference(x0,one))),
inference(transitivity,[status(thm)],[587,584]) ).
tff(589,plain,
quotient(product(product(i(i(x0)),i(i(x0))),difference(x0,one)),difference(x0,one)) = quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),
inference(monotonicity,[status(thm)],[588]) ).
tff(590,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(i(i(x0)),i(i(x0))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),i(i(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(591,plain,
quotient(product(product(i(i(x0)),i(i(x0))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),i(i(x0))),
inference(unit_resolution,[status(thm)],[590,143]) ).
tff(592,plain,
product(i(i(x0)),i(i(x0))) = quotient(product(product(i(i(x0)),i(i(x0))),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[591]) ).
tff(593,plain,
product(i(i(x0)),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = product(i(i(x0)),i(i(x0))),
inference(monotonicity,[status(thm)],[411]) ).
tff(594,plain,
product(i(i(x0)),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = product(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),
inference(transitivity,[status(thm)],[593,592,589,414,266,574]) ).
tff(595,plain,
quotient(product(i(i(x0)),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) = quotient(product(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(monotonicity,[status(thm)],[594]) ).
tff(596,plain,
quotient(product(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) = quotient(product(i(i(x0)),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(symmetry,[status(thm)],[595]) ).
tff(597,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(598,plain,
difference(difference(x0,one),product(product(difference(x0,one),x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[597,104]) ).
tff(599,plain,
product(product(difference(x0,one),x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(monotonicity,[status(thm)],[89]) ).
tff(600,plain,
product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(product(difference(x0,one),x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(symmetry,[status(thm)],[599]) ).
tff(601,plain,
difference(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = difference(difference(x0,one),product(product(difference(x0,one),x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),
inference(monotonicity,[status(thm)],[600]) ).
tff(602,plain,
difference(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = difference(difference(x0,one),product(x0,x0)),
inference(transitivity,[status(thm)],[601,598,596,572,569,562]) ).
tff(603,plain,
product(difference(x0,one),difference(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(difference(x0,one),difference(difference(x0,one),product(x0,x0))),
inference(monotonicity,[status(thm)],[602]) ).
tff(604,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(difference(x0,one),difference(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(605,plain,
product(difference(x0,one),difference(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(unit_resolution,[status(thm)],[604,7]) ).
tff(606,plain,
product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(difference(x0,one),difference(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))),
inference(symmetry,[status(thm)],[605]) ).
tff(607,plain,
product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(x0,x0),
inference(transitivity,[status(thm)],[606,603,554]) ).
tff(608,plain,
product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(difference(x0,one),product(x0,x0)),
inference(monotonicity,[status(thm)],[607]) ).
tff(609,plain,
product(difference(x0,one),product(x0,x0)) = product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),
inference(symmetry,[status(thm)],[608]) ).
tff(610,plain,
product(product(j(x0),x0),x0) = product(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),
inference(symmetry,[status(thm)],[213]) ).
tff(611,plain,
product(one,x0) = product(product(j(x0),x0),x0),
inference(symmetry,[status(thm)],[200]) ).
tff(612,plain,
product(x0,product(j(x0),x0)) = product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(x0,product(x0,j(x0))),x0)),
inference(transitivity,[status(thm)],[359,162,172,357,611,610,215,609,552,549]) ).
tff(613,plain,
quotient(product(eta(x0),x0),x0) = quotient(product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),
inference(symmetry,[status(thm)],[507]) ).
tff(614,plain,
eta(x0) = quotient(product(eta(x0),x0),x0),
inference(symmetry,[status(thm)],[503]) ).
tff(615,plain,
eta(x0) = quotient(product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),
inference(transitivity,[status(thm)],[614,613]) ).
tff(616,plain,
quotient(eta(x0),product(x0,product(x0,j(x0)))) = quotient(quotient(product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(monotonicity,[status(thm)],[615,305]) ).
tff(617,plain,
quotient(quotient(product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) = quotient(eta(x0),product(x0,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[616]) ).
tff(618,plain,
quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = quotient(eta(x0),product(x0,product(x0,j(x0)))),
inference(transitivity,[status(thm)],[526,523,511,617]) ).
tff(619,plain,
product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0)))) = product(quotient(eta(x0),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))),
inference(monotonicity,[status(thm)],[618]) ).
tff(620,plain,
product(quotient(eta(x0),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))) = product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[619]) ).
tff(621,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(eta(x0),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))) = eta(x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(622,plain,
product(quotient(eta(x0),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))) = eta(x0),
inference(unit_resolution,[status(thm)],[621,35]) ).
tff(623,plain,
eta(x0) = product(quotient(eta(x0),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[622]) ).
tff(624,plain,
product(x0,j(x0)) = product(i(x0),x0),
inference(symmetry,[status(thm)],[58]) ).
tff(625,plain,
product(x0,j(x0)) = product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0)))),
inference(transitivity,[status(thm)],[624,77,623,620]) ).
tff(626,plain,
difference(product(x0,j(x0)),product(x0,product(j(x0),x0))) = difference(product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(x0,product(x0,j(x0)))),product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(x0,product(x0,j(x0))),x0))),
inference(monotonicity,[status(thm)],[625,612]) ).
tff(627,plain,
product(x0,product(x0,difference(x0,one))) = product(x0,product(j(x0),x0)),
inference(symmetry,[status(thm)],[359]) ).
tff(628,plain,
product(difference(x0,one),product(x0,x0)) = product(x0,product(j(x0),x0)),
inference(transitivity,[status(thm)],[216,213,200,198,173,163,627]) ).
tff(629,plain,
difference(product(difference(x0,one),x0),product(difference(x0,one),product(x0,x0))) = difference(product(x0,j(x0)),product(x0,product(j(x0),x0))),
inference(monotonicity,[status(thm)],[289,628]) ).
tff(630,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(difference(x0,one),x0),product(difference(x0,one),product(x0,x0))) = quotient(quotient(product(x0,product(difference(x0,one),x0)),x0),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(631,plain,
difference(product(difference(x0,one),x0),product(difference(x0,one),product(x0,x0))) = quotient(quotient(product(x0,product(difference(x0,one),x0)),x0),difference(x0,one)),
inference(unit_resolution,[status(thm)],[630,16]) ).
tff(632,plain,
quotient(quotient(product(x0,product(difference(x0,one),x0)),x0),difference(x0,one)) = difference(product(difference(x0,one),x0),product(difference(x0,one),product(x0,x0))),
inference(symmetry,[status(thm)],[631]) ).
tff(633,plain,
quotient(quotient(product(x0,product(difference(x0,one),x0)),x0),difference(x0,one)) = quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),
inference(transitivity,[status(thm)],[632,629,626,547,545,496,388,391,495,492,470,304,302,299,288]) ).
tff(634,plain,
product(quotient(quotient(product(x0,product(difference(x0,one),x0)),x0),difference(x0,one)),difference(x0,one)) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),difference(x0,one)),
inference(monotonicity,[status(thm)],[633]) ).
tff(635,plain,
product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),difference(x0,one)) = product(quotient(quotient(product(x0,product(difference(x0,one),x0)),x0),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[634]) ).
tff(636,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one))) = quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(637,plain,
product(one,quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one))) = quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[636,74]) ).
tff(638,plain,
product(difference(x0,one),difference(difference(x0,one),one)) = product(difference(x0,one),i(i(x0))),
inference(symmetry,[status(thm)],[158]) ).
tff(639,plain,
one = product(difference(x0,one),difference(difference(x0,one),one)),
inference(symmetry,[status(thm)],[154]) ).
tff(640,plain,
one = product(difference(x0,one),i(i(x0))),
inference(transitivity,[status(thm)],[639,638]) ).
tff(641,plain,
difference(one,product(difference(x0,one),product(i(i(x0)),x0))) = difference(product(difference(x0,one),i(i(x0))),product(difference(x0,one),product(i(i(x0)),x0))),
inference(monotonicity,[status(thm)],[640]) ).
tff(642,plain,
difference(product(difference(x0,one),i(i(x0))),product(difference(x0,one),product(i(i(x0)),x0))) = difference(one,product(difference(x0,one),product(i(i(x0)),x0))),
inference(symmetry,[status(thm)],[641]) ).
tff(643,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(difference(x0,one),i(i(x0))),product(difference(x0,one),product(i(i(x0)),x0))) = quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(644,plain,
difference(product(difference(x0,one),i(i(x0))),product(difference(x0,one),product(i(i(x0)),x0))) = quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[643,16]) ).
tff(645,plain,
quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)) = difference(product(difference(x0,one),i(i(x0))),product(difference(x0,one),product(i(i(x0)),x0))),
inference(symmetry,[status(thm)],[644]) ).
tff(646,plain,
quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)) = difference(one,product(difference(x0,one),product(i(i(x0)),x0))),
inference(transitivity,[status(thm)],[645,642]) ).
tff(647,plain,
product(one,quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one))) = product(one,difference(one,product(difference(x0,one),product(i(i(x0)),x0)))),
inference(monotonicity,[status(thm)],[646]) ).
tff(648,plain,
product(one,difference(one,product(difference(x0,one),product(i(i(x0)),x0)))) = product(one,quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one))),
inference(symmetry,[status(thm)],[647]) ).
tff(649,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(one,difference(one,product(difference(x0,one),product(i(i(x0)),x0)))) = product(difference(x0,one),product(i(i(x0)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(650,plain,
product(one,difference(one,product(difference(x0,one),product(i(i(x0)),x0)))) = product(difference(x0,one),product(i(i(x0)),x0)),
inference(unit_resolution,[status(thm)],[649,7]) ).
tff(651,plain,
product(difference(x0,one),product(i(i(x0)),x0)) = product(one,difference(one,product(difference(x0,one),product(i(i(x0)),x0)))),
inference(symmetry,[status(thm)],[650]) ).
tff(652,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),x0) = product(difference(x0,one),product(i(i(x0)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(653,plain,
product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),x0) = product(difference(x0,one),product(i(i(x0)),x0)),
inference(unit_resolution,[status(thm)],[652,35]) ).
tff(654,plain,
quotient(product(x0,product(x0,j(x0))),x0) = quotient(product(x0,product(difference(x0,one),x0)),x0),
inference(monotonicity,[status(thm)],[291]) ).
tff(655,plain,
quotient(product(x0,product(difference(x0,one),x0)),x0) = quotient(product(x0,product(x0,j(x0))),x0),
inference(symmetry,[status(thm)],[654]) ).
tff(656,plain,
quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0) = quotient(product(x0,product(x0,j(x0))),x0),
inference(transitivity,[status(thm)],[237,280,283,655]) ).
tff(657,plain,
product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),x0) = product(quotient(product(x0,product(x0,j(x0))),x0),x0),
inference(monotonicity,[status(thm)],[656]) ).
tff(658,plain,
product(quotient(product(x0,product(x0,j(x0))),x0),x0) = product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),x0),
inference(symmetry,[status(thm)],[657]) ).
tff(659,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(x0,product(x0,j(x0))),x0),x0) = product(x0,product(x0,j(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(660,plain,
product(quotient(product(x0,product(x0,j(x0))),x0),x0) = product(x0,product(x0,j(x0))),
inference(unit_resolution,[status(thm)],[659,35]) ).
tff(661,plain,
product(x0,product(x0,j(x0))) = product(quotient(product(x0,product(x0,j(x0))),x0),x0),
inference(symmetry,[status(thm)],[660]) ).
tff(662,plain,
quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0) = quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)),
inference(transitivity,[status(thm)],[500,298,301,661,658,653,651,648,637]) ).
tff(663,plain,
product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),difference(x0,one)) = product(quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[662]) ).
tff(664,plain,
product(quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)),difference(x0,one)) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),difference(x0,one)),
inference(symmetry,[status(thm)],[663]) ).
tff(665,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)),difference(x0,one)) = quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(666,plain,
product(quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)),difference(x0,one)) = quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),
inference(unit_resolution,[status(thm)],[665,35]) ).
tff(667,plain,
quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))) = product(quotient(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[666]) ).
tff(668,plain,
quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))) = quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),
inference(transitivity,[status(thm)],[667,664,635,286,284,281,236]) ).
tff(669,plain,
product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(product(x0,x1),difference(x0,one)),x0)) = product(quotient(product(difference(x0,one),product(i(i(x0)),x0)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),
inference(monotonicity,[status(thm)],[668]) ).
tff(670,plain,
product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(product(x0,x1),difference(x0,one)),x0)) = product(x0,product(product(x1,difference(x0,one)),x0)),
inference(transitivity,[status(thm)],[669,250,247,184]) ).
tff(671,plain,
product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(product(x0,x1),difference(x0,one)),x0)),j(x0)) = product(product(x0,product(product(x1,difference(x0,one)),x0)),j(x0)),
inference(monotonicity,[status(thm)],[670]) ).
tff(672,plain,
product(product(x0,product(product(x1,difference(x0,one)),x0)),j(x0)) = product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(product(x0,x1),difference(x0,one)),x0)),j(x0)),
inference(symmetry,[status(thm)],[671]) ).
tff(673,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(x0,difference(x0,product(product(x0,product(product(x1,difference(x0,one)),x0)),j(x0)))) = product(product(x0,product(product(x1,difference(x0,one)),x0)),j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(674,plain,
product(x0,difference(x0,product(product(x0,product(product(x1,difference(x0,one)),x0)),j(x0)))) = product(product(x0,product(product(x1,difference(x0,one)),x0)),j(x0)),
inference(unit_resolution,[status(thm)],[673,7]) ).
tff(675,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(x1,difference(x0,one)),x0),x0) = product(x1,difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(676,plain,
quotient(product(product(x1,difference(x0,one)),x0),x0) = product(x1,difference(x0,one)),
inference(unit_resolution,[status(thm)],[675,143]) ).
tff(677,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(product(product(x1,difference(x0,one)),x0),difference(product(product(x1,difference(x0,one)),x0),product(product(x1,difference(x0,one)),x0))) = product(product(x1,difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(678,plain,
product(product(product(x1,difference(x0,one)),x0),difference(product(product(x1,difference(x0,one)),x0),product(product(x1,difference(x0,one)),x0))) = product(product(x1,difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[677,7]) ).
tff(679,plain,
product(product(x1,difference(x0,one)),product(x0,one)) = product(product(x1,difference(x0,one)),x0),
inference(monotonicity,[status(thm)],[172]) ).
tff(680,plain,
product(product(x1,difference(x0,one)),x0) = product(product(x1,difference(x0,one)),product(x0,one)),
inference(symmetry,[status(thm)],[679]) ).
tff(681,plain,
difference(product(product(x1,difference(x0,one)),x0),product(product(x1,difference(x0,one)),x0)) = difference(product(product(x1,difference(x0,one)),x0),product(product(x1,difference(x0,one)),product(x0,one))),
inference(monotonicity,[status(thm)],[680]) ).
tff(682,plain,
difference(product(product(x1,difference(x0,one)),x0),product(product(x1,difference(x0,one)),product(x0,one))) = difference(product(product(x1,difference(x0,one)),x0),product(product(x1,difference(x0,one)),x0)),
inference(symmetry,[status(thm)],[681]) ).
tff(683,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(product(x1,difference(x0,one)),x0),product(product(x1,difference(x0,one)),product(x0,one))) = quotient(quotient(product(one,product(product(x1,difference(x0,one)),x0)),x0),product(x1,difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(684,plain,
difference(product(product(x1,difference(x0,one)),x0),product(product(x1,difference(x0,one)),product(x0,one))) = quotient(quotient(product(one,product(product(x1,difference(x0,one)),x0)),x0),product(x1,difference(x0,one))),
inference(unit_resolution,[status(thm)],[683,16]) ).
tff(685,plain,
quotient(quotient(product(one,product(product(x1,difference(x0,one)),x0)),x0),product(x1,difference(x0,one))) = difference(product(product(x1,difference(x0,one)),x0),product(product(x1,difference(x0,one)),product(x0,one))),
inference(symmetry,[status(thm)],[684]) ).
tff(686,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,product(x1,difference(x0,one))) = product(x1,difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(687,plain,
product(one,product(x1,difference(x0,one))) = product(x1,difference(x0,one)),
inference(unit_resolution,[status(thm)],[686,74]) ).
tff(688,plain,
product(x1,difference(x0,one)) = product(one,product(x1,difference(x0,one))),
inference(symmetry,[status(thm)],[687]) ).
tff(689,plain,
product(product(x0,one),product(x1,difference(x0,one))) = product(x0,product(x1,difference(x0,one))),
inference(monotonicity,[status(thm)],[172]) ).
tff(690,plain,
difference(x0,product(product(x0,one),product(x1,difference(x0,one)))) = difference(x0,product(x0,product(x1,difference(x0,one)))),
inference(monotonicity,[status(thm)],[689]) ).
tff(691,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,one),product(x1,difference(x0,one)))) = quotient(product(one,product(product(x1,difference(x0,one)),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(692,plain,
difference(x0,product(product(x0,one),product(x1,difference(x0,one)))) = quotient(product(one,product(product(x1,difference(x0,one)),x0)),x0),
inference(unit_resolution,[status(thm)],[691,104]) ).
tff(693,plain,
quotient(product(one,product(product(x1,difference(x0,one)),x0)),x0) = difference(x0,product(product(x0,one),product(x1,difference(x0,one)))),
inference(symmetry,[status(thm)],[692]) ).
tff(694,plain,
quotient(product(one,product(product(x1,difference(x0,one)),x0)),x0) = product(one,product(x1,difference(x0,one))),
inference(transitivity,[status(thm)],[693,690,147,688]) ).
tff(695,plain,
quotient(quotient(product(one,product(product(x1,difference(x0,one)),x0)),x0),product(x1,difference(x0,one))) = quotient(product(one,product(x1,difference(x0,one))),product(x1,difference(x0,one))),
inference(monotonicity,[status(thm)],[694]) ).
tff(696,plain,
quotient(product(one,product(x1,difference(x0,one))),product(x1,difference(x0,one))) = quotient(quotient(product(one,product(product(x1,difference(x0,one)),x0)),x0),product(x1,difference(x0,one))),
inference(symmetry,[status(thm)],[695]) ).
tff(697,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(one,product(x1,difference(x0,one))),product(x1,difference(x0,one))) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(698,plain,
quotient(product(one,product(x1,difference(x0,one))),product(x1,difference(x0,one))) = one,
inference(unit_resolution,[status(thm)],[697,143]) ).
tff(699,plain,
one = quotient(product(one,product(x1,difference(x0,one))),product(x1,difference(x0,one))),
inference(symmetry,[status(thm)],[698]) ).
tff(700,plain,
one = difference(product(product(x1,difference(x0,one)),x0),product(product(x1,difference(x0,one)),x0)),
inference(transitivity,[status(thm)],[699,696,685,682]) ).
tff(701,plain,
product(product(product(x1,difference(x0,one)),x0),one) = product(product(product(x1,difference(x0,one)),x0),difference(product(product(x1,difference(x0,one)),x0),product(product(x1,difference(x0,one)),x0))),
inference(monotonicity,[status(thm)],[700]) ).
tff(702,plain,
product(product(product(x1,difference(x0,one)),x0),product(j(x0),x0)) = product(product(product(x1,difference(x0,one)),x0),one),
inference(monotonicity,[status(thm)],[199]) ).
tff(703,plain,
product(product(product(x1,difference(x0,one)),x0),product(j(x0),x0)) = product(product(x1,difference(x0,one)),x0),
inference(transitivity,[status(thm)],[702,701,678]) ).
tff(704,plain,
quotient(product(product(product(x1,difference(x0,one)),x0),product(j(x0),x0)),x0) = quotient(product(product(x1,difference(x0,one)),x0),x0),
inference(monotonicity,[status(thm)],[703]) ).
tff(705,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,product(product(x1,difference(x0,one)),x0)),j(x0))) = quotient(product(product(product(x1,difference(x0,one)),x0),product(j(x0),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(706,plain,
difference(x0,product(product(x0,product(product(x1,difference(x0,one)),x0)),j(x0))) = quotient(product(product(product(x1,difference(x0,one)),x0),product(j(x0),x0)),x0),
inference(unit_resolution,[status(thm)],[705,104]) ).
tff(707,plain,
difference(x0,product(product(x0,product(product(x1,difference(x0,one)),x0)),j(x0))) = product(x1,difference(x0,one)),
inference(transitivity,[status(thm)],[706,704,676]) ).
tff(708,plain,
product(x0,difference(x0,product(product(x0,product(product(x1,difference(x0,one)),x0)),j(x0)))) = product(x0,product(x1,difference(x0,one))),
inference(monotonicity,[status(thm)],[707]) ).
tff(709,plain,
product(x0,product(x1,difference(x0,one))) = product(x0,difference(x0,product(product(x0,product(product(x1,difference(x0,one)),x0)),j(x0)))),
inference(symmetry,[status(thm)],[708]) ).
tff(710,plain,
product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))),product(x1,difference(x0,one))) = product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(product(x0,x1),difference(x0,one)),x0)),j(x0)),
inference(transitivity,[status(thm)],[179,709,674,672]) ).
tff(711,plain,
difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))),product(x1,difference(x0,one)))) = difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(product(x0,x1),difference(x0,one)),x0)),j(x0))),
inference(monotonicity,[status(thm)],[710]) ).
tff(712,plain,
difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(product(x0,x1),difference(x0,one)),x0)),j(x0))) = difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))),product(x1,difference(x0,one)))),
inference(symmetry,[status(thm)],[711]) ).
tff(713,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(product(x0,x1),difference(x0,one)),x0)),j(x0))) = quotient(product(product(product(product(x0,x1),difference(x0,one)),x0),product(j(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(714,plain,
difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(product(x0,x1),difference(x0,one)),x0)),j(x0))) = quotient(product(product(product(product(x0,x1),difference(x0,one)),x0),product(j(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(unit_resolution,[status(thm)],[713,104]) ).
tff(715,plain,
quotient(product(product(product(product(x0,x1),difference(x0,one)),x0),product(j(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(product(product(x0,x1),difference(x0,one)),x0)),j(x0))),
inference(symmetry,[status(thm)],[714]) ).
tff(716,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(difference(x0,one),product(difference(x0,one),x0)) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(717,plain,
difference(difference(x0,one),product(difference(x0,one),x0)) = x0,
inference(unit_resolution,[status(thm)],[716,26]) ).
tff(718,plain,
product(product(difference(x0,one),i(i(x0))),eta(x0)) = product(one,product(difference(x0,one),x0)),
inference(monotonicity,[status(thm)],[191,92]) ).
tff(719,plain,
product(product(difference(x0,one),i(i(x0))),eta(x0)) = product(difference(x0,one),x0),
inference(transitivity,[status(thm)],[718,90,76,67,91]) ).
tff(720,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),eta(x0))) = difference(difference(x0,one),product(difference(x0,one),x0)),
inference(monotonicity,[status(thm)],[719]) ).
tff(721,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),eta(x0))) = quotient(product(i(i(x0)),product(eta(x0),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(722,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),eta(x0))) = quotient(product(i(i(x0)),product(eta(x0),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[721,104]) ).
tff(723,plain,
quotient(product(i(i(x0)),product(eta(x0),difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),eta(x0))),
inference(symmetry,[status(thm)],[722]) ).
tff(724,plain,
quotient(product(i(i(x0)),product(eta(x0),difference(x0,one))),difference(x0,one)) = x0,
inference(transitivity,[status(thm)],[723,720,717]) ).
tff(725,plain,
product(quotient(product(i(i(x0)),product(eta(x0),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(x0,difference(x0,one)),
inference(monotonicity,[status(thm)],[724]) ).
tff(726,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(i(i(x0)),product(eta(x0),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(eta(x0),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(727,plain,
product(quotient(product(i(i(x0)),product(eta(x0),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(eta(x0),difference(x0,one))),
inference(unit_resolution,[status(thm)],[726,35]) ).
tff(728,plain,
product(i(i(x0)),product(eta(x0),difference(x0,one))) = product(quotient(product(i(i(x0)),product(eta(x0),difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[727]) ).
tff(729,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(i(i(x0)),product(i(i(x0)),product(eta(x0),difference(x0,one)))) = product(eta(x0),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(730,plain,
difference(i(i(x0)),product(i(i(x0)),product(eta(x0),difference(x0,one)))) = product(eta(x0),difference(x0,one)),
inference(unit_resolution,[status(thm)],[729,26]) ).
tff(731,plain,
product(i(i(x0)),product(eta(x0),difference(x0,one))) = one,
inference(transitivity,[status(thm)],[728,725,94]) ).
tff(732,plain,
difference(i(i(x0)),product(i(i(x0)),product(eta(x0),difference(x0,one)))) = difference(i(i(x0)),one),
inference(monotonicity,[status(thm)],[731]) ).
tff(733,plain,
difference(i(i(x0)),one) = difference(i(i(x0)),product(i(i(x0)),product(eta(x0),difference(x0,one)))),
inference(symmetry,[status(thm)],[732]) ).
tff(734,plain,
( ~ ! [A: $i] : ( i(A) = difference(A,one) )
| ( i(i(i(x0))) = difference(i(i(x0)),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(735,plain,
i(i(i(x0))) = difference(i(i(x0)),one),
inference(unit_resolution,[status(thm)],[734,84]) ).
tff(736,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(i(i(i(x0))),i(i(x0))),i(i(x0))) = i(i(i(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(737,plain,
quotient(product(i(i(i(x0))),i(i(x0))),i(i(x0))) = i(i(i(x0))),
inference(unit_resolution,[status(thm)],[736,143]) ).
tff(738,plain,
product(difference(x0,one),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))) = product(i(x0),x0),
inference(monotonicity,[status(thm)],[87,178]) ).
tff(739,plain,
product(i(x0),x0) = product(difference(x0,one),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),
inference(symmetry,[status(thm)],[738]) ).
tff(740,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(difference(x0,one),i(i(x0))),i(i(x0))) = difference(x0,one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(741,plain,
quotient(product(difference(x0,one),i(i(x0))),i(i(x0))) = difference(x0,one),
inference(unit_resolution,[status(thm)],[740,143]) ).
tff(742,plain,
quotient(one,i(i(x0))) = quotient(product(difference(x0,one),i(i(x0))),i(i(x0))),
inference(monotonicity,[status(thm)],[640]) ).
tff(743,plain,
( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
| ( j(i(i(x0))) = quotient(one,i(i(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(744,plain,
j(i(i(x0))) = quotient(one,i(i(x0))),
inference(unit_resolution,[status(thm)],[743,44]) ).
tff(745,plain,
j(i(i(x0))) = i(x0),
inference(transitivity,[status(thm)],[744,742,741,87]) ).
tff(746,plain,
product(i(i(x0)),j(i(i(x0)))) = product(i(i(x0)),i(x0)),
inference(monotonicity,[status(thm)],[745]) ).
tff(747,plain,
( ~ ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
| ( product(i(i(i(x0))),i(i(x0))) = product(i(i(x0)),j(i(i(x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(748,plain,
product(i(i(i(x0))),i(i(x0))) = product(i(i(x0)),j(i(i(x0)))),
inference(unit_resolution,[status(thm)],[747,56]) ).
tff(749,plain,
product(i(i(i(x0))),i(i(x0))) = product(difference(x0,one),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),
inference(transitivity,[status(thm)],[748,746,316,325,739]) ).
tff(750,plain,
quotient(product(i(i(i(x0))),i(i(x0))),i(i(x0))) = quotient(product(difference(x0,one),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))),
inference(monotonicity,[status(thm)],[749]) ).
tff(751,plain,
quotient(product(difference(x0,one),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))) = quotient(product(i(i(i(x0))),i(i(x0))),i(i(x0))),
inference(symmetry,[status(thm)],[750]) ).
tff(752,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(i(i(x0)),product(product(i(i(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = quotient(product(difference(x0,one),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(753,plain,
difference(i(i(x0)),product(product(i(i(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = quotient(product(difference(x0,one),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))),
inference(unit_resolution,[status(thm)],[752,104]) ).
tff(754,plain,
product(i(i(x0)),difference(x0,one)) = eta(x0),
inference(transitivity,[status(thm)],[313,316,325,77]) ).
tff(755,plain,
product(product(i(i(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(monotonicity,[status(thm)],[754]) ).
tff(756,plain,
product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = product(product(i(i(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(symmetry,[status(thm)],[755]) ).
tff(757,plain,
difference(i(i(x0)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = difference(i(i(x0)),product(product(i(i(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),
inference(monotonicity,[status(thm)],[756]) ).
tff(758,plain,
difference(i(i(x0)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = product(eta(x0),difference(x0,one)),
inference(transitivity,[status(thm)],[757,753,751,737,735,733,730]) ).
tff(759,plain,
product(i(i(x0)),difference(i(i(x0)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))))) = product(i(i(x0)),product(eta(x0),difference(x0,one))),
inference(monotonicity,[status(thm)],[758]) ).
tff(760,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(i(i(x0)),difference(i(i(x0)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))))) = product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(761,plain,
product(i(i(x0)),difference(i(i(x0)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))))) = product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(unit_resolution,[status(thm)],[760,7]) ).
tff(762,plain,
product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = product(i(i(x0)),difference(i(i(x0)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))))),
inference(symmetry,[status(thm)],[761]) ).
tff(763,plain,
product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = one,
inference(transitivity,[status(thm)],[762,759,728,725,94]) ).
tff(764,plain,
product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),one),
inference(monotonicity,[status(thm)],[763]) ).
tff(765,plain,
product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),one) = product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),
inference(symmetry,[status(thm)],[764]) ).
tff(766,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),one) = product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(767,plain,
product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),one) = product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),
inference(unit_resolution,[status(thm)],[766,170]) ).
tff(768,plain,
product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)) = product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),one),
inference(symmetry,[status(thm)],[767]) ).
tff(769,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(difference(x0,one),product(x0,x0)),product(x0,x0)) = difference(x0,one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(770,plain,
quotient(product(difference(x0,one),product(x0,x0)),product(x0,x0)) = difference(x0,one),
inference(unit_resolution,[status(thm)],[769,143]) ).
tff(771,plain,
quotient(product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) = quotient(one,difference(x0,one)),
inference(monotonicity,[status(thm)],[428]) ).
tff(772,plain,
quotient(product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) = product(difference(x0,one),product(x0,x0)),
inference(transitivity,[status(thm)],[771,320,319,357,611,610,215]) ).
tff(773,plain,
quotient(quotient(product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))) = quotient(product(difference(x0,one),product(x0,x0)),product(x0,x0)),
inference(monotonicity,[status(thm)],[772,415]) ).
tff(774,plain,
quotient(one,difference(x0,one)) = quotient(product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(symmetry,[status(thm)],[771]) ).
tff(775,plain,
quotient(product(x0,difference(x0,one)),difference(x0,one)) = quotient(one,difference(x0,one)),
inference(symmetry,[status(thm)],[320]) ).
tff(776,plain,
x0 = quotient(product(x0,difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[319]) ).
tff(777,plain,
difference(product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,difference(x0,one)))) = difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),eta(x0))),
inference(symmetry,[status(thm)],[523]) ).
tff(778,plain,
quotient(quotient(product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) = difference(product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,difference(x0,one)))),
inference(symmetry,[status(thm)],[511]) ).
tff(779,plain,
quotient(product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))) = quotient(quotient(product(difference(x0,one),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(symmetry,[status(thm)],[509]) ).
tff(780,plain,
product(x0,product(difference(x0,one),difference(x0,one))) = quotient(product(product(x0,product(difference(x0,one),difference(x0,one))),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[499]) ).
tff(781,plain,
j(x0) = quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(transitivity,[status(thm)],[468,467,451,449,780,779,778,777,525]) ).
tff(782,plain,
product(j(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(quotient(product(difference(x0,one),product(eta(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(monotonicity,[status(thm)],[781]) ).
tff(783,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(difference(x0,one),difference(x0,one)),product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(784,plain,
difference(product(difference(x0,one),difference(x0,one)),product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[783,26]) ).
tff(785,plain,
product(difference(x0,one),difference(difference(x0,one),one)) = product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))),
inference(symmetry,[status(thm)],[336]) ).
tff(786,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(j(x0),difference(j(x0),product(product(j(x0),x0),x0))) = product(product(j(x0),x0),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(787,plain,
product(j(x0),difference(j(x0),product(product(j(x0),x0),x0))) = product(product(j(x0),x0),x0),
inference(unit_resolution,[status(thm)],[786,7]) ).
tff(788,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(j(x0),product(product(j(x0),x0),x0)) = quotient(product(x0,product(x0,j(x0))),j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(789,plain,
difference(j(x0),product(product(j(x0),x0),x0)) = quotient(product(x0,product(x0,j(x0))),j(x0)),
inference(unit_resolution,[status(thm)],[788,104]) ).
tff(790,plain,
quotient(product(x0,product(x0,j(x0))),j(x0)) = difference(j(x0),product(product(j(x0),x0),x0)),
inference(symmetry,[status(thm)],[789]) ).
tff(791,plain,
product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))) = product(j(x0),difference(j(x0),product(product(j(x0),x0),x0))),
inference(monotonicity,[status(thm)],[790]) ).
tff(792,plain,
product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))) = x0,
inference(transitivity,[status(thm)],[791,787,200,198]) ).
tff(793,plain,
product(j(x0),product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0)))) = product(j(x0),x0),
inference(monotonicity,[status(thm)],[792]) ).
tff(794,plain,
product(j(x0),product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0)))) = product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(transitivity,[status(thm)],[793,47,37,639,785,338]) ).
tff(795,plain,
product(quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),difference(x0,one)),difference(x0,one)) = product(difference(x0,one),difference(x0,one)),
inference(symmetry,[status(thm)],[446]) ).
tff(796,plain,
quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)) = product(quotient(quotient(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(j(x0),product(x0,x0))),product(x0,x0)),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[406]) ).
tff(797,plain,
product(j(x0),j(x0)) = product(difference(x0,one),difference(x0,one)),
inference(transitivity,[status(thm)],[400,403,796,795]) ).
tff(798,plain,
difference(product(j(x0),j(x0)),product(j(x0),product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))))) = difference(product(difference(x0,one),difference(x0,one)),product(product(difference(x0,one),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),
inference(monotonicity,[status(thm)],[797,794]) ).
tff(799,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(j(x0),j(x0)),product(j(x0),product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))))) = quotient(quotient(product(quotient(product(x0,product(x0,j(x0))),j(x0)),product(j(x0),j(x0))),j(x0)),j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(800,plain,
difference(product(j(x0),j(x0)),product(j(x0),product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))))) = quotient(quotient(product(quotient(product(x0,product(x0,j(x0))),j(x0)),product(j(x0),j(x0))),j(x0)),j(x0)),
inference(unit_resolution,[status(thm)],[799,16]) ).
tff(801,plain,
quotient(quotient(product(quotient(product(x0,product(x0,j(x0))),j(x0)),product(j(x0),j(x0))),j(x0)),j(x0)) = difference(product(j(x0),j(x0)),product(j(x0),product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))))),
inference(symmetry,[status(thm)],[800]) ).
tff(802,plain,
quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0) = j(x0),
inference(transitivity,[status(thm)],[487,310]) ).
tff(803,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(j(x0),product(product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))),j(x0))) = quotient(product(quotient(product(x0,product(x0,j(x0))),j(x0)),product(j(x0),j(x0))),j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(804,plain,
difference(j(x0),product(product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))),j(x0))) = quotient(product(quotient(product(x0,product(x0,j(x0))),j(x0)),product(j(x0),j(x0))),j(x0)),
inference(unit_resolution,[status(thm)],[803,104]) ).
tff(805,plain,
product(product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))),j(x0)) = product(x0,j(x0)),
inference(monotonicity,[status(thm)],[792]) ).
tff(806,plain,
product(product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))),j(x0)) = product(product(j(x0),x0),eta(x0)),
inference(transitivity,[status(thm)],[805,624,77,473,472,471]) ).
tff(807,plain,
difference(j(x0),product(product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))),j(x0))) = difference(j(x0),product(product(j(x0),x0),eta(x0))),
inference(monotonicity,[status(thm)],[806]) ).
tff(808,plain,
difference(j(x0),product(product(j(x0),x0),eta(x0))) = difference(j(x0),product(product(j(x0),quotient(product(x0,product(x0,j(x0))),j(x0))),j(x0))),
inference(symmetry,[status(thm)],[807]) ).
tff(809,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(j(x0),product(x0,x0)),x0),x0) = product(j(x0),product(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(810,plain,
product(quotient(product(j(x0),product(x0,x0)),x0),x0) = product(j(x0),product(x0,x0)),
inference(unit_resolution,[status(thm)],[809,35]) ).
tff(811,plain,
product(quotient(product(j(x0),product(x0,x0)),x0),product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0))) = product(quotient(product(j(x0),product(x0,x0)),x0),x0),
inference(monotonicity,[status(thm)],[376]) ).
tff(812,plain,
product(quotient(product(j(x0),product(x0,x0)),x0),product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0))) = quotient(product(quotient(product(x0,product(x0,j(x0))),j(x0)),product(j(x0),j(x0))),j(x0)),
inference(transitivity,[status(thm)],[811,810,495,492,808,804]) ).
tff(813,plain,
quotient(product(quotient(product(j(x0),product(x0,x0)),x0),product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0))),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)) = quotient(quotient(product(quotient(product(x0,product(x0,j(x0))),j(x0)),product(j(x0),j(x0))),j(x0)),j(x0)),
inference(monotonicity,[status(thm)],[812,802]) ).
tff(814,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0))) = quotient(product(quotient(product(j(x0),product(x0,x0)),x0),product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0))),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(815,plain,
difference(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0))) = quotient(product(quotient(product(j(x0),product(x0,x0)),x0),product(product(x0,x0),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0))),quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0)),
inference(unit_resolution,[status(thm)],[814,104]) ).
tff(816,plain,
difference(j(x0),product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0))) = difference(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0))),
inference(monotonicity,[status(thm)],[489]) ).
tff(817,plain,
difference(j(x0),product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0))) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),
inference(transitivity,[status(thm)],[816,815,813,801,798,784]) ).
tff(818,plain,
product(j(x0),difference(j(x0),product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)))) = product(j(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(monotonicity,[status(thm)],[817]) ).
tff(819,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(j(x0),difference(j(x0),product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)))) = product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(820,plain,
product(j(x0),difference(j(x0),product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)))) = product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)),
inference(unit_resolution,[status(thm)],[819,7]) ).
tff(821,plain,
product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)) = product(j(x0),difference(j(x0),product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)))),
inference(symmetry,[status(thm)],[820]) ).
tff(822,plain,
product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)) = quotient(product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(transitivity,[status(thm)],[821,818,782,551,608,216,213,200,198,776,775,774]) ).
tff(823,plain,
quotient(product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)),product(x0,x0)) = quotient(quotient(product(difference(x0,one),product(quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(i(i(x0)),product(x0,difference(x0,one))),difference(x0,one))),
inference(monotonicity,[status(thm)],[822,268]) ).
tff(824,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)),product(x0,x0)) = product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(825,plain,
quotient(product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)),product(x0,x0)) = product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),
inference(unit_resolution,[status(thm)],[824,143]) ).
tff(826,plain,
product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)) = quotient(product(product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),product(x0,x0)),product(x0,x0)),
inference(symmetry,[status(thm)],[825]) ).
tff(827,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,j(x0)),x0)) = quotient(product(j(x0),product(x0,x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(828,plain,
difference(x0,product(product(x0,j(x0)),x0)) = quotient(product(j(x0),product(x0,x0)),x0),
inference(unit_resolution,[status(thm)],[827,104]) ).
tff(829,plain,
product(one,i(i(x0))) = product(product(x0,difference(x0,one)),i(i(x0))),
inference(symmetry,[status(thm)],[232]) ).
tff(830,plain,
difference(i(x0),one) = i(i(x0)),
inference(symmetry,[status(thm)],[134]) ).
tff(831,plain,
product(eta(x0),x0) = difference(difference(x0,one),product(difference(x0,one),product(eta(x0),x0))),
inference(symmetry,[status(thm)],[28]) ).
tff(832,plain,
product(x0,j(x0)) = eta(x0),
inference(transitivity,[status(thm)],[624,77]) ).
tff(833,plain,
product(product(x0,j(x0)),x0) = product(eta(x0),x0),
inference(monotonicity,[status(thm)],[832]) ).
tff(834,plain,
product(product(x0,j(x0)),x0) = product(product(x0,difference(x0,one)),i(i(x0))),
inference(transitivity,[status(thm)],[833,831,131,830,577,829]) ).
tff(835,plain,
difference(x0,product(product(x0,j(x0)),x0)) = difference(x0,product(product(x0,difference(x0,one)),i(i(x0)))),
inference(monotonicity,[status(thm)],[834]) ).
tff(836,plain,
difference(x0,product(product(x0,difference(x0,one)),i(i(x0)))) = difference(x0,product(product(x0,j(x0)),x0)),
inference(symmetry,[status(thm)],[835]) ).
tff(837,plain,
quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))) = quotient(product(j(x0),product(x0,x0)),x0),
inference(transitivity,[status(thm)],[667,664,635,286,284,281,836,828]) ).
tff(838,plain,
product(j(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = product(quotient(quotient(product(difference(x0,one),product(x0,x0)),x0),x0),quotient(product(j(x0),product(x0,x0)),x0)),
inference(monotonicity,[status(thm)],[489,837]) ).
tff(839,plain,
product(j(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = difference(x0,one),
inference(transitivity,[status(thm)],[838,826,823,773,770]) ).
tff(840,plain,
product(product(product(product(x0,x1),difference(x0,one)),x0),product(j(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),
inference(monotonicity,[status(thm)],[839]) ).
tff(841,plain,
product(product(product(product(x0,x1),difference(x0,one)),x0),product(j(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),
inference(transitivity,[status(thm)],[840,768,765]) ).
tff(842,plain,
quotient(product(product(product(product(x0,x1),difference(x0,one)),x0),product(j(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = quotient(product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(monotonicity,[status(thm)],[841]) ).
tff(843,plain,
quotient(product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = quotient(product(product(product(product(x0,x1),difference(x0,one)),x0),product(j(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(symmetry,[status(thm)],[842]) ).
tff(844,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(i(i(x0)),difference(i(i(x0)),product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))))) = product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(845,plain,
product(i(i(x0)),difference(i(i(x0)),product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))))) = product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(unit_resolution,[status(thm)],[844,7]) ).
tff(846,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(i(i(x0)),product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one)))) = product(product(x1,eta(x0)),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(847,plain,
difference(i(i(x0)),product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one)))) = product(product(x1,eta(x0)),difference(x0,one)),
inference(unit_resolution,[status(thm)],[846,26]) ).
tff(848,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(849,plain,
product(quotient(product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))),
inference(unit_resolution,[status(thm)],[848,35]) ).
tff(850,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(difference(x0,one),product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0))) = product(product(product(x0,x1),difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(851,plain,
difference(difference(x0,one),product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0))) = product(product(product(x0,x1),difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[850,26]) ).
tff(852,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0),x0) = product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(853,plain,
product(quotient(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0),x0) = product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),
inference(unit_resolution,[status(thm)],[852,35]) ).
tff(854,plain,
product(x1,product(difference(x0,one),x0)) = product(x1,eta(x0)),
inference(monotonicity,[status(thm)],[89]) ).
tff(855,plain,
product(x1,eta(x0)) = product(x1,product(difference(x0,one),x0)),
inference(symmetry,[status(thm)],[854]) ).
tff(856,plain,
quotient(product(x1,eta(x0)),x0) = quotient(product(x1,product(difference(x0,one),x0)),x0),
inference(monotonicity,[status(thm)],[855]) ).
tff(857,plain,
quotient(product(x1,product(difference(x0,one),x0)),x0) = quotient(product(x1,eta(x0)),x0),
inference(symmetry,[status(thm)],[856]) ).
tff(858,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,x1),difference(x0,one))) = quotient(product(x1,product(difference(x0,one),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(859,plain,
difference(x0,product(product(x0,x1),difference(x0,one))) = quotient(product(x1,product(difference(x0,one),x0)),x0),
inference(unit_resolution,[status(thm)],[858,104]) ).
tff(860,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,product(product(x0,x1),difference(x0,one))) = product(product(x0,x1),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(861,plain,
product(one,product(product(x0,x1),difference(x0,one))) = product(product(x0,x1),difference(x0,one)),
inference(unit_resolution,[status(thm)],[860,74]) ).
tff(862,plain,
product(product(x0,difference(x0,one)),product(product(x0,x1),difference(x0,one))) = product(one,product(product(x0,x1),difference(x0,one))),
inference(monotonicity,[status(thm)],[94]) ).
tff(863,plain,
product(product(x0,difference(x0,one)),product(product(x0,x1),difference(x0,one))) = product(product(x0,x1),difference(x0,one)),
inference(transitivity,[status(thm)],[862,861]) ).
tff(864,plain,
difference(x0,product(product(x0,difference(x0,one)),product(product(x0,x1),difference(x0,one)))) = difference(x0,product(product(x0,x1),difference(x0,one))),
inference(monotonicity,[status(thm)],[863]) ).
tff(865,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,difference(x0,one)),product(product(x0,x1),difference(x0,one)))) = quotient(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(866,plain,
difference(x0,product(product(x0,difference(x0,one)),product(product(x0,x1),difference(x0,one)))) = quotient(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0),
inference(unit_resolution,[status(thm)],[865,104]) ).
tff(867,plain,
quotient(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0) = difference(x0,product(product(x0,difference(x0,one)),product(product(x0,x1),difference(x0,one)))),
inference(symmetry,[status(thm)],[866]) ).
tff(868,plain,
quotient(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0) = quotient(product(x1,eta(x0)),x0),
inference(transitivity,[status(thm)],[867,864,859,857]) ).
tff(869,plain,
product(quotient(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0),x0) = product(quotient(product(x1,eta(x0)),x0),x0),
inference(monotonicity,[status(thm)],[868]) ).
tff(870,plain,
product(quotient(product(x1,eta(x0)),x0),x0) = product(quotient(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0),x0),
inference(symmetry,[status(thm)],[869]) ).
tff(871,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(x1,eta(x0)),x0),x0) = product(x1,eta(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(872,plain,
product(quotient(product(x1,eta(x0)),x0),x0) = product(x1,eta(x0)),
inference(unit_resolution,[status(thm)],[871,35]) ).
tff(873,plain,
product(x1,eta(x0)) = product(quotient(product(x1,eta(x0)),x0),x0),
inference(symmetry,[status(thm)],[872]) ).
tff(874,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,product(x1,eta(x0))) = product(x1,eta(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(875,plain,
product(one,product(x1,eta(x0))) = product(x1,eta(x0)),
inference(unit_resolution,[status(thm)],[874,74]) ).
tff(876,plain,
product(product(difference(x0,one),i(i(x0))),product(x1,eta(x0))) = product(one,product(x1,eta(x0))),
inference(monotonicity,[status(thm)],[191]) ).
tff(877,plain,
product(product(difference(x0,one),i(i(x0))),product(x1,eta(x0))) = product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),
inference(transitivity,[status(thm)],[876,875,873,870,853]) ).
tff(878,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(x1,eta(x0)))) = difference(difference(x0,one),product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0))),
inference(monotonicity,[status(thm)],[877]) ).
tff(879,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(x1,eta(x0)))) = quotient(product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(880,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(x1,eta(x0)))) = quotient(product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[879,104]) ).
tff(881,plain,
quotient(product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(x1,eta(x0)))),
inference(symmetry,[status(thm)],[880]) ).
tff(882,plain,
quotient(product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))),difference(x0,one)) = product(product(product(x0,x1),difference(x0,one)),x0),
inference(transitivity,[status(thm)],[881,878,851]) ).
tff(883,plain,
product(quotient(product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),
inference(monotonicity,[status(thm)],[882]) ).
tff(884,plain,
product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)) = product(quotient(product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[883]) ).
tff(885,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(x0,product(x0,product(product(x0,x1),difference(x0,one)))) = product(product(x0,x1),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(886,plain,
difference(x0,product(x0,product(product(x0,x1),difference(x0,one)))) = product(product(x0,x1),difference(x0,one)),
inference(unit_resolution,[status(thm)],[885,26]) ).
tff(887,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(x0,product(product(x0,x1),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(x0,product(product(x0,x1),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(888,plain,
product(quotient(product(x0,product(product(x0,x1),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(x0,product(product(x0,x1),difference(x0,one))),
inference(unit_resolution,[status(thm)],[887,35]) ).
tff(889,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),x0),product(x0,x1))) = quotient(product(x0,product(product(x0,x1),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(890,plain,
difference(difference(x0,one),product(product(difference(x0,one),x0),product(x0,x1))) = quotient(product(x0,product(product(x0,x1),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[889,104]) ).
tff(891,plain,
product(product(difference(x0,one),x0),product(x0,x1)) = product(eta(x0),product(x0,x1)),
inference(monotonicity,[status(thm)],[89]) ).
tff(892,plain,
product(eta(x0),product(x0,x1)) = product(product(difference(x0,one),x0),product(x0,x1)),
inference(symmetry,[status(thm)],[891]) ).
tff(893,plain,
product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(eta(x0),x0),
inference(transitivity,[status(thm)],[116,119]) ).
tff(894,plain,
product(product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0))) = product(product(eta(x0),x0),difference(product(eta(x0),x0),product(eta(x0),product(x0,x1)))),
inference(monotonicity,[status(thm)],[893,19]) ).
tff(895,plain,
product(product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0))) = product(product(difference(x0,one),x0),product(x0,x1)),
inference(transitivity,[status(thm)],[894,9,892]) ).
tff(896,plain,
difference(difference(x0,one),product(product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)))) = difference(difference(x0,one),product(product(difference(x0,one),x0),product(x0,x1))),
inference(monotonicity,[status(thm)],[895]) ).
tff(897,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)))) = quotient(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(898,plain,
difference(difference(x0,one),product(product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)))) = quotient(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[897,104]) ).
tff(899,plain,
quotient(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)))),
inference(symmetry,[status(thm)],[898]) ).
tff(900,plain,
quotient(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),difference(x0,one)) = quotient(product(x0,product(product(x0,x1),difference(x0,one))),difference(x0,one)),
inference(transitivity,[status(thm)],[899,896,890]) ).
tff(901,plain,
product(quotient(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(quotient(product(x0,product(product(x0,x1),difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[900]) ).
tff(902,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(903,plain,
product(quotient(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),
inference(unit_resolution,[status(thm)],[902,35]) ).
tff(904,plain,
product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = product(quotient(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[903]) ).
tff(905,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),one) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(906,plain,
product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),one) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[905,170]) ).
tff(907,plain,
product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0)))) = product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),one),
inference(monotonicity,[status(thm)],[191]) ).
tff(908,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(x0,difference(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0)))))) = product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(909,plain,
product(x0,difference(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0)))))) = product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0)))),
inference(unit_resolution,[status(thm)],[908,7]) ).
tff(910,plain,
product(x0,product(x0,difference(x0,one))) = product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[328]) ).
tff(911,plain,
x0 = product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(transitivity,[status(thm)],[173,163,910]) ).
tff(912,plain,
difference(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0))))) = difference(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0))))),
inference(monotonicity,[status(thm)],[911]) ).
tff(913,plain,
difference(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0))))) = difference(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0))))),
inference(symmetry,[status(thm)],[912]) ).
tff(914,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0))))) = quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(915,plain,
difference(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0))))) = quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(unit_resolution,[status(thm)],[914,16]) ).
tff(916,plain,
quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = difference(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0))))),
inference(symmetry,[status(thm)],[915]) ).
tff(917,plain,
quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = difference(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0))))),
inference(transitivity,[status(thm)],[916,913]) ).
tff(918,plain,
product(x0,quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(x0,difference(x0,product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0)))))),
inference(monotonicity,[status(thm)],[917]) ).
tff(919,plain,
product(x0,quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),
inference(transitivity,[status(thm)],[918,909,907,906]) ).
tff(920,plain,
product(product(x0,quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),
inference(monotonicity,[status(thm)],[919]) ).
tff(921,plain,
product(product(x0,quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = product(x0,product(product(x0,x1),difference(x0,one))),
inference(transitivity,[status(thm)],[920,904,901,888]) ).
tff(922,plain,
difference(x0,product(product(x0,quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))) = difference(x0,product(x0,product(product(x0,x1),difference(x0,one)))),
inference(monotonicity,[status(thm)],[921]) ).
tff(923,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))) = quotient(product(quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(924,plain,
difference(x0,product(product(x0,quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))) = quotient(product(quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),
inference(unit_resolution,[status(thm)],[923,104]) ).
tff(925,plain,
quotient(product(quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0) = difference(x0,product(product(x0,quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))),
inference(symmetry,[status(thm)],[924]) ).
tff(926,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),product(quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),i(i(x0)))) = i(i(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(927,plain,
difference(quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),product(quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),i(i(x0)))) = i(i(x0)),
inference(unit_resolution,[status(thm)],[926,26]) ).
tff(928,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),i(i(x0))) = quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(929,plain,
product(quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),i(i(x0))) = quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[928,35]) ).
tff(930,plain,
quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)) = product(quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),i(i(x0))),
inference(symmetry,[status(thm)],[929]) ).
tff(931,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),i(i(x0)))) = quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(932,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),i(i(x0)))) = quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[931,104]) ).
tff(933,plain,
product(product(difference(x0,one),i(i(x0))),i(i(x0))) = product(product(x0,difference(x0,one)),i(i(x0))),
inference(monotonicity,[status(thm)],[159]) ).
tff(934,plain,
product(product(difference(x0,one),i(i(x0))),i(i(x0))) = product(product(difference(x0,one),x0),x0),
inference(transitivity,[status(thm)],[933,232,231,134,132,28,109]) ).
tff(935,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),i(i(x0)))) = difference(difference(x0,one),product(product(difference(x0,one),x0),x0)),
inference(monotonicity,[status(thm)],[934]) ).
tff(936,plain,
difference(difference(x0,one),product(product(difference(x0,one),x0),x0)) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),i(i(x0)))),
inference(symmetry,[status(thm)],[935]) ).
tff(937,plain,
product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0)))) = product(quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),i(i(x0))),
inference(transitivity,[status(thm)],[907,906,114,936,932,930]) ).
tff(938,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(i(i(x0)),difference(x0,one)),product(i(i(x0)),product(difference(x0,one),i(i(x0))))) = quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(939,plain,
difference(product(i(i(x0)),difference(x0,one)),product(i(i(x0)),product(difference(x0,one),i(i(x0))))) = quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),
inference(unit_resolution,[status(thm)],[938,16]) ).
tff(940,plain,
product(i(i(x0)),product(difference(x0,one),i(i(x0)))) = product(eta(x0),x0),
inference(transitivity,[status(thm)],[578,274,277,134,132,28]) ).
tff(941,plain,
difference(product(i(i(x0)),difference(x0,one)),product(i(i(x0)),product(difference(x0,one),i(i(x0))))) = difference(eta(x0),product(eta(x0),x0)),
inference(monotonicity,[status(thm)],[754,940]) ).
tff(942,plain,
difference(eta(x0),product(eta(x0),x0)) = difference(product(i(i(x0)),difference(x0,one)),product(i(i(x0)),product(difference(x0,one),i(i(x0))))),
inference(symmetry,[status(thm)],[941]) ).
tff(943,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(eta(x0),product(eta(x0),x0)) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(944,plain,
difference(eta(x0),product(eta(x0),x0)) = x0,
inference(unit_resolution,[status(thm)],[943,26]) ).
tff(945,plain,
x0 = difference(eta(x0),product(eta(x0),x0)),
inference(symmetry,[status(thm)],[944]) ).
tff(946,plain,
product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)) = quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),
inference(transitivity,[status(thm)],[328,162,172,945,942,939]) ).
tff(947,plain,
difference(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(difference(x0,one),i(i(x0))))) = difference(quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),product(quotient(quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),i(i(x0))),i(i(x0)))),
inference(monotonicity,[status(thm)],[946,937]) ).
tff(948,plain,
quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = i(i(x0)),
inference(transitivity,[status(thm)],[916,947,927]) ).
tff(949,plain,
product(quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)) = product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),
inference(monotonicity,[status(thm)],[948]) ).
tff(950,plain,
product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)) = product(quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),
inference(symmetry,[status(thm)],[949]) ).
tff(951,plain,
quotient(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0) = quotient(product(quotient(quotient(product(i(i(x0)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),
inference(monotonicity,[status(thm)],[950]) ).
tff(952,plain,
quotient(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0) = product(product(x0,x1),difference(x0,one)),
inference(transitivity,[status(thm)],[951,925,922,886]) ).
tff(953,plain,
product(quotient(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),x0) = product(product(product(x0,x1),difference(x0,one)),x0),
inference(monotonicity,[status(thm)],[952]) ).
tff(954,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),x0) = product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(955,plain,
product(quotient(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),x0) = product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),
inference(unit_resolution,[status(thm)],[954,35]) ).
tff(956,plain,
product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)) = product(quotient(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),x0),
inference(symmetry,[status(thm)],[955]) ).
tff(957,plain,
product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)) = product(product(product(x0,x1),difference(x0,one)),x0),
inference(transitivity,[status(thm)],[956,953]) ).
tff(958,plain,
product(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),difference(x0,one)) = product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),
inference(monotonicity,[status(thm)],[957]) ).
tff(959,plain,
product(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),difference(x0,one)) = product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))),
inference(transitivity,[status(thm)],[958,884,849]) ).
tff(960,plain,
difference(i(i(x0)),product(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),difference(x0,one))) = difference(i(i(x0)),product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one)))),
inference(monotonicity,[status(thm)],[959]) ).
tff(961,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(i(i(x0)),product(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),difference(x0,one))) = quotient(product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(difference(x0,one),i(i(x0)))),i(i(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(962,plain,
difference(i(i(x0)),product(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),difference(x0,one))) = quotient(product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(difference(x0,one),i(i(x0)))),i(i(x0))),
inference(unit_resolution,[status(thm)],[961,104]) ).
tff(963,plain,
quotient(product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(difference(x0,one),i(i(x0)))),i(i(x0))) = difference(i(i(x0)),product(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),difference(x0,one))),
inference(symmetry,[status(thm)],[962]) ).
tff(964,plain,
product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(difference(x0,one),i(i(x0)))) = product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),one),
inference(monotonicity,[status(thm)],[191]) ).
tff(965,plain,
product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),one) = product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(difference(x0,one),i(i(x0)))),
inference(symmetry,[status(thm)],[964]) ).
tff(966,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(x0,one)) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),
inference(monotonicity,[status(thm)],[172]) ).
tff(967,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(x0,one)),
inference(symmetry,[status(thm)],[966]) ).
tff(968,plain,
difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)) = difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(x0,one))),
inference(monotonicity,[status(thm)],[967]) ).
tff(969,plain,
difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(x0,one))) = difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),
inference(symmetry,[status(thm)],[968]) ).
tff(970,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(x0,one))) = quotient(quotient(product(one,product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(971,plain,
difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(x0,one))) = quotient(quotient(product(one,product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),
inference(unit_resolution,[status(thm)],[970,16]) ).
tff(972,plain,
quotient(quotient(product(one,product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(x0,one))),
inference(symmetry,[status(thm)],[971]) ).
tff(973,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(974,plain,
product(one,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),
inference(unit_resolution,[status(thm)],[973,74]) ).
tff(975,plain,
product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)) = product(one,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),
inference(symmetry,[status(thm)],[974]) ).
tff(976,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(x0,product(x0,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))) = product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(977,plain,
difference(x0,product(x0,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))) = product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),
inference(unit_resolution,[status(thm)],[976,26]) ).
tff(978,plain,
product(product(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = product(x0,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),
inference(monotonicity,[status(thm)],[172]) ).
tff(979,plain,
difference(x0,product(product(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))) = difference(x0,product(x0,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))),
inference(monotonicity,[status(thm)],[978]) ).
tff(980,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))) = quotient(product(one,product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(981,plain,
difference(x0,product(product(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))) = quotient(product(one,product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),
inference(unit_resolution,[status(thm)],[980,104]) ).
tff(982,plain,
quotient(product(one,product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0) = difference(x0,product(product(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))),
inference(symmetry,[status(thm)],[981]) ).
tff(983,plain,
quotient(product(one,product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0) = product(one,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),
inference(transitivity,[status(thm)],[982,979,977,975]) ).
tff(984,plain,
quotient(quotient(product(one,product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = quotient(product(one,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),
inference(monotonicity,[status(thm)],[983]) ).
tff(985,plain,
quotient(product(one,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = quotient(quotient(product(one,product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),
inference(symmetry,[status(thm)],[984]) ).
tff(986,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(one,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(987,plain,
quotient(product(one,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = one,
inference(unit_resolution,[status(thm)],[986,143]) ).
tff(988,plain,
one = quotient(product(one,product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),
inference(symmetry,[status(thm)],[987]) ).
tff(989,plain,
one = difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),
inference(transitivity,[status(thm)],[988,985,972,969]) ).
tff(990,plain,
product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),one) = product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0))),
inference(monotonicity,[status(thm)],[989]) ).
tff(991,plain,
product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0))) = product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),one),
inference(symmetry,[status(thm)],[990]) ).
tff(992,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0))) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(993,plain,
product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0))) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[992,7]) ).
tff(994,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0) = product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),difference(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0))),
inference(symmetry,[status(thm)],[993]) ).
tff(995,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),
inference(monotonicity,[status(thm)],[178]) ).
tff(996,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))) = product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(difference(x0,one),i(i(x0)))),
inference(transitivity,[status(thm)],[995,994,991,965]) ).
tff(997,plain,
quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))) = quotient(product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(difference(x0,one),i(i(x0)))),i(i(x0))),
inference(monotonicity,[status(thm)],[996]) ).
tff(998,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(i(i(x0)),product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(999,plain,
difference(i(i(x0)),product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))),
inference(unit_resolution,[status(thm)],[998,104]) ).
tff(1000,plain,
difference(i(i(x0)),product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = product(product(x1,eta(x0)),difference(x0,one)),
inference(transitivity,[status(thm)],[999,997,963,960,847]) ).
tff(1001,plain,
product(i(i(x0)),difference(i(i(x0)),product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))))) = product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))),
inference(monotonicity,[status(thm)],[1000]) ).
tff(1002,plain,
product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one))) = product(i(i(x0)),difference(i(i(x0)),product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))))),
inference(symmetry,[status(thm)],[1001]) ).
tff(1003,plain,
product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(transitivity,[status(thm)],[764,767,884,849,1002,845]) ).
tff(1004,plain,
quotient(product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = quotient(product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(monotonicity,[status(thm)],[1003]) ).
tff(1005,plain,
quotient(product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = quotient(product(product(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(symmetry,[status(thm)],[1004]) ).
tff(1006,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1007,plain,
quotient(product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),
inference(unit_resolution,[status(thm)],[1006,143]) ).
tff(1008,plain,
product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = quotient(product(product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(symmetry,[status(thm)],[1007]) ).
tff(1009,plain,
product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(x0,product(x1,difference(x0,one)))),
inference(transitivity,[status(thm)],[1008,1005,843,715,712,182]) ).
tff(1010,plain,
product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))) = product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),difference(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(x0,product(x1,difference(x0,one))))),
inference(monotonicity,[status(thm)],[1009]) ).
tff(1011,plain,
product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)))) = product(x0,product(x1,difference(x0,one))),
inference(transitivity,[status(thm)],[1010,149]) ).
tff(1012,plain,
difference(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))))) = difference(x0,product(x0,product(x1,difference(x0,one)))),
inference(monotonicity,[status(thm)],[178,1011]) ).
tff(1013,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))))) = quotient(quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1014,plain,
difference(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))))) = quotient(quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(unit_resolution,[status(thm)],[1013,16]) ).
tff(1015,plain,
quotient(quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = difference(product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0))),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),product(i(i(x0)),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))))),
inference(symmetry,[status(thm)],[1014]) ).
tff(1016,plain,
quotient(product(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),product(difference(x0,one),i(i(x0)))),i(i(x0))) = quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))),
inference(symmetry,[status(thm)],[997]) ).
tff(1017,plain,
difference(i(i(x0)),product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one)))) = difference(i(i(x0)),product(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),difference(x0,one))),
inference(symmetry,[status(thm)],[960]) ).
tff(1018,plain,
product(product(x1,eta(x0)),difference(x0,one)) = difference(i(i(x0)),product(i(i(x0)),product(product(x1,eta(x0)),difference(x0,one)))),
inference(symmetry,[status(thm)],[847]) ).
tff(1019,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(product(product(x1,eta(x0)),difference(x0,one)),one) = product(product(x1,eta(x0)),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1020,plain,
product(product(product(x1,eta(x0)),difference(x0,one)),one) = product(product(x1,eta(x0)),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1019,170]) ).
tff(1021,plain,
product(product(product(x1,eta(x0)),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = product(product(product(x1,eta(x0)),difference(x0,one)),one),
inference(monotonicity,[status(thm)],[763]) ).
tff(1022,plain,
product(product(product(x1,eta(x0)),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))) = quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))),
inference(transitivity,[status(thm)],[1021,1020,1018,1017,962,1016]) ).
tff(1023,plain,
quotient(product(product(product(x1,eta(x0)),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = quotient(quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),i(i(x0)))),i(i(x0))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(monotonicity,[status(thm)],[1022]) ).
tff(1024,plain,
product(product(product(x1,eta(x0)),difference(x0,one)),one) = product(product(product(x1,eta(x0)),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),
inference(symmetry,[status(thm)],[1021]) ).
tff(1025,plain,
product(product(x1,eta(x0)),difference(x0,one)) = product(product(product(x1,eta(x0)),difference(x0,one)),one),
inference(symmetry,[status(thm)],[1020]) ).
tff(1026,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(difference(x0,one),product(difference(x0,one),product(x1,eta(x0)))) = product(x1,eta(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1027,plain,
difference(difference(x0,one),product(difference(x0,one),product(x1,eta(x0)))) = product(x1,eta(x0)),
inference(unit_resolution,[status(thm)],[1026,26]) ).
tff(1028,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(difference(x0,one),product(x1,eta(x0))),x0),x0) = product(difference(x0,one),product(x1,eta(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1029,plain,
quotient(product(product(difference(x0,one),product(x1,eta(x0))),x0),x0) = product(difference(x0,one),product(x1,eta(x0))),
inference(unit_resolution,[status(thm)],[1028,143]) ).
tff(1030,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(x1,eta(x0))),x0))) = product(product(difference(x0,one),product(x1,eta(x0))),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1031,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(x1,eta(x0))),x0))) = product(product(difference(x0,one),product(x1,eta(x0))),x0),
inference(unit_resolution,[status(thm)],[1030,7]) ).
tff(1032,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),product(x1,eta(x0))),x0)) = quotient(product(product(x1,eta(x0)),product(x0,difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1033,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(x1,eta(x0))),x0)) = quotient(product(product(x1,eta(x0)),product(x0,difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1032,104]) ).
tff(1034,plain,
quotient(product(product(x1,eta(x0)),product(x0,difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),product(x1,eta(x0))),x0)),
inference(symmetry,[status(thm)],[1033]) ).
tff(1035,plain,
product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = product(quotient(product(x1,eta(x0)),x0),x0),
inference(monotonicity,[status(thm)],[857,329]) ).
tff(1036,plain,
product(quotient(product(x1,eta(x0)),x0),x0) = product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),
inference(symmetry,[status(thm)],[1035]) ).
tff(1037,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(product(x1,eta(x0)),difference(product(x1,eta(x0)),product(x1,eta(x0)))) = product(x1,eta(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1038,plain,
product(product(x1,eta(x0)),difference(product(x1,eta(x0)),product(x1,eta(x0)))) = product(x1,eta(x0)),
inference(unit_resolution,[status(thm)],[1037,7]) ).
tff(1039,plain,
product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,one)) = product(quotient(product(x1,eta(x0)),x0),x0),
inference(monotonicity,[status(thm)],[857,172]) ).
tff(1040,plain,
product(quotient(product(x1,eta(x0)),x0),x0) = product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,one)),
inference(symmetry,[status(thm)],[1039]) ).
tff(1041,plain,
product(x1,eta(x0)) = product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,one)),
inference(transitivity,[status(thm)],[873,1040]) ).
tff(1042,plain,
product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0) = product(quotient(product(x1,eta(x0)),x0),x0),
inference(monotonicity,[status(thm)],[857]) ).
tff(1043,plain,
product(quotient(product(x1,eta(x0)),x0),x0) = product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0),
inference(symmetry,[status(thm)],[1042]) ).
tff(1044,plain,
product(x1,eta(x0)) = product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0),
inference(transitivity,[status(thm)],[873,1043]) ).
tff(1045,plain,
difference(product(x1,eta(x0)),product(x1,eta(x0))) = difference(product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0),product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,one))),
inference(monotonicity,[status(thm)],[1044,1041]) ).
tff(1046,plain,
difference(product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0),product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,one))) = difference(product(x1,eta(x0)),product(x1,eta(x0))),
inference(symmetry,[status(thm)],[1045]) ).
tff(1047,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0),product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,one))) = quotient(quotient(product(one,product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0)),x0),quotient(product(x1,product(difference(x0,one),x0)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1048,plain,
difference(product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0),product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,one))) = quotient(quotient(product(one,product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0)),x0),quotient(product(x1,product(difference(x0,one),x0)),x0)),
inference(unit_resolution,[status(thm)],[1047,16]) ).
tff(1049,plain,
quotient(quotient(product(one,product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0)),x0),quotient(product(x1,product(difference(x0,one),x0)),x0)) = difference(product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0),product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,one))),
inference(symmetry,[status(thm)],[1048]) ).
tff(1050,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,quotient(product(x1,product(difference(x0,one),x0)),x0)) = quotient(product(x1,product(difference(x0,one),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1051,plain,
product(one,quotient(product(x1,product(difference(x0,one),x0)),x0)) = quotient(product(x1,product(difference(x0,one),x0)),x0),
inference(unit_resolution,[status(thm)],[1050,74]) ).
tff(1052,plain,
quotient(product(x1,product(difference(x0,one),x0)),x0) = product(one,quotient(product(x1,product(difference(x0,one),x0)),x0)),
inference(symmetry,[status(thm)],[1051]) ).
tff(1053,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(x0,difference(x0,product(product(x0,x1),difference(x0,one)))) = product(product(x0,x1),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1054,plain,
product(x0,difference(x0,product(product(x0,x1),difference(x0,one)))) = product(product(x0,x1),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1053,7]) ).
tff(1055,plain,
quotient(product(x1,product(difference(x0,one),x0)),x0) = difference(x0,product(product(x0,x1),difference(x0,one))),
inference(symmetry,[status(thm)],[859]) ).
tff(1056,plain,
product(product(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)) = product(x0,difference(x0,product(product(x0,x1),difference(x0,one)))),
inference(monotonicity,[status(thm)],[172,1055]) ).
tff(1057,plain,
product(product(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)) = product(product(x0,x1),difference(x0,one)),
inference(transitivity,[status(thm)],[1056,1054]) ).
tff(1058,plain,
difference(x0,product(product(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) = difference(x0,product(product(x0,x1),difference(x0,one))),
inference(monotonicity,[status(thm)],[1057]) ).
tff(1059,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) = quotient(product(one,product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1060,plain,
difference(x0,product(product(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) = quotient(product(one,product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0)),x0),
inference(unit_resolution,[status(thm)],[1059,104]) ).
tff(1061,plain,
quotient(product(one,product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0)),x0) = difference(x0,product(product(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),
inference(symmetry,[status(thm)],[1060]) ).
tff(1062,plain,
quotient(product(one,product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0)),x0) = product(one,quotient(product(x1,product(difference(x0,one),x0)),x0)),
inference(transitivity,[status(thm)],[1061,1058,859,1052]) ).
tff(1063,plain,
quotient(quotient(product(one,product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0)),x0),quotient(product(x1,product(difference(x0,one),x0)),x0)) = quotient(product(one,quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x1,product(difference(x0,one),x0)),x0)),
inference(monotonicity,[status(thm)],[1062]) ).
tff(1064,plain,
quotient(product(one,quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x1,product(difference(x0,one),x0)),x0)) = quotient(quotient(product(one,product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0)),x0),quotient(product(x1,product(difference(x0,one),x0)),x0)),
inference(symmetry,[status(thm)],[1063]) ).
tff(1065,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(one,quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x1,product(difference(x0,one),x0)),x0)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1066,plain,
quotient(product(one,quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x1,product(difference(x0,one),x0)),x0)) = one,
inference(unit_resolution,[status(thm)],[1065,143]) ).
tff(1067,plain,
one = quotient(product(one,quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x1,product(difference(x0,one),x0)),x0)),
inference(symmetry,[status(thm)],[1066]) ).
tff(1068,plain,
one = difference(product(x1,eta(x0)),product(x1,eta(x0))),
inference(transitivity,[status(thm)],[1067,1064,1049,1046]) ).
tff(1069,plain,
product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0) = product(x1,eta(x0)),
inference(transitivity,[status(thm)],[1042,872]) ).
tff(1070,plain,
product(product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0),one) = product(product(x1,eta(x0)),difference(product(x1,eta(x0)),product(x1,eta(x0)))),
inference(monotonicity,[status(thm)],[1069,1068]) ).
tff(1071,plain,
product(product(x1,eta(x0)),product(x0,difference(x0,one))) = product(product(quotient(product(x1,product(difference(x0,one),x0)),x0),x0),one),
inference(monotonicity,[status(thm)],[1044,94]) ).
tff(1072,plain,
product(product(x1,eta(x0)),product(x0,difference(x0,one))) = product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),
inference(transitivity,[status(thm)],[1071,1070,1038,873,1036]) ).
tff(1073,plain,
quotient(product(product(x1,eta(x0)),product(x0,difference(x0,one))),difference(x0,one)) = quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(monotonicity,[status(thm)],[1072]) ).
tff(1074,plain,
quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) = quotient(product(product(x1,eta(x0)),product(x0,difference(x0,one))),difference(x0,one)),
inference(symmetry,[status(thm)],[1073]) ).
tff(1075,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1076,plain,
difference(difference(x0,one),product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1075,104]) ).
tff(1077,plain,
difference(difference(x0,one),product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = difference(difference(x0,one),product(product(difference(x0,one),product(x1,eta(x0))),x0)),
inference(transitivity,[status(thm)],[1076,1074,1034]) ).
tff(1078,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(x1,eta(x0))),x0))),
inference(monotonicity,[status(thm)],[1077]) ).
tff(1079,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1080,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(unit_resolution,[status(thm)],[1079,7]) ).
tff(1081,plain,
product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))),
inference(symmetry,[status(thm)],[1080]) ).
tff(1082,plain,
product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)) = product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(monotonicity,[status(thm)],[341]) ).
tff(1083,plain,
product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)) = product(product(difference(x0,one),product(x1,eta(x0))),x0),
inference(transitivity,[status(thm)],[1082,1081,1078,1031]) ).
tff(1084,plain,
quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0) = quotient(product(product(difference(x0,one),product(x1,eta(x0))),x0),x0),
inference(monotonicity,[status(thm)],[1083]) ).
tff(1085,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))) = quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1086,plain,
product(quotient(quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))) = quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),
inference(unit_resolution,[status(thm)],[1085,35]) ).
tff(1087,plain,
quotient(quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),product(x0,product(x0,j(x0)))) = quotient(quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(monotonicity,[status(thm)],[305]) ).
tff(1088,plain,
quotient(quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) = quotient(quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),product(x0,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[1087]) ).
tff(1089,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))))) = quotient(quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1090,plain,
difference(product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))))) = quotient(quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(unit_resolution,[status(thm)],[1089,16]) ).
tff(1091,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(x0,difference(x0,product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))))) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1092,plain,
product(x0,difference(x0,product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))))) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))),
inference(unit_resolution,[status(thm)],[1091,7]) ).
tff(1093,plain,
product(x0,eta(x0)) = product(x0,product(x0,j(x0))),
inference(monotonicity,[status(thm)],[519]) ).
tff(1094,plain,
product(x0,eta(x0)) = quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),
inference(transitivity,[status(thm)],[1093,302,299,288]) ).
tff(1095,plain,
product(product(x0,eta(x0)),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))),
inference(monotonicity,[status(thm)],[1094]) ).
tff(1096,plain,
product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))) = product(product(x0,eta(x0)),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))),
inference(symmetry,[status(thm)],[1095]) ).
tff(1097,plain,
difference(x0,product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))))) = difference(x0,product(product(x0,eta(x0)),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))))),
inference(monotonicity,[status(thm)],[1096]) ).
tff(1098,plain,
difference(x0,product(product(x0,eta(x0)),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))))) = difference(x0,product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))))),
inference(symmetry,[status(thm)],[1097]) ).
tff(1099,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,eta(x0)),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))))) = quotient(product(eta(x0),product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1100,plain,
difference(x0,product(product(x0,eta(x0)),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))))) = quotient(product(eta(x0),product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),x0)),x0),
inference(unit_resolution,[status(thm)],[1099,104]) ).
tff(1101,plain,
quotient(product(eta(x0),product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),x0)),x0) = difference(x0,product(product(x0,eta(x0)),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))))),
inference(symmetry,[status(thm)],[1100]) ).
tff(1102,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(x1,one) = x1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1103,plain,
product(x1,one) = x1,
inference(unit_resolution,[status(thm)],[1102,170]) ).
tff(1104,plain,
product(x1,product(j(x0),x0)) = product(x1,one),
inference(monotonicity,[status(thm)],[199]) ).
tff(1105,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(x1,product(j(x0),x0)),x0),x0) = product(x1,product(j(x0),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1106,plain,
product(quotient(product(x1,product(j(x0),x0)),x0),x0) = product(x1,product(j(x0),x0)),
inference(unit_resolution,[status(thm)],[1105,35]) ).
tff(1107,plain,
product(quotient(product(x1,product(j(x0),x0)),x0),x0) = x1,
inference(transitivity,[status(thm)],[1106,1104,1103]) ).
tff(1108,plain,
product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),product(quotient(product(x1,product(j(x0),x0)),x0),x0)) = product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1),
inference(monotonicity,[status(thm)],[1107]) ).
tff(1109,plain,
product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1) = product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),product(quotient(product(x1,product(j(x0),x0)),x0),x0)),
inference(symmetry,[status(thm)],[1108]) ).
tff(1110,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(quotient(product(difference(x0,one),product(x0,x1)),x1),difference(quotient(product(difference(x0,one),product(x0,x1)),x1),product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1))) = product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1111,plain,
product(quotient(product(difference(x0,one),product(x0,x1)),x1),difference(quotient(product(difference(x0,one),product(x0,x1)),x1),product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1))) = product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1),
inference(unit_resolution,[status(thm)],[1110,7]) ).
tff(1112,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1)),quotient(product(difference(x0,one),product(x0,x1)),x1)) = x1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1113,plain,
quotient(product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1)),quotient(product(difference(x0,one),product(x0,x1)),x1)) = x1,
inference(unit_resolution,[status(thm)],[1112,143]) ).
tff(1114,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x1,product(product(x1,difference(x0,one)),x0)) = quotient(product(difference(x0,one),product(x0,x1)),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1115,plain,
difference(x1,product(product(x1,difference(x0,one)),x0)) = quotient(product(difference(x0,one),product(x0,x1)),x1),
inference(unit_resolution,[status(thm)],[1114,104]) ).
tff(1116,plain,
quotient(product(difference(x0,one),product(x0,x1)),x1) = difference(x1,product(product(x1,difference(x0,one)),x0)),
inference(symmetry,[status(thm)],[1115]) ).
tff(1117,plain,
product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1)) = product(x1,difference(x1,product(product(x1,difference(x0,one)),x0))),
inference(monotonicity,[status(thm)],[1116]) ).
tff(1118,plain,
product(x1,difference(x1,product(product(x1,difference(x0,one)),x0))) = product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1)),
inference(symmetry,[status(thm)],[1117]) ).
tff(1119,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(x1,difference(x1,product(product(x1,difference(x0,one)),x0))) = product(product(x1,difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1120,plain,
product(x1,difference(x1,product(product(x1,difference(x0,one)),x0))) = product(product(x1,difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[1119,7]) ).
tff(1121,plain,
product(product(x1,difference(x0,one)),x0) = product(x1,difference(x1,product(product(x1,difference(x0,one)),x0))),
inference(symmetry,[status(thm)],[1120]) ).
tff(1122,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,product(product(x1,difference(x0,one)),x0)) = product(product(x1,difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1123,plain,
product(one,product(product(x1,difference(x0,one)),x0)) = product(product(x1,difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[1122,74]) ).
tff(1124,plain,
product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1)) = product(product(x1,difference(x0,one)),x0),
inference(transitivity,[status(thm)],[1117,1120]) ).
tff(1125,plain,
product(one,product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1))) = product(one,product(product(x1,difference(x0,one)),x0)),
inference(monotonicity,[status(thm)],[1124]) ).
tff(1126,plain,
product(one,product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1))) = product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1)),
inference(transitivity,[status(thm)],[1125,1123,1121,1118]) ).
tff(1127,plain,
quotient(product(one,product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1))),quotient(product(difference(x0,one),product(x0,x1)),x1)) = quotient(product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1)),quotient(product(difference(x0,one),product(x0,x1)),x1)),
inference(monotonicity,[status(thm)],[1126]) ).
tff(1128,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(quotient(product(difference(x0,one),product(x0,x1)),x1),product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1)) = quotient(product(one,product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1))),quotient(product(difference(x0,one),product(x0,x1)),x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1129,plain,
difference(quotient(product(difference(x0,one),product(x0,x1)),x1),product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1)) = quotient(product(one,product(x1,quotient(product(difference(x0,one),product(x0,x1)),x1))),quotient(product(difference(x0,one),product(x0,x1)),x1)),
inference(unit_resolution,[status(thm)],[1128,104]) ).
tff(1130,plain,
difference(quotient(product(difference(x0,one),product(x0,x1)),x1),product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1)) = x1,
inference(transitivity,[status(thm)],[1129,1127,1113]) ).
tff(1131,plain,
product(quotient(product(difference(x0,one),product(x0,x1)),x1),difference(quotient(product(difference(x0,one),product(x0,x1)),x1),product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1))) = product(quotient(product(difference(x0,one),product(x0,x1)),x1),x1),
inference(monotonicity,[status(thm)],[1130]) ).
tff(1132,plain,
product(quotient(product(difference(x0,one),product(x0,x1)),x1),x1) = product(quotient(product(difference(x0,one),product(x0,x1)),x1),difference(quotient(product(difference(x0,one),product(x0,x1)),x1),product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1))),
inference(symmetry,[status(thm)],[1131]) ).
tff(1133,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(difference(x0,one),product(x0,x1)),x1),x1) = product(difference(x0,one),product(x0,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1134,plain,
product(quotient(product(difference(x0,one),product(x0,x1)),x1),x1) = product(difference(x0,one),product(x0,x1)),
inference(unit_resolution,[status(thm)],[1133,35]) ).
tff(1135,plain,
product(difference(x0,one),product(x0,x1)) = product(quotient(product(difference(x0,one),product(x0,x1)),x1),x1),
inference(symmetry,[status(thm)],[1134]) ).
tff(1136,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(eta(x0),difference(eta(x0),product(difference(x0,one),product(x0,x1)))) = product(difference(x0,one),product(x0,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1137,plain,
product(eta(x0),difference(eta(x0),product(difference(x0,one),product(x0,x1)))) = product(difference(x0,one),product(x0,x1)),
inference(unit_resolution,[status(thm)],[1136,7]) ).
tff(1138,plain,
difference(eta(x0),product(difference(x0,one),product(x0,x1))) = difference(product(difference(x0,one),x0),product(difference(x0,one),product(x0,x1))),
inference(monotonicity,[status(thm)],[92]) ).
tff(1139,plain,
difference(product(difference(x0,one),x0),product(difference(x0,one),product(x0,x1))) = difference(eta(x0),product(difference(x0,one),product(x0,x1))),
inference(symmetry,[status(thm)],[1138]) ).
tff(1140,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(difference(x0,one),x0),product(difference(x0,one),product(x0,x1))) = quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1141,plain,
difference(product(difference(x0,one),x0),product(difference(x0,one),product(x0,x1))) = quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1140,16]) ).
tff(1142,plain,
quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)) = difference(product(difference(x0,one),x0),product(difference(x0,one),product(x0,x1))),
inference(symmetry,[status(thm)],[1141]) ).
tff(1143,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),x0),x0) = quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1144,plain,
product(quotient(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),x0),x0) = quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1143,35]) ).
tff(1145,plain,
product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),product(j(x0),x0)) = product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),one),
inference(monotonicity,[status(thm)],[199]) ).
tff(1146,plain,
product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),one) = product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),product(j(x0),x0)),
inference(symmetry,[status(thm)],[1145]) ).
tff(1147,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),one) = quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1148,plain,
product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),one) = quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1147,170]) ).
tff(1149,plain,
quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)) = product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),one),
inference(symmetry,[status(thm)],[1148]) ).
tff(1150,plain,
quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)) = product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),product(j(x0),x0)),
inference(transitivity,[status(thm)],[1149,1146]) ).
tff(1151,plain,
quotient(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),x0) = quotient(product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),product(j(x0),x0)),x0),
inference(monotonicity,[status(thm)],[1150]) ).
tff(1152,plain,
quotient(product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),product(j(x0),x0)),x0) = quotient(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),x0),
inference(symmetry,[status(thm)],[1151]) ).
tff(1153,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(quotient(product(x1,product(difference(x0,one),x0)),x0),one) = quotient(product(x1,product(difference(x0,one),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1154,plain,
product(quotient(product(x1,product(difference(x0,one),x0)),x0),one) = quotient(product(x1,product(difference(x0,one),x0)),x0),
inference(unit_resolution,[status(thm)],[1153,170]) ).
tff(1155,plain,
product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,difference(x0,one))) = product(quotient(product(x1,product(difference(x0,one),x0)),x0),one),
inference(monotonicity,[status(thm)],[94]) ).
tff(1156,plain,
product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,difference(x0,one))) = quotient(product(x1,product(difference(x0,one),x0)),x0),
inference(transitivity,[status(thm)],[1155,1154]) ).
tff(1157,plain,
quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,difference(x0,one))),difference(x0,one)) = quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),
inference(monotonicity,[status(thm)],[1156]) ).
tff(1158,plain,
quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)) = quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,difference(x0,one))),difference(x0,one)),
inference(symmetry,[status(thm)],[1157]) ).
tff(1159,plain,
product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),product(j(x0),x0)) = quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,difference(x0,one))),difference(x0,one)),
inference(transitivity,[status(thm)],[1145,1148,1158]) ).
tff(1160,plain,
quotient(product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),product(j(x0),x0)),x0) = quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,difference(x0,one))),difference(x0,one)),x0),
inference(monotonicity,[status(thm)],[1159]) ).
tff(1161,plain,
quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,difference(x0,one))),difference(x0,one)),x0) = quotient(product(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),product(j(x0),x0)),x0),
inference(symmetry,[status(thm)],[1160]) ).
tff(1162,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))) = quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,difference(x0,one))),difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1163,plain,
difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))) = quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,difference(x0,one))),difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[1162,16]) ).
tff(1164,plain,
product(product(one,x0),product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) = product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),
inference(monotonicity,[status(thm)],[198]) ).
tff(1165,plain,
product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) = product(product(one,x0),product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),
inference(symmetry,[status(thm)],[1164]) ).
tff(1166,plain,
difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))) = difference(one,product(product(one,x0),product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))),
inference(monotonicity,[status(thm)],[94,1165]) ).
tff(1167,plain,
difference(one,product(product(one,x0),product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))) = difference(product(x0,difference(x0,one)),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))),
inference(symmetry,[status(thm)],[1166]) ).
tff(1168,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(one,product(product(one,x0),product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))) = quotient(product(x0,product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),one)),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1169,plain,
difference(one,product(product(one,x0),product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))) = quotient(product(x0,product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),one)),one),
inference(unit_resolution,[status(thm)],[1168,104]) ).
tff(1170,plain,
quotient(product(x0,product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),one)),one) = difference(one,product(product(one,x0),product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))),
inference(symmetry,[status(thm)],[1169]) ).
tff(1171,plain,
product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(x0,product(x0,j(x0)))) = product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(monotonicity,[status(thm)],[305]) ).
tff(1172,plain,
product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)) = product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(x0,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[1171]) ).
tff(1173,plain,
product(x0,product(x0,j(x0))) = difference(one,product(x0,product(x0,j(x0)))),
inference(transitivity,[status(thm)],[302,299,288,296,293]) ).
tff(1174,plain,
product(one,product(x0,product(x0,j(x0)))) = product(one,difference(one,product(x0,product(x0,j(x0))))),
inference(monotonicity,[status(thm)],[1173]) ).
tff(1175,plain,
product(one,product(x0,product(x0,j(x0)))) = quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),
inference(transitivity,[status(thm)],[1174,299,288]) ).
tff(1176,plain,
product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(one,product(x0,product(x0,j(x0))))) = product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0)),
inference(monotonicity,[status(thm)],[1175]) ).
tff(1177,plain,
product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(one,product(x0,product(x0,j(x0))))) = product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(x0,product(x0,j(x0)))),
inference(transitivity,[status(thm)],[1176,1172]) ).
tff(1178,plain,
quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(one,product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))) = quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))),
inference(monotonicity,[status(thm)],[1177]) ).
tff(1179,plain,
quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))) = quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(one,product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[1178]) ).
tff(1180,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))) = product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1181,plain,
quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))) = product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),
inference(unit_resolution,[status(thm)],[1180,143]) ).
tff(1182,plain,
product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) = quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[1181]) ).
tff(1183,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),one) = product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1184,plain,
product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),one) = product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),
inference(unit_resolution,[status(thm)],[1183,170]) ).
tff(1185,plain,
product(x0,product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),one)) = product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),
inference(monotonicity,[status(thm)],[1184]) ).
tff(1186,plain,
product(x0,product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),one)) = quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(one,product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))),
inference(transitivity,[status(thm)],[1185,1182,1179]) ).
tff(1187,plain,
quotient(product(x0,product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),one)),one) = quotient(quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(one,product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))),one),
inference(monotonicity,[status(thm)],[1186]) ).
tff(1188,plain,
quotient(quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(one,product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))),one) = quotient(product(x0,product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),one)),one),
inference(symmetry,[status(thm)],[1187]) ).
tff(1189,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),one) = product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1190,plain,
product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),one) = product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),
inference(unit_resolution,[status(thm)],[1189,170]) ).
tff(1191,plain,
product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) = product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),one),
inference(symmetry,[status(thm)],[1190]) ).
tff(1192,plain,
quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(one,product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))) = product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),one),
inference(transitivity,[status(thm)],[1178,1181,1191]) ).
tff(1193,plain,
quotient(quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(one,product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))),one) = quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),one),one),
inference(monotonicity,[status(thm)],[1192]) ).
tff(1194,plain,
quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),one),one) = quotient(quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),product(one,product(x0,product(x0,j(x0))))),product(x0,product(x0,j(x0)))),one),
inference(symmetry,[status(thm)],[1193]) ).
tff(1195,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),one),one) = product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1196,plain,
quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),one),one) = product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),
inference(unit_resolution,[status(thm)],[1195,143]) ).
tff(1197,plain,
product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) = quotient(product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),one),one),
inference(symmetry,[status(thm)],[1196]) ).
tff(1198,plain,
product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))) = quotient(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),x0),
inference(transitivity,[status(thm)],[1197,1194,1188,1170,1167,1163,1161,1152]) ).
tff(1199,plain,
product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),x0) = product(quotient(quotient(quotient(product(x1,product(difference(x0,one),x0)),x0),difference(x0,one)),x0),x0),
inference(monotonicity,[status(thm)],[1198]) ).
tff(1200,plain,
product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),x0) = difference(eta(x0),product(difference(x0,one),product(x0,x1))),
inference(transitivity,[status(thm)],[1199,1144,1142,1139]) ).
tff(1201,plain,
product(eta(x0),product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),x0)) = product(eta(x0),difference(eta(x0),product(difference(x0,one),product(x0,x1)))),
inference(monotonicity,[status(thm)],[1200]) ).
tff(1202,plain,
product(eta(x0),product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),x0)) = product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),product(quotient(product(x1,product(j(x0),x0)),x0),x0)),
inference(transitivity,[status(thm)],[1201,1137,1135,1132,1111,1109]) ).
tff(1203,plain,
quotient(product(eta(x0),product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),x0)),x0) = quotient(product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),product(quotient(product(x1,product(j(x0),x0)),x0),x0)),x0),
inference(monotonicity,[status(thm)],[1202]) ).
tff(1204,plain,
quotient(product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),product(quotient(product(x1,product(j(x0),x0)),x0),x0)),x0) = quotient(product(eta(x0),product(product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))),x0)),x0),
inference(symmetry,[status(thm)],[1203]) ).
tff(1205,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0))) = product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1206,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0))) = product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0),
inference(unit_resolution,[status(thm)],[1205,7]) ).
tff(1207,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(x0,x1),difference(x0,one)),difference(x0,one)) = product(x0,x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1208,plain,
quotient(product(product(x0,x1),difference(x0,one)),difference(x0,one)) = product(x0,x1),
inference(unit_resolution,[status(thm)],[1207,143]) ).
tff(1209,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(product(product(x0,x1),difference(x0,one)),one) = product(product(x0,x1),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1210,plain,
product(product(product(x0,x1),difference(x0,one)),one) = product(product(x0,x1),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1209,170]) ).
tff(1211,plain,
product(product(product(x0,x1),difference(x0,one)),product(x0,difference(x0,one))) = product(product(product(x0,x1),difference(x0,one)),one),
inference(monotonicity,[status(thm)],[94]) ).
tff(1212,plain,
product(product(product(x0,x1),difference(x0,one)),product(x0,difference(x0,one))) = product(product(x0,x1),difference(x0,one)),
inference(transitivity,[status(thm)],[1211,1210]) ).
tff(1213,plain,
quotient(product(product(product(x0,x1),difference(x0,one)),product(x0,difference(x0,one))),difference(x0,one)) = quotient(product(product(x0,x1),difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[1212]) ).
tff(1214,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0)) = quotient(product(product(product(x0,x1),difference(x0,one)),product(x0,difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1215,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0)) = quotient(product(product(product(x0,x1),difference(x0,one)),product(x0,difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1214,104]) ).
tff(1216,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0)) = product(x0,x1),
inference(transitivity,[status(thm)],[1215,1213,1208]) ).
tff(1217,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0))) = product(difference(x0,one),product(x0,x1)),
inference(monotonicity,[status(thm)],[1216]) ).
tff(1218,plain,
product(difference(x0,one),product(x0,x1)) = product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0))),
inference(symmetry,[status(thm)],[1217]) ).
tff(1219,plain,
product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1) = product(quotient(product(difference(x0,one),product(x0,x1)),x1),difference(quotient(product(difference(x0,one),product(x0,x1)),x1),product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),x1))),
inference(symmetry,[status(thm)],[1111]) ).
tff(1220,plain,
product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),product(quotient(product(x1,product(j(x0),x0)),x0),x0)) = product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0),
inference(transitivity,[status(thm)],[1108,1219,1131,1134,1218,1206]) ).
tff(1221,plain,
quotient(product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),product(quotient(product(x1,product(j(x0),x0)),x0),x0)),x0) = quotient(product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0),x0),
inference(monotonicity,[status(thm)],[1220]) ).
tff(1222,plain,
quotient(product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0),x0) = quotient(product(product(quotient(product(difference(x0,one),product(x0,x1)),x1),one),product(quotient(product(x1,product(j(x0),x0)),x0),x0)),x0),
inference(symmetry,[status(thm)],[1221]) ).
tff(1223,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0),x0) = product(difference(x0,one),product(product(x0,x1),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1224,plain,
quotient(product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0),x0) = product(difference(x0,one),product(product(x0,x1),difference(x0,one))),
inference(unit_resolution,[status(thm)],[1223,143]) ).
tff(1225,plain,
product(difference(x0,one),product(product(x0,x1),difference(x0,one))) = quotient(product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),x0),x0),
inference(symmetry,[status(thm)],[1224]) ).
tff(1226,plain,
product(difference(x0,one),product(product(x0,x1),difference(x0,one))) = difference(x0,product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))))),
inference(transitivity,[status(thm)],[1225,1222,1204,1101,1098]) ).
tff(1227,plain,
product(x0,product(difference(x0,one),product(product(x0,x1),difference(x0,one)))) = product(x0,difference(x0,product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))))),
inference(monotonicity,[status(thm)],[1226]) ).
tff(1228,plain,
product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(difference(x0,one),product(product(x0,x1),difference(x0,one)))) = product(x0,product(difference(x0,one),product(product(x0,x1),difference(x0,one)))),
inference(monotonicity,[status(thm)],[329]) ).
tff(1229,plain,
product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(difference(x0,one),product(product(x0,x1),difference(x0,one)))) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)))),
inference(transitivity,[status(thm)],[1228,1227,1092]) ).
tff(1230,plain,
difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(difference(x0,one),product(product(x0,x1),difference(x0,one))))) = difference(product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),product(x0,product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0))))),
inference(monotonicity,[status(thm)],[522,1229]) ).
tff(1231,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(difference(x0,one),product(product(x0,x1),difference(x0,one))))) = quotient(product(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1232,plain,
difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(difference(x0,one),product(product(x0,x1),difference(x0,one))))) = quotient(product(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(unit_resolution,[status(thm)],[1231,104]) ).
tff(1233,plain,
quotient(product(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = difference(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),product(product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),product(difference(x0,one),product(product(x0,x1),difference(x0,one))))),
inference(symmetry,[status(thm)],[1232]) ).
tff(1234,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(x0,product(x0,product(x1,eta(x0)))) = product(x1,eta(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1235,plain,
difference(x0,product(x0,product(x1,eta(x0)))) = product(x1,eta(x0)),
inference(unit_resolution,[status(thm)],[1234,26]) ).
tff(1236,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,product(x0,product(x1,eta(x0)))) = product(x0,product(x1,eta(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1237,plain,
product(one,product(x0,product(x1,eta(x0)))) = product(x0,product(x1,eta(x0))),
inference(unit_resolution,[status(thm)],[1236,74]) ).
tff(1238,plain,
quotient(product(x0,product(j(x0),x0)),x0) = one,
inference(transitivity,[status(thm)],[361,364]) ).
tff(1239,plain,
product(quotient(product(x0,product(j(x0),x0)),x0),product(x0,product(x1,eta(x0)))) = product(one,product(x0,product(x1,eta(x0)))),
inference(monotonicity,[status(thm)],[1238]) ).
tff(1240,plain,
product(x0,difference(x0,one)) = quotient(product(x0,product(j(x0),x0)),x0),
inference(transitivity,[status(thm)],[94,365,362]) ).
tff(1241,plain,
product(product(x0,difference(x0,one)),product(x0,product(x1,eta(x0)))) = product(quotient(product(x0,product(j(x0),x0)),x0),product(x0,product(x1,eta(x0)))),
inference(monotonicity,[status(thm)],[1240]) ).
tff(1242,plain,
product(product(x0,difference(x0,one)),product(x0,product(x1,eta(x0)))) = product(x0,product(x1,eta(x0))),
inference(transitivity,[status(thm)],[1241,1239,1237]) ).
tff(1243,plain,
difference(x0,product(product(x0,difference(x0,one)),product(x0,product(x1,eta(x0))))) = difference(x0,product(x0,product(x1,eta(x0)))),
inference(monotonicity,[status(thm)],[1242]) ).
tff(1244,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,difference(x0,one)),product(x0,product(x1,eta(x0))))) = quotient(product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1245,plain,
difference(x0,product(product(x0,difference(x0,one)),product(x0,product(x1,eta(x0))))) = quotient(product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),x0),
inference(unit_resolution,[status(thm)],[1244,104]) ).
tff(1246,plain,
quotient(product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),x0) = difference(x0,product(product(x0,difference(x0,one)),product(x0,product(x1,eta(x0))))),
inference(symmetry,[status(thm)],[1245]) ).
tff(1247,plain,
quotient(product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),x0) = product(x1,eta(x0)),
inference(transitivity,[status(thm)],[1246,1243,1235]) ).
tff(1248,plain,
product(quotient(product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),x0),x0) = product(product(x1,eta(x0)),x0),
inference(monotonicity,[status(thm)],[1247]) ).
tff(1249,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),x0),x0) = product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1250,plain,
product(quotient(product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),x0),x0) = product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),
inference(unit_resolution,[status(thm)],[1249,35]) ).
tff(1251,plain,
product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)) = product(quotient(product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),x0),x0),
inference(symmetry,[status(thm)],[1250]) ).
tff(1252,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(difference(x0,one),product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0))) = product(product(x0,product(x1,eta(x0))),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1253,plain,
difference(difference(x0,one),product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0))) = product(product(x0,product(x1,eta(x0))),x0),
inference(unit_resolution,[status(thm)],[1252,26]) ).
tff(1254,plain,
product(product(x1,eta(x0)),x0) = product(quotient(product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),x0),x0),
inference(symmetry,[status(thm)],[1248]) ).
tff(1255,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,product(product(x1,eta(x0)),x0)) = product(product(x1,eta(x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1256,plain,
product(one,product(product(x1,eta(x0)),x0)) = product(product(x1,eta(x0)),x0),
inference(unit_resolution,[status(thm)],[1255,74]) ).
tff(1257,plain,
product(product(difference(x0,one),i(i(x0))),product(product(x1,eta(x0)),x0)) = product(one,product(product(x1,eta(x0)),x0)),
inference(monotonicity,[status(thm)],[191]) ).
tff(1258,plain,
product(product(difference(x0,one),i(i(x0))),product(product(x1,eta(x0)),x0)) = product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),
inference(transitivity,[status(thm)],[1257,1256,1254,1250]) ).
tff(1259,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(product(x1,eta(x0)),x0))) = difference(difference(x0,one),product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0))),
inference(monotonicity,[status(thm)],[1258]) ).
tff(1260,plain,
product(one,product(product(x1,eta(x0)),x0)) = product(product(difference(x0,one),i(i(x0))),product(product(x1,eta(x0)),x0)),
inference(symmetry,[status(thm)],[1257]) ).
tff(1261,plain,
product(product(x1,eta(x0)),x0) = product(one,product(product(x1,eta(x0)),x0)),
inference(symmetry,[status(thm)],[1256]) ).
tff(1262,plain,
product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)) = product(quotient(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0),x0),
inference(symmetry,[status(thm)],[853]) ).
tff(1263,plain,
product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)) = product(x1,eta(x0)),
inference(transitivity,[status(thm)],[1262,869,872]) ).
tff(1264,plain,
product(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0) = product(product(x1,eta(x0)),x0),
inference(monotonicity,[status(thm)],[1263]) ).
tff(1265,plain,
product(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0) = product(product(difference(x0,one),i(i(x0))),product(product(x1,eta(x0)),x0)),
inference(transitivity,[status(thm)],[1264,1261,1260]) ).
tff(1266,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0)) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(product(x1,eta(x0)),x0))),
inference(monotonicity,[status(thm)],[1265]) ).
tff(1267,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0)) = quotient(product(product(product(product(x0,x1),difference(x0,one)),x0),product(x0,difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1268,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0)) = quotient(product(product(product(product(x0,x1),difference(x0,one)),x0),product(x0,difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1267,104]) ).
tff(1269,plain,
quotient(product(product(product(product(x0,x1),difference(x0,one)),x0),product(x0,difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0)),
inference(symmetry,[status(thm)],[1268]) ).
tff(1270,plain,
product(product(product(product(x0,x1),difference(x0,one)),x0),product(x0,difference(x0,one))) = product(product(product(product(x0,x1),difference(x0,one)),x0),one),
inference(monotonicity,[status(thm)],[94]) ).
tff(1271,plain,
product(product(product(product(x0,x1),difference(x0,one)),x0),one) = product(product(product(product(x0,x1),difference(x0,one)),x0),product(x0,difference(x0,one))),
inference(symmetry,[status(thm)],[1270]) ).
tff(1272,plain,
product(product(product(x0,x1),difference(x0,one)),product(x0,one)) = product(product(product(x0,x1),difference(x0,one)),x0),
inference(monotonicity,[status(thm)],[172]) ).
tff(1273,plain,
product(product(product(x0,x1),difference(x0,one)),x0) = product(product(product(x0,x1),difference(x0,one)),product(x0,one)),
inference(symmetry,[status(thm)],[1272]) ).
tff(1274,plain,
difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),x0)) = difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),product(x0,one))),
inference(monotonicity,[status(thm)],[1273]) ).
tff(1275,plain,
difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),product(x0,one))) = difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),
inference(symmetry,[status(thm)],[1274]) ).
tff(1276,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),product(x0,one))) = quotient(quotient(product(one,product(product(product(x0,x1),difference(x0,one)),x0)),x0),product(product(x0,x1),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1277,plain,
difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),product(x0,one))) = quotient(quotient(product(one,product(product(product(x0,x1),difference(x0,one)),x0)),x0),product(product(x0,x1),difference(x0,one))),
inference(unit_resolution,[status(thm)],[1276,16]) ).
tff(1278,plain,
quotient(quotient(product(one,product(product(product(x0,x1),difference(x0,one)),x0)),x0),product(product(x0,x1),difference(x0,one))) = difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),product(x0,one))),
inference(symmetry,[status(thm)],[1277]) ).
tff(1279,plain,
product(product(x0,x1),difference(x0,one)) = product(one,product(product(x0,x1),difference(x0,one))),
inference(symmetry,[status(thm)],[861]) ).
tff(1280,plain,
product(product(x0,one),product(product(x0,x1),difference(x0,one))) = product(x0,product(product(x0,x1),difference(x0,one))),
inference(monotonicity,[status(thm)],[172]) ).
tff(1281,plain,
difference(x0,product(product(x0,one),product(product(x0,x1),difference(x0,one)))) = difference(x0,product(x0,product(product(x0,x1),difference(x0,one)))),
inference(monotonicity,[status(thm)],[1280]) ).
tff(1282,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,one),product(product(x0,x1),difference(x0,one)))) = quotient(product(one,product(product(product(x0,x1),difference(x0,one)),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1283,plain,
difference(x0,product(product(x0,one),product(product(x0,x1),difference(x0,one)))) = quotient(product(one,product(product(product(x0,x1),difference(x0,one)),x0)),x0),
inference(unit_resolution,[status(thm)],[1282,104]) ).
tff(1284,plain,
quotient(product(one,product(product(product(x0,x1),difference(x0,one)),x0)),x0) = difference(x0,product(product(x0,one),product(product(x0,x1),difference(x0,one)))),
inference(symmetry,[status(thm)],[1283]) ).
tff(1285,plain,
quotient(product(one,product(product(product(x0,x1),difference(x0,one)),x0)),x0) = product(one,product(product(x0,x1),difference(x0,one))),
inference(transitivity,[status(thm)],[1284,1281,886,1279]) ).
tff(1286,plain,
quotient(quotient(product(one,product(product(product(x0,x1),difference(x0,one)),x0)),x0),product(product(x0,x1),difference(x0,one))) = quotient(product(one,product(product(x0,x1),difference(x0,one))),product(product(x0,x1),difference(x0,one))),
inference(monotonicity,[status(thm)],[1285]) ).
tff(1287,plain,
quotient(product(one,product(product(x0,x1),difference(x0,one))),product(product(x0,x1),difference(x0,one))) = quotient(quotient(product(one,product(product(product(x0,x1),difference(x0,one)),x0)),x0),product(product(x0,x1),difference(x0,one))),
inference(symmetry,[status(thm)],[1286]) ).
tff(1288,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(one,product(product(x0,x1),difference(x0,one))),product(product(x0,x1),difference(x0,one))) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1289,plain,
quotient(product(one,product(product(x0,x1),difference(x0,one))),product(product(x0,x1),difference(x0,one))) = one,
inference(unit_resolution,[status(thm)],[1288,143]) ).
tff(1290,plain,
one = quotient(product(one,product(product(x0,x1),difference(x0,one))),product(product(x0,x1),difference(x0,one))),
inference(symmetry,[status(thm)],[1289]) ).
tff(1291,plain,
one = difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),x0)),
inference(transitivity,[status(thm)],[1290,1287,1278,1275]) ).
tff(1292,plain,
product(product(product(product(x0,x1),difference(x0,one)),x0),one) = product(product(product(product(x0,x1),difference(x0,one)),x0),difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),x0))),
inference(monotonicity,[status(thm)],[1291]) ).
tff(1293,plain,
product(product(product(product(x0,x1),difference(x0,one)),x0),difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),x0))) = product(product(product(product(x0,x1),difference(x0,one)),x0),one),
inference(symmetry,[status(thm)],[1292]) ).
tff(1294,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(product(product(product(x0,x1),difference(x0,one)),x0),difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),x0))) = product(product(product(x0,x1),difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1295,plain,
product(product(product(product(x0,x1),difference(x0,one)),x0),difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),x0))) = product(product(product(x0,x1),difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[1294,7]) ).
tff(1296,plain,
product(product(product(x0,x1),difference(x0,one)),x0) = product(product(product(product(x0,x1),difference(x0,one)),x0),difference(product(product(product(x0,x1),difference(x0,one)),x0),product(product(product(x0,x1),difference(x0,one)),x0))),
inference(symmetry,[status(thm)],[1295]) ).
tff(1297,plain,
product(product(product(x0,x1),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = product(product(product(x0,x1),difference(x0,one)),x0),
inference(monotonicity,[status(thm)],[329]) ).
tff(1298,plain,
product(product(product(x0,x1),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = product(product(product(product(x0,x1),difference(x0,one)),x0),product(x0,difference(x0,one))),
inference(transitivity,[status(thm)],[1297,1296,1293,1271]) ).
tff(1299,plain,
quotient(product(product(product(x0,x1),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) = quotient(product(product(product(product(x0,x1),difference(x0,one)),x0),product(x0,difference(x0,one))),difference(x0,one)),
inference(monotonicity,[status(thm)],[1298]) ).
tff(1300,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(product(product(x0,x1),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1301,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(product(product(x0,x1),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1300,104]) ).
tff(1302,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(product(x0,product(x1,eta(x0))),x0),
inference(transitivity,[status(thm)],[1301,1299,1269,1266,1259,1253]) ).
tff(1303,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0)),
inference(monotonicity,[status(thm)],[1302]) ).
tff(1304,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1305,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(unit_resolution,[status(thm)],[1304,7]) ).
tff(1306,plain,
product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))),
inference(symmetry,[status(thm)],[1305]) ).
tff(1307,plain,
product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(product(x1,eta(x0)),x0),
inference(transitivity,[status(thm)],[1306,1303,1251,1248]) ).
tff(1308,plain,
product(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(difference(x0,one),product(product(x1,eta(x0)),x0)),
inference(monotonicity,[status(thm)],[1307]) ).
tff(1309,plain,
product(difference(x0,one),product(product(x1,eta(x0)),x0)) = product(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),
inference(symmetry,[status(thm)],[1308]) ).
tff(1310,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(difference(x0,one),product(product(x1,eta(x0)),x0)),x0),x0) = product(difference(x0,one),product(product(x1,eta(x0)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1311,plain,
product(quotient(product(difference(x0,one),product(product(x1,eta(x0)),x0)),x0),x0) = product(difference(x0,one),product(product(x1,eta(x0)),x0)),
inference(unit_resolution,[status(thm)],[1310,35]) ).
tff(1312,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,difference(x0,one)),product(x1,eta(x0)))) = quotient(product(difference(x0,one),product(product(x1,eta(x0)),x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1313,plain,
difference(x0,product(product(x0,difference(x0,one)),product(x1,eta(x0)))) = quotient(product(difference(x0,one),product(product(x1,eta(x0)),x0)),x0),
inference(unit_resolution,[status(thm)],[1312,104]) ).
tff(1314,plain,
product(product(x0,difference(x0,one)),product(x1,eta(x0))) = product(one,product(x1,eta(x0))),
inference(monotonicity,[status(thm)],[94]) ).
tff(1315,plain,
product(one,product(x1,eta(x0))) = product(product(x0,difference(x0,one)),product(x1,eta(x0))),
inference(symmetry,[status(thm)],[1314]) ).
tff(1316,plain,
product(x1,eta(x0)) = product(one,product(x1,eta(x0))),
inference(symmetry,[status(thm)],[875]) ).
tff(1317,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(x1,eta(x0)),j(x0)),j(x0)) = product(x1,eta(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1318,plain,
product(quotient(product(x1,eta(x0)),j(x0)),j(x0)) = product(x1,eta(x0)),
inference(unit_resolution,[status(thm)],[1317,35]) ).
tff(1319,plain,
product(x1,product(x0,j(x0))) = product(x1,eta(x0)),
inference(monotonicity,[status(thm)],[832]) ).
tff(1320,plain,
product(x1,eta(x0)) = product(x1,product(x0,j(x0))),
inference(symmetry,[status(thm)],[1319]) ).
tff(1321,plain,
quotient(product(x1,eta(x0)),j(x0)) = quotient(product(x1,product(x0,j(x0))),j(x0)),
inference(monotonicity,[status(thm)],[1320]) ).
tff(1322,plain,
quotient(product(x1,product(x0,j(x0))),j(x0)) = quotient(product(x1,eta(x0)),j(x0)),
inference(symmetry,[status(thm)],[1321]) ).
tff(1323,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(j(x0),product(product(j(x0),x1),x0)) = quotient(product(x1,product(x0,j(x0))),j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1324,plain,
difference(j(x0),product(product(j(x0),x1),x0)) = quotient(product(x1,product(x0,j(x0))),j(x0)),
inference(unit_resolution,[status(thm)],[1323,104]) ).
tff(1325,plain,
( ~ ! [A: $i] : ( product(one,A) = A )
| ( product(one,product(product(j(x0),x1),x0)) = product(product(j(x0),x1),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1326,plain,
product(one,product(product(j(x0),x1),x0)) = product(product(j(x0),x1),x0),
inference(unit_resolution,[status(thm)],[1325,74]) ).
tff(1327,plain,
product(product(j(x0),x0),product(product(j(x0),x1),x0)) = product(one,product(product(j(x0),x1),x0)),
inference(monotonicity,[status(thm)],[199]) ).
tff(1328,plain,
product(product(j(x0),x0),product(product(j(x0),x1),x0)) = product(product(j(x0),x1),x0),
inference(transitivity,[status(thm)],[1327,1326]) ).
tff(1329,plain,
difference(j(x0),product(product(j(x0),x0),product(product(j(x0),x1),x0))) = difference(j(x0),product(product(j(x0),x1),x0)),
inference(monotonicity,[status(thm)],[1328]) ).
tff(1330,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(j(x0),product(product(j(x0),x0),product(product(j(x0),x1),x0))) = quotient(product(x0,product(product(product(j(x0),x1),x0),j(x0))),j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1331,plain,
difference(j(x0),product(product(j(x0),x0),product(product(j(x0),x1),x0))) = quotient(product(x0,product(product(product(j(x0),x1),x0),j(x0))),j(x0)),
inference(unit_resolution,[status(thm)],[1330,104]) ).
tff(1332,plain,
quotient(product(x0,product(product(product(j(x0),x1),x0),j(x0))),j(x0)) = difference(j(x0),product(product(j(x0),x0),product(product(j(x0),x1),x0))),
inference(symmetry,[status(thm)],[1331]) ).
tff(1333,plain,
quotient(product(x0,product(product(product(j(x0),x1),x0),j(x0))),j(x0)) = quotient(product(x1,eta(x0)),j(x0)),
inference(transitivity,[status(thm)],[1332,1329,1324,1322]) ).
tff(1334,plain,
product(quotient(product(x0,product(product(product(j(x0),x1),x0),j(x0))),j(x0)),j(x0)) = product(quotient(product(x1,eta(x0)),j(x0)),j(x0)),
inference(monotonicity,[status(thm)],[1333]) ).
tff(1335,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(x0,product(product(product(j(x0),x1),x0),j(x0))),j(x0)),j(x0)) = product(x0,product(product(product(j(x0),x1),x0),j(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1336,plain,
product(quotient(product(x0,product(product(product(j(x0),x1),x0),j(x0))),j(x0)),j(x0)) = product(x0,product(product(product(j(x0),x1),x0),j(x0))),
inference(unit_resolution,[status(thm)],[1335,35]) ).
tff(1337,plain,
product(x0,product(product(product(j(x0),x1),x0),j(x0))) = product(quotient(product(x0,product(product(product(j(x0),x1),x0),j(x0))),j(x0)),j(x0)),
inference(symmetry,[status(thm)],[1336]) ).
tff(1338,plain,
product(x0,product(product(product(j(x0),x1),x0),j(x0))) = product(product(x0,difference(x0,one)),product(x1,eta(x0))),
inference(transitivity,[status(thm)],[1337,1334,1318,1316,1315]) ).
tff(1339,plain,
difference(x0,product(x0,product(product(product(j(x0),x1),x0),j(x0)))) = difference(x0,product(product(x0,difference(x0,one)),product(x1,eta(x0)))),
inference(monotonicity,[status(thm)],[1338]) ).
tff(1340,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(x0,product(x0,product(product(product(j(x0),x1),x0),j(x0)))) = product(product(product(j(x0),x1),x0),j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1341,plain,
difference(x0,product(x0,product(product(product(j(x0),x1),x0),j(x0)))) = product(product(product(j(x0),x1),x0),j(x0)),
inference(unit_resolution,[status(thm)],[1340,26]) ).
tff(1342,plain,
product(product(product(j(x0),x1),x0),j(x0)) = difference(x0,product(x0,product(product(product(j(x0),x1),x0),j(x0)))),
inference(symmetry,[status(thm)],[1341]) ).
tff(1343,plain,
product(product(product(j(x0),x1),x0),j(x0)) = quotient(product(difference(x0,one),product(product(x1,eta(x0)),x0)),x0),
inference(transitivity,[status(thm)],[1342,1339,1313]) ).
tff(1344,plain,
product(product(product(product(j(x0),x1),x0),j(x0)),x0) = product(quotient(product(difference(x0,one),product(product(x1,eta(x0)),x0)),x0),x0),
inference(monotonicity,[status(thm)],[1343]) ).
tff(1345,plain,
product(j(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = x0,
inference(transitivity,[status(thm)],[782,551,608,216,213,200,198]) ).
tff(1346,plain,
product(product(product(product(j(x0),x1),x0),j(x0)),product(j(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(product(product(product(j(x0),x1),x0),j(x0)),x0),
inference(monotonicity,[status(thm)],[1345]) ).
tff(1347,plain,
product(product(product(product(j(x0),x1),x0),j(x0)),product(j(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),
inference(transitivity,[status(thm)],[1346,1344,1311,1309]) ).
tff(1348,plain,
quotient(product(product(product(product(j(x0),x1),x0),j(x0)),product(j(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = quotient(product(difference(x0,one),product(product(difference(x0,one),product(product(x0,x1),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(monotonicity,[status(thm)],[1347]) ).
tff(1349,plain,
product(product(product(product(j(x0),x1),x0),j(x0)),x0) = product(product(product(product(j(x0),x1),x0),j(x0)),product(j(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),
inference(symmetry,[status(thm)],[1346]) ).
tff(1350,plain,
product(quotient(product(difference(x0,one),product(product(x1,eta(x0)),x0)),x0),x0) = product(product(product(product(j(x0),x1),x0),j(x0)),x0),
inference(symmetry,[status(thm)],[1344]) ).
tff(1351,plain,
product(difference(x0,one),product(product(x1,eta(x0)),x0)) = product(quotient(product(difference(x0,one),product(product(x1,eta(x0)),x0)),x0),x0),
inference(symmetry,[status(thm)],[1311]) ).
tff(1352,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(product(x1,eta(x0)),x0),difference(x0,one)),difference(x0,one)) = product(product(x1,eta(x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1353,plain,
quotient(product(product(product(x1,eta(x0)),x0),difference(x0,one)),difference(x0,one)) = product(product(x1,eta(x0)),x0),
inference(unit_resolution,[status(thm)],[1352,143]) ).
tff(1354,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(i(i(x0)),product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one)))) = product(product(product(x1,eta(x0)),x0),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1355,plain,
difference(i(i(x0)),product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one)))) = product(product(product(x1,eta(x0)),x0),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1354,26]) ).
tff(1356,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0),x0),x0) = quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1357,plain,
product(quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0),x0),x0) = quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0),
inference(unit_resolution,[status(thm)],[1356,35]) ).
tff(1358,plain,
quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0) = product(quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0),x0),x0),
inference(symmetry,[status(thm)],[1357]) ).
tff(1359,plain,
quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),i(i(x0)))),
inference(symmetry,[status(thm)],[932]) ).
tff(1360,plain,
product(i(i(x0)),difference(x0,one)) = product(difference(x0,one),x0),
inference(transitivity,[status(thm)],[313,316,325,91]) ).
tff(1361,plain,
product(i(i(x0)),product(i(i(x0)),difference(x0,one))) = product(i(i(x0)),product(difference(x0,one),x0)),
inference(monotonicity,[status(thm)],[1360]) ).
tff(1362,plain,
product(i(i(x0)),product(difference(x0,one),x0)) = product(i(i(x0)),product(i(i(x0)),difference(x0,one))),
inference(symmetry,[status(thm)],[1361]) ).
tff(1363,plain,
quotient(product(i(i(x0)),product(difference(x0,one),x0)),difference(x0,one)) = quotient(product(i(i(x0)),product(i(i(x0)),difference(x0,one))),difference(x0,one)),
inference(monotonicity,[status(thm)],[1362]) ).
tff(1364,plain,
quotient(product(i(i(x0)),product(difference(x0,one),x0)),difference(x0,one)) = quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),
inference(transitivity,[status(thm)],[1363,1359,935,113]) ).
tff(1365,plain,
product(quotient(product(i(i(x0)),product(difference(x0,one),x0)),difference(x0,one)),difference(x0,one)) = product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[1364]) ).
tff(1366,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(i(i(x0)),product(difference(x0,one),x0)),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(difference(x0,one),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1367,plain,
product(quotient(product(i(i(x0)),product(difference(x0,one),x0)),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(difference(x0,one),x0)),
inference(unit_resolution,[status(thm)],[1366,35]) ).
tff(1368,plain,
product(i(i(x0)),product(difference(x0,one),x0)) = product(quotient(product(i(i(x0)),product(difference(x0,one),x0)),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[1367]) ).
tff(1369,plain,
product(i(i(x0)),eta(x0)) = product(i(i(x0)),product(difference(x0,one),x0)),
inference(monotonicity,[status(thm)],[92]) ).
tff(1370,plain,
product(i(i(x0)),eta(x0)) = x0,
inference(transitivity,[status(thm)],[1369,1368,1365,328,162,172]) ).
tff(1371,plain,
product(product(i(i(x0)),eta(x0)),quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0)) = product(x0,product(quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0),x0),x0)),
inference(monotonicity,[status(thm)],[1370,1358]) ).
tff(1372,plain,
product(x0,product(quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0),x0),x0)) = product(product(i(i(x0)),eta(x0)),quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0)),
inference(symmetry,[status(thm)],[1371]) ).
tff(1373,plain,
product(x0,quotient(product(x1,product(difference(x0,one),x0)),x0)) = product(x0,difference(x0,product(product(x0,x1),difference(x0,one)))),
inference(monotonicity,[status(thm)],[1055]) ).
tff(1374,plain,
product(x0,quotient(product(x1,product(difference(x0,one),x0)),x0)) = product(product(x0,x1),difference(x0,one)),
inference(transitivity,[status(thm)],[1373,1054]) ).
tff(1375,plain,
product(product(x0,quotient(product(x1,product(difference(x0,one),x0)),x0)),x0) = product(product(product(x0,x1),difference(x0,one)),x0),
inference(monotonicity,[status(thm)],[1374]) ).
tff(1376,plain,
product(product(product(x0,x1),difference(x0,one)),x0) = product(product(x0,quotient(product(x1,product(difference(x0,one),x0)),x0)),x0),
inference(symmetry,[status(thm)],[1375]) ).
tff(1377,plain,
difference(x0,product(product(product(x0,x1),difference(x0,one)),x0)) = difference(x0,product(product(x0,quotient(product(x1,product(difference(x0,one),x0)),x0)),x0)),
inference(monotonicity,[status(thm)],[1376]) ).
tff(1378,plain,
difference(x0,product(product(x0,quotient(product(x1,product(difference(x0,one),x0)),x0)),x0)) = difference(x0,product(product(product(x0,x1),difference(x0,one)),x0)),
inference(symmetry,[status(thm)],[1377]) ).
tff(1379,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,quotient(product(x1,product(difference(x0,one),x0)),x0)),x0)) = quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1380,plain,
difference(x0,product(product(x0,quotient(product(x1,product(difference(x0,one),x0)),x0)),x0)) = quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0),
inference(unit_resolution,[status(thm)],[1379,104]) ).
tff(1381,plain,
quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0) = difference(x0,product(product(x0,quotient(product(x1,product(difference(x0,one),x0)),x0)),x0)),
inference(symmetry,[status(thm)],[1380]) ).
tff(1382,plain,
product(quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0),x0),x0) = difference(x0,product(product(product(x0,x1),difference(x0,one)),x0)),
inference(transitivity,[status(thm)],[1357,1381,1378]) ).
tff(1383,plain,
product(x0,product(quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0),x0),x0)) = product(x0,difference(x0,product(product(product(x0,x1),difference(x0,one)),x0))),
inference(monotonicity,[status(thm)],[1382]) ).
tff(1384,plain,
product(x0,difference(x0,product(product(product(x0,x1),difference(x0,one)),x0))) = product(x0,product(quotient(quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0),x0),x0)),
inference(symmetry,[status(thm)],[1383]) ).
tff(1385,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(x0,difference(x0,product(product(product(x0,x1),difference(x0,one)),x0))) = product(product(product(x0,x1),difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1386,plain,
product(x0,difference(x0,product(product(product(x0,x1),difference(x0,one)),x0))) = product(product(product(x0,x1),difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[1385,7]) ).
tff(1387,plain,
product(product(product(x0,x1),difference(x0,one)),x0) = product(x0,difference(x0,product(product(product(x0,x1),difference(x0,one)),x0))),
inference(symmetry,[status(thm)],[1386]) ).
tff(1388,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),difference(x0,one)) = product(product(product(x0,x1),difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1389,plain,
product(quotient(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),difference(x0,one)) = product(product(product(x0,x1),difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[1388,35]) ).
tff(1390,plain,
product(product(product(x0,x1),difference(x0,one)),x0) = product(product(product(x0,x1),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),
inference(symmetry,[status(thm)],[1297]) ).
tff(1391,plain,
quotient(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)) = quotient(product(product(product(x0,x1),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(monotonicity,[status(thm)],[1390]) ).
tff(1392,plain,
quotient(product(product(product(x0,x1),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) = quotient(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),
inference(symmetry,[status(thm)],[1391]) ).
tff(1393,plain,
quotient(product(product(product(product(x0,x1),difference(x0,one)),x0),product(x0,difference(x0,one))),difference(x0,one)) = quotient(product(product(product(x0,x1),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(symmetry,[status(thm)],[1299]) ).
tff(1394,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(product(x1,eta(x0)),x0))) = difference(difference(x0,one),product(product(difference(x0,one),product(product(product(x0,x1),difference(x0,one)),x0)),x0)),
inference(symmetry,[status(thm)],[1266]) ).
tff(1395,plain,
difference(difference(x0,one),product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0))) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(product(x1,eta(x0)),x0))),
inference(symmetry,[status(thm)],[1259]) ).
tff(1396,plain,
product(product(x0,product(x1,eta(x0))),x0) = difference(difference(x0,one),product(difference(x0,one),product(product(x0,product(x1,eta(x0))),x0))),
inference(symmetry,[status(thm)],[1253]) ).
tff(1397,plain,
product(product(x0,product(x1,eta(x0))),x0) = quotient(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),
inference(transitivity,[status(thm)],[1396,1395,1394,1268,1393,1392]) ).
tff(1398,plain,
product(product(product(x0,product(x1,eta(x0))),x0),difference(x0,one)) = product(quotient(product(product(product(x0,x1),difference(x0,one)),x0),difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[1397]) ).
tff(1399,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(product(x1,eta(x0)),x0))) = quotient(product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1400,plain,
difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(product(x1,eta(x0)),x0))) = quotient(product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1399,104]) ).
tff(1401,plain,
quotient(product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),i(i(x0))),product(product(x1,eta(x0)),x0))),
inference(symmetry,[status(thm)],[1400]) ).
tff(1402,plain,
quotient(product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))),difference(x0,one)) = product(product(x0,product(x1,eta(x0))),x0),
inference(transitivity,[status(thm)],[1401,1259,1253]) ).
tff(1403,plain,
product(quotient(product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(product(product(x0,product(x1,eta(x0))),x0),difference(x0,one)),
inference(monotonicity,[status(thm)],[1402]) ).
tff(1404,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1405,plain,
product(quotient(product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))),difference(x0,one)),difference(x0,one)) = product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))),
inference(unit_resolution,[status(thm)],[1404,35]) ).
tff(1406,plain,
product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))) = product(quotient(product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[1405]) ).
tff(1407,plain,
product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one))) = product(product(i(i(x0)),eta(x0)),quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0)),
inference(transitivity,[status(thm)],[1406,1403,1398,1389,1387,1384,1372]) ).
tff(1408,plain,
difference(i(i(x0)),product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one)))) = difference(i(i(x0)),product(product(i(i(x0)),eta(x0)),quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0))),
inference(monotonicity,[status(thm)],[1407]) ).
tff(1409,plain,
difference(i(i(x0)),product(product(i(i(x0)),eta(x0)),quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0))) = difference(i(i(x0)),product(i(i(x0)),product(product(product(x1,eta(x0)),x0),difference(x0,one)))),
inference(symmetry,[status(thm)],[1408]) ).
tff(1410,plain,
product(product(product(x0,x1),difference(x0,one)),x0) = product(quotient(product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),x0),x0),
inference(symmetry,[status(thm)],[953]) ).
tff(1411,plain,
product(product(i(i(x0)),eta(x0)),quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0)) = product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0)),
inference(transitivity,[status(thm)],[1371,1383,1386,1410,955]) ).
tff(1412,plain,
difference(i(i(x0)),product(product(i(i(x0)),eta(x0)),quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0))) = difference(i(i(x0)),product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0))),
inference(monotonicity,[status(thm)],[1411]) ).
tff(1413,plain,
difference(i(i(x0)),product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0))) = difference(i(i(x0)),product(product(i(i(x0)),eta(x0)),quotient(product(quotient(product(x1,product(difference(x0,one),x0)),x0),product(x0,x0)),x0))),
inference(symmetry,[status(thm)],[1412]) ).
tff(1414,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(i(i(x0)),product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0))) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1415,plain,
difference(i(i(x0)),product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0))) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),
inference(unit_resolution,[status(thm)],[1414,26]) ).
tff(1416,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0) = difference(i(i(x0)),product(i(i(x0)),product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0))),
inference(symmetry,[status(thm)],[1415]) ).
tff(1417,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),x0),
inference(monotonicity,[status(thm)],[329]) ).
tff(1418,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))) = product(product(product(x1,eta(x0)),x0),difference(x0,one)),
inference(transitivity,[status(thm)],[1417,1416,1413,1409,1355]) ).
tff(1419,plain,
quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) = quotient(product(product(product(x1,eta(x0)),x0),difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[1418]) ).
tff(1420,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1421,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1420,104]) ).
tff(1422,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))) = product(product(x1,eta(x0)),x0),
inference(transitivity,[status(thm)],[1421,1419,1353]) ).
tff(1423,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(difference(x0,one),product(product(x1,eta(x0)),x0)),
inference(monotonicity,[status(thm)],[1422]) ).
tff(1424,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1425,plain,
product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))) = product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(unit_resolution,[status(thm)],[1424,7]) ).
tff(1426,plain,
product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(difference(x0,one),difference(difference(x0,one),product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))))),
inference(symmetry,[status(thm)],[1425]) ).
tff(1427,plain,
product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(product(product(product(j(x0),x1),x0),j(x0)),product(j(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),
inference(transitivity,[status(thm)],[1426,1423,1351,1350,1349]) ).
tff(1428,plain,
quotient(product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = quotient(product(product(product(product(j(x0),x1),x0),j(x0)),product(j(x0),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(monotonicity,[status(thm)],[1427]) ).
tff(1429,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1430,plain,
quotient(product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))) = product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),
inference(unit_resolution,[status(thm)],[1429,143]) ).
tff(1431,plain,
product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = quotient(product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one))),
inference(symmetry,[status(thm)],[1430]) ).
tff(1432,plain,
product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))) = quotient(quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),product(x0,product(x0,j(x0)))),
inference(transitivity,[status(thm)],[1431,1428,1348,1233,1230,1090,1088]) ).
tff(1433,plain,
product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),product(x0,product(x0,j(x0)))) = product(quotient(quotient(product(product(difference(x0,one),quotient(product(x1,product(difference(x0,one),x0)),x0)),product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),x0)),x0),product(x0,product(x0,j(x0)))),product(x0,product(x0,j(x0)))),
inference(monotonicity,[status(thm)],[1432]) ).
tff(1434,plain,
product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),product(x0,product(x0,j(x0)))) = product(difference(x0,one),product(x1,eta(x0))),
inference(transitivity,[status(thm)],[1433,1086,1084,1029]) ).
tff(1435,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),product(x0,product(x0,j(x0))))) = difference(difference(x0,one),product(difference(x0,one),product(x1,eta(x0)))),
inference(monotonicity,[status(thm)],[1434]) ).
tff(1436,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(difference(x0,one),product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),product(x0,product(x0,j(x0))))) = quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(product(x0,product(x0,j(x0))),difference(x0,one))),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1437,plain,
difference(difference(x0,one),product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),product(x0,product(x0,j(x0))))) = quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(product(x0,product(x0,j(x0))),difference(x0,one))),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1436,104]) ).
tff(1438,plain,
quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(product(x0,product(x0,j(x0))),difference(x0,one))),difference(x0,one)) = difference(difference(x0,one),product(product(difference(x0,one),product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one))),product(x0,product(x0,j(x0))))),
inference(symmetry,[status(thm)],[1437]) ).
tff(1439,plain,
product(product(x0,product(x0,j(x0))),difference(x0,one)) = product(quotient(quotient(product(x0,product(x0,difference(x0,one))),difference(x0,one)),x0),difference(x0,one)),
inference(monotonicity,[status(thm)],[305]) ).
tff(1440,plain,
product(product(x0,product(x0,j(x0))),difference(x0,one)) = quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))),
inference(transitivity,[status(thm)],[1439,663,666]) ).
tff(1441,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(product(x0,product(x0,j(x0))),difference(x0,one))) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(monotonicity,[status(thm)],[1440]) ).
tff(1442,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(product(x0,product(x0,j(x0))),difference(x0,one))),
inference(symmetry,[status(thm)],[1441]) ).
tff(1443,plain,
quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),difference(x0,one)) = quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),product(product(x0,product(x0,j(x0))),difference(x0,one))),difference(x0,one)),
inference(monotonicity,[status(thm)],[1442]) ).
tff(1444,plain,
quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),difference(x0,one)) = product(x1,eta(x0)),
inference(transitivity,[status(thm)],[1443,1438,1435,1027]) ).
tff(1445,plain,
product(quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),difference(x0,one)),difference(x0,one)) = product(product(x1,eta(x0)),difference(x0,one)),
inference(monotonicity,[status(thm)],[1444]) ).
tff(1446,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),difference(x0,one)),difference(x0,one)) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1447,plain,
product(quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),difference(x0,one)),difference(x0,one)) = product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(unit_resolution,[status(thm)],[1446,35]) ).
tff(1448,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = product(quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[1447]) ).
tff(1449,plain,
product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = product(product(product(x1,eta(x0)),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),
inference(transitivity,[status(thm)],[1448,1445,1025,1024]) ).
tff(1450,plain,
quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = quotient(product(product(product(x1,eta(x0)),difference(x0,one)),product(eta(x0),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0))))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(monotonicity,[status(thm)],[1449]) ).
tff(1451,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1452,plain,
quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))) = product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),
inference(unit_resolution,[status(thm)],[1451,143]) ).
tff(1453,plain,
product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)) = quotient(product(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),quotient(product(x0,product(difference(x0,one),i(i(x0)))),i(i(x0)))),
inference(symmetry,[status(thm)],[1452]) ).
tff(1454,plain,
product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)) = product(x1,difference(x0,one)),
inference(transitivity,[status(thm)],[1453,1450,1023,1015,1012,147]) ).
tff(1455,plain,
quotient(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),difference(x0,one)) = quotient(product(x1,difference(x0,one)),difference(x0,one)),
inference(monotonicity,[status(thm)],[1454]) ).
tff(1456,plain,
quotient(product(x1,difference(x0,one)),difference(x0,one)) = quotient(product(quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[1455]) ).
tff(1457,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(x1,difference(x0,one)),difference(x0,one)) = x1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1458,plain,
quotient(product(x1,difference(x0,one)),difference(x0,one)) = x1,
inference(unit_resolution,[status(thm)],[1457,143]) ).
tff(1459,plain,
x1 = quotient(product(x1,difference(x0,one)),difference(x0,one)),
inference(symmetry,[status(thm)],[1458]) ).
tff(1460,plain,
x1 = quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0)),
inference(transitivity,[status(thm)],[1459,1456,145]) ).
tff(1461,plain,
product(i(i(x0)),x1) = product(i(i(x0)),quotient(quotient(product(x1,product(eta(x0),x0)),x0),eta(x0))),
inference(monotonicity,[status(thm)],[1460]) ).
tff(1462,plain,
product(i(i(x0)),x1) = product(eta(x0),product(x0,x1)),
inference(transitivity,[status(thm)],[1461,136,9]) ).
tff(1463,plain,
( ( product(i(i(x0)),x1) != product(eta(x0),product(x0,x1)) )
<=> ( product(i(i(x0)),x1) != product(eta(x0),product(x0,x1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1464,axiom,
product(i(i(x0)),x1) != product(eta(x0),product(x0,x1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(1465,plain,
product(i(i(x0)),x1) != product(eta(x0),product(x0,x1)),
inference(modus_ponens,[status(thm)],[1464,1463]) ).
tff(1466,plain,
$false,
inference(unit_resolution,[status(thm)],[1465,1462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP765-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 20:53:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 130.05/83.38 % SZS status Unsatisfiable
% 130.05/83.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------