TSTP Solution File: TOP053-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP053-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 30 01:56:08 EDT 2022
% Result : Unsatisfiable 1.22s 1.00s
% Output : Proof 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 176
% Syntax : Number of formulae : 1029 ( 861 unt; 17 typ; 0 def)
% Number of atoms : 1169 (1165 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 295 ( 141 ~; 131 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 18 ( 3 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 16 ( 2 >; 14 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 15 con; 0-14 aty)
% Number of variables : 399 ( 393 !; 0 ?; 399 :)
% Comments :
%------------------------------------------------------------------------------
tff(tuple_type,type,
tuple: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(product_type,type,
product: ( $i * $i ) > $i ).
tff(a3_type,type,
a3: $i ).
tff(a6_type,type,
a6: $i ).
tff(a4_type,type,
a4: $i ).
tff(a1_type,type,
a1: $i ).
tff(a11_type,type,
a11: $i ).
tff(a2_type,type,
a2: $i ).
tff(a8_type,type,
a8: $i ).
tff(a13_type,type,
a13: $i ).
tff(a15_type,type,
a15: $i ).
tff(a10_type,type,
a10: $i ).
tff(a14_type,type,
a14: $i ).
tff(a12_type,type,
a12: $i ).
tff(a9_type,type,
a9: $i ).
tff(a7_type,type,
a7: $i ).
tff(a5_type,type,
a5: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
<=> ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_02) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( ( product(X,X) = X )
<=> ( product(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : ( product(X,X) = X )
<=> ! [X: $i] : ( product(X,X) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( product(X,X) = X )
<=> ! [X: $i] : ( product(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : ( product(X,X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle) ).
tff(14,plain,
! [X: $i] : ( product(X,X) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( product(X,X) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( product(X,X) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(a3,product(product(a3,a4),a6)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(a3,product(product(a3,a4),a6)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
product(a3,product(product(a3,a4),a6)) = product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(product(a3,a4),a6),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(product(a3,a4),a6),a3)),
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),a3),product(product(product(a3,a4),a6),a3)) = a6 )
<=> ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(product(a3,a4),a6),a3)) = a6 ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( product(a13,a8) = a6 )
<=> ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),a3),product(product(product(a3,a4),a6),a3)) = a6 ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( product(a13,a8) = a6 )
<=> ( product(a13,a8) = a6 ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
product(a13,a8) = a6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_10) ).
tff(27,plain,
product(a13,a8) = a6,
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),a3),product(product(product(a3,a4),a6),a3)) = a6,
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(product(a3,a4),a6),a3)) = a6,
inference(modus_ponens,[status(thm)],[28,23]) ).
tff(30,plain,
a6 = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
a6 = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),
inference(transitivity,[status(thm)],[30,22]) ).
tff(32,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3) = product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3) = product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)) = product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
( ( product(product(product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11)),a3),product(product(product(a3,a4),a6),a3)) = a4 )
<=> ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3)) = a4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( product(a15,a8) = a4 )
<=> ( product(product(product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11)),a3),product(product(product(a3,a4),a6),a3)) = a4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( product(a15,a8) = a4 )
<=> ( product(a15,a8) = a4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
product(a15,a8) = a4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_14) ).
tff(39,plain,
product(a15,a8) = a4,
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
product(product(product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11)),a3),product(product(product(a3,a4),a6),a3)) = a4,
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3)) = a4,
inference(modus_ponens,[status(thm)],[40,35]) ).
tff(42,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3)),
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3) = a4,
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a3,a3) = a3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
product(a3,a3) = a3,
inference(unit_resolution,[status(thm)],[45,16]) ).
tff(47,plain,
product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)) = product(a3,a4),
inference(monotonicity,[status(thm)],[46,44]) ).
tff(48,plain,
product(a3,a4) = product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
product(a3,a4) = product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),
inference(transitivity,[status(thm)],[48,34]) ).
tff(50,plain,
product(product(a3,a4),a6) = product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),
inference(monotonicity,[status(thm)],[49,31]) ).
tff(51,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)) = product(product(a3,a4),a6),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3) = product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3) = product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),
inference(unit_resolution,[status(thm)],[52,7]) ).
tff(54,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3) = product(product(a3,a4),a6),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
product(product(a3,a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)) = product(a3,product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[46,54]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(a3,a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(a3,a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
( ( product(a1,a2) = a3 )
<=> ( product(a1,product(a6,product(product(a3,a4),a6))) = a3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( product(a1,a2) = a3 )
<=> ( product(a1,a2) = a3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
product(a1,a2) = a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot) ).
tff(61,plain,
product(a1,a2) = a3,
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
product(a1,product(a6,product(product(a3,a4),a6))) = a3,
inference(modus_ponens,[status(thm)],[61,58]) ).
tff(63,plain,
product(a6,product(product(a3,a4),a6)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[31]) ).
tff(64,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(a3,a4),a6)) = product(a6,product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(a3,a4),a6)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(a3,a4),a6)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[65,7]) ).
tff(67,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(a6,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[67,64]) ).
tff(69,plain,
product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(a1,product(a6,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = a3,
inference(transitivity,[status(thm)],[69,62]) ).
tff(71,plain,
product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a6,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[68]) ).
tff(72,plain,
product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a6,product(product(a3,a4),a6))) = product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
^ [Y: $i,X: $i] :
refl(
( ( product(product(X,Y),Y) = X )
<=> ( product(product(X,Y),Y) = X ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
<=> ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
<=> ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).
tff(77,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a6,product(product(a3,a4),a6))) = product(product(product(a3,a4),a6),a3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a6,product(product(a3,a4),a6))) = product(product(product(a3,a4),a6),a3),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
product(product(product(a3,a4),a6),a3) = product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a6,product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),a3) = product(product(product(a3,a4),a6),a3),
inference(monotonicity,[status(thm)],[54]) ).
tff(84,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),a3) = product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),a3) = product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[84,79]) ).
tff(86,plain,
product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),a3),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[86,83,82,72]) ).
tff(88,plain,
product(a1,product(a6,product(product(a3,a4),a6))) = product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[69]) ).
tff(89,plain,
a3 = product(a1,product(a6,product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[62]) ).
tff(90,plain,
a3 = product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[89,88]) ).
tff(91,plain,
product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) = product(product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[90,87]) ).
tff(92,plain,
product(product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[93,7]) ).
tff(95,plain,
product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),
inference(monotonicity,[status(thm)],[95,70]) ).
tff(97,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[97,7]) ).
tff(99,plain,
product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[9]) ).
tff(100,plain,
product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(a3,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[99,18]) ).
tff(101,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[101,79]) ).
tff(103,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[103,100]) ).
tff(105,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1) = product(product(a1,a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1) = product(product(a1,a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),
inference(unit_resolution,[status(thm)],[105,7]) ).
tff(107,plain,
product(product(a1,a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( ( product(a11,product(product(product(product(product(a3,a4),a6),a3),a2),a1)) = a1 )
<=> ( product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = a1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( product(a11,a10) = a1 )
<=> ( product(a11,product(product(product(product(product(a3,a4),a6),a3),a2),a1)) = a1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( product(a11,a10) = a1 )
<=> ( product(a11,a10) = a1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,axiom,
product(a11,a10) = a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_16) ).
tff(112,plain,
product(a11,a10) = a1,
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
product(a11,product(product(product(product(product(a3,a4),a6),a3),a2),a1)) = a1,
inference(modus_ponens,[status(thm)],[112,109]) ).
tff(114,plain,
product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = a1,
inference(modus_ponens,[status(thm)],[113,108]) ).
tff(115,plain,
a1 = product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a1,a1) = a1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
product(a1,a1) = a1,
inference(unit_resolution,[status(thm)],[116,16]) ).
tff(118,plain,
product(a1,a1) = product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),
inference(transitivity,[status(thm)],[117,115]) ).
tff(119,plain,
product(product(a1,a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(product(a1,a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(a4,product(product(a3,a4),a6)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(a4,product(product(a3,a4),a6)),
inference(unit_resolution,[status(thm)],[121,79]) ).
tff(123,plain,
product(a4,product(product(a3,a4),a6)) = product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6))) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[102]) ).
tff(125,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[125,7]) ).
tff(127,plain,
product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[126,124]) ).
tff(128,plain,
product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)) = product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)) = product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[129,79]) ).
tff(131,plain,
product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[131,128]) ).
tff(133,plain,
product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3) = product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),
inference(symmetry,[status(thm)],[43]) ).
tff(136,plain,
a4 = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[41]) ).
tff(137,plain,
a4 = product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),
inference(transitivity,[status(thm)],[136,135,134]) ).
tff(138,plain,
product(a4,product(product(a3,a4),a6)) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),product(product(a3,a4),a6)) = product(a4,product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),product(product(a3,a4),a6)) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),product(product(a3,a4),a6)) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[140,7]) ).
tff(142,plain,
product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[127]) ).
tff(144,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[100]) ).
tff(146,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),
inference(transitivity,[status(thm)],[145,144,142,139,123,120,107]) ).
tff(147,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[146,104]) ).
tff(148,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[148,7]) ).
tff(150,plain,
product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[68]) ).
tff(151,plain,
product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(155,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[154,79]) ).
tff(156,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[104,156,153]) ).
tff(158,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[159,79]) ).
tff(161,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[161,158,149,147,98,96,57,55,19,9]) ).
tff(163,plain,
product(a6,product(product(a3,a4),a6)) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[63,66,156,153]) ).
tff(164,plain,
product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[163,162]) ).
tff(165,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[156,153]) ).
tff(167,plain,
product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[167,149,147,98,96,57,55,19,9]) ).
tff(169,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[157,168]) ).
tff(170,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[170,7]) ).
tff(172,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(173,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[172,7]) ).
tff(174,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(a4,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[142,139]) ).
tff(176,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[176,176]) ).
tff(178,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(180,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[179,16]) ).
tff(181,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[181,178,174]) ).
tff(183,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
product(a1,product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),
inference(monotonicity,[status(thm)],[115]) ).
tff(186,plain,
product(a1,product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[185,122,138,141]) ).
tff(187,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(a1,product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(a1,product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(189,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(a1,product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1))),
inference(unit_resolution,[status(thm)],[188,7]) ).
tff(190,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[189,187]) ).
tff(191,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(193,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[192,7]) ).
tff(194,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(196,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[195,7]) ).
tff(197,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
product(product(product(a3,a4),a6),a3) = product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),a3),
inference(symmetry,[status(thm)],[83]) ).
tff(199,plain,
product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[71,81,198,85]) ).
tff(200,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),
inference(monotonicity,[status(thm)],[199,70]) ).
tff(201,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)) = product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),
inference(symmetry,[status(thm)],[53]) ).
tff(203,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[202,201,197]) ).
tff(204,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[204,7]) ).
tff(206,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(a3,a4),a6),
inference(transitivity,[status(thm)],[196,200,53,51]) ).
tff(208,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,a4),a6),a3),
inference(monotonicity,[status(thm)],[207,70]) ).
tff(209,plain,
product(product(product(a3,a4),a6),a3) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3) = product(product(product(a3,a4),a6),a3),
inference(monotonicity,[status(thm)],[51]) ).
tff(211,plain,
product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[210,209,206]) ).
tff(212,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[211,203]) ).
tff(213,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(214,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(unit_resolution,[status(thm)],[213,7]) ).
tff(215,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(a3,product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[51]) ).
tff(217,plain,
product(a3,product(product(a3,a4),a6)) = product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = a6 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(219,plain,
product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = a6,
inference(unit_resolution,[status(thm)],[218,79]) ).
tff(220,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[128]) ).
tff(221,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[220,130]) ).
tff(222,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(224,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[223,7]) ).
tff(225,plain,
product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[166]) ).
tff(226,plain,
product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)) = a6,
inference(transitivity,[status(thm)],[225,224,222,219]) ).
tff(227,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[145]) ).
tff(228,plain,
product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[143,227]) ).
tff(229,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[229]) ).
tff(231,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(232,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[231,7]) ).
tff(233,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[100]) ).
tff(235,plain,
product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)) = a3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(237,plain,
product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)) = a3,
inference(unit_resolution,[status(thm)],[236,79]) ).
tff(238,plain,
a3 = product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[237]) ).
tff(239,plain,
a3 = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[238,235]) ).
tff(240,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
a4 = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[136,135,240,233,230]) ).
tff(242,plain,
product(a3,a4) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[239,241]) ).
tff(243,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(a3,a4),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(245,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[244,7]) ).
tff(246,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(a3,a4),
inference(transitivity,[status(thm)],[245,243]) ).
tff(247,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(product(a3,a4),a6),
inference(monotonicity,[status(thm)],[246,226]) ).
tff(248,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(249,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[248,7]) ).
tff(250,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[51]) ).
tff(251,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(a3,a4),a6),
inference(transitivity,[status(thm)],[250,249,247]) ).
tff(252,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[100,51]) ).
tff(253,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = a3,
inference(transitivity,[status(thm)],[252,237]) ).
tff(254,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(a3,product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[253,251]) ).
tff(255,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(256,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(unit_resolution,[status(thm)],[255,7]) ).
tff(257,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(transitivity,[status(thm)],[256,254,217]) ).
tff(258,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(monotonicity,[status(thm)],[257]) ).
tff(259,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[256]) ).
tff(260,plain,
product(a3,product(product(a3,a4),a6)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(symmetry,[status(thm)],[254]) ).
tff(261,plain,
product(a3,product(product(a3,a4),a6)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(transitivity,[status(thm)],[260,259]) ).
tff(262,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),
inference(unit_resolution,[status(thm)],[262,16]) ).
tff(264,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)) = product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
product(product(a3,a4),a6) = product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(transitivity,[status(thm)],[50,264]) ).
tff(266,plain,
product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(monotonicity,[status(thm)],[265,261]) ).
tff(267,plain,
product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),a6) = product(product(a3,a4),a6),
inference(monotonicity,[status(thm)],[47]) ).
tff(268,plain,
product(product(a3,a4),a6) = product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),a6),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)) = product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),a6),
inference(transitivity,[status(thm)],[51,268]) ).
tff(270,plain,
product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),a6),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),a6),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),a6),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(273,plain,
product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),a6),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(unit_resolution,[status(thm)],[272,7]) ).
tff(274,plain,
product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),a6),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(a6,product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[51]) ).
tff(276,plain,
product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[275,63,66]) ).
tff(277,plain,
product(a4,product(product(a3,a4),a6)) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[138,141]) ).
tff(278,plain,
product(a3,product(product(a3,a4),a6)) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[19,9]) ).
tff(279,plain,
product(product(a3,product(product(a3,a4),a6)),product(a4,product(product(a3,a4),a6))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[278,277]) ).
tff(280,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a3,a4),product(product(a3,a4),a6)) = product(product(a3,product(product(a3,a4),a6)),product(a4,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(281,plain,
product(product(a3,a4),product(product(a3,a4),a6)) = product(product(a3,product(product(a3,a4),a6)),product(a4,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[280,7]) ).
tff(282,plain,
product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(a3,a4),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[47,51]) ).
tff(283,plain,
product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[282,281,279]) ).
tff(284,plain,
product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[283,276]) ).
tff(285,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(a3,a4),a6),
inference(transitivity,[status(thm)],[285,274,271,263,51]) ).
tff(287,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[286,100]) ).
tff(288,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[104]) ).
tff(289,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(290,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[289,7]) ).
tff(291,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[100,100]) ).
tff(293,plain,
product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[99,293]) ).
tff(295,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[294,228]) ).
tff(296,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[295,291]) ).
tff(297,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[296,288]) ).
tff(298,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[297]) ).
tff(299,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(300,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[299,7]) ).
tff(301,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[300,298]) ).
tff(302,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[301]) ).
tff(303,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(304,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(unit_resolution,[status(thm)],[303,79]) ).
tff(305,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[305,302,287,266,258,215,212,194,191,184]) ).
tff(307,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[306]) ).
tff(308,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[302]) ).
tff(309,plain,
product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[287]) ).
tff(310,plain,
product(a3,product(a3,product(product(a3,a4),a6))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[239]) ).
tff(311,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(a3,product(a3,product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[310]) ).
tff(312,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[311]) ).
tff(313,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(a3,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[312,99,18]) ).
tff(314,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(a3,product(product(a3,a4),a6))) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(315,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(a3,product(product(a3,a4),a6))) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(unit_resolution,[status(thm)],[314,79]) ).
tff(316,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(317,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[316,79]) ).
tff(318,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[143]) ).
tff(319,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[318]) ).
tff(320,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(321,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(unit_resolution,[status(thm)],[320,7]) ).
tff(322,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[321,319]) ).
tff(323,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[322]) ).
tff(324,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[323,317,143]) ).
tff(325,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[324,100]) ).
tff(326,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(327,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[326,7]) ).
tff(328,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[327,325,315]) ).
tff(329,plain,
product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[328,313]) ).
tff(330,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(331,plain,
product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[330,7]) ).
tff(332,plain,
product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[331,329,144]) ).
tff(333,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[312,332]) ).
tff(334,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[333]) ).
tff(335,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(a3,a4),a6),
inference(transitivity,[status(thm)],[334,285,274,271,263,51]) ).
tff(336,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[335,100]) ).
tff(337,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(338,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[337,7]) ).
tff(339,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[338]) ).
tff(340,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[333]) ).
tff(341,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[340]) ).
tff(342,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(343,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[342,7]) ).
tff(344,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[343]) ).
tff(345,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[143,100]) ).
tff(346,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(a3,product(product(a3,a4),a6))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[345]) ).
tff(347,plain,
product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(a3,product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[315]) ).
tff(348,plain,
product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[347,346]) ).
tff(349,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[294,348]) ).
tff(350,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),a3) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(351,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),a3) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(unit_resolution,[status(thm)],[350,79]) ).
tff(352,plain,
product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[57,55,19,9]) ).
tff(353,plain,
product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),a3)) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[352,351]) ).
tff(354,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)),a3) = product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(355,plain,
product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)),a3) = product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),a3)),
inference(unit_resolution,[status(thm)],[354,7]) ).
tff(356,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(a3,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[256,254]) ).
tff(357,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[356,51]) ).
tff(358,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(359,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[358,79]) ).
tff(360,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[359]) ).
tff(361,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[292,9]) ).
tff(362,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[361,301]) ).
tff(363,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(364,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[363,7]) ).
tff(365,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[305,302,287]) ).
tff(366,plain,
product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[312]) ).
tff(367,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[366,365]) ).
tff(368,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(370,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[369,79]) ).
tff(371,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[370]) ).
tff(372,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[371,368]) ).
tff(373,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = a3,
inference(transitivity,[status(thm)],[373,364,362,360,357,237]) ).
tff(375,plain,
product(product(a3,a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)) = product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),
inference(symmetry,[status(thm)],[57]) ).
tff(376,plain,
product(a3,product(product(a3,a4),a6)) = product(product(a3,a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)),
inference(symmetry,[status(thm)],[55]) ).
tff(377,plain,
product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),
inference(transitivity,[status(thm)],[99,18,376,375]) ).
tff(378,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3) = product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3),
inference(monotonicity,[status(thm)],[377]) ).
tff(379,plain,
product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3) = product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(381,plain,
product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3) = product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(unit_resolution,[status(thm)],[380,79]) ).
tff(382,plain,
product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) = product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),
inference(transitivity,[status(thm)],[382,379]) ).
tff(384,plain,
product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)),
inference(monotonicity,[status(thm)],[383]) ).
tff(385,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)) = product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)),
inference(symmetry,[status(thm)],[384]) ).
tff(386,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),a3) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(387,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),a3) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)),
inference(unit_resolution,[status(thm)],[386,7]) ).
tff(388,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = a3,
inference(transitivity,[status(thm)],[364,362,360,357,237]) ).
tff(389,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[349]) ).
tff(390,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[341]) ).
tff(391,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[390,343,389]) ).
tff(392,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),a3),
inference(monotonicity,[status(thm)],[391,388]) ).
tff(393,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(394,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[393,7]) ).
tff(395,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[367,370]) ).
tff(396,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[395]) ).
tff(397,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[396]) ).
tff(398,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[397]) ).
tff(399,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)),
inference(transitivity,[status(thm)],[398,394,392,387,385]) ).
tff(400,plain,
product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)),a3),
inference(monotonicity,[status(thm)],[399,374]) ).
tff(401,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(402,plain,
product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[401,7]) ).
tff(403,plain,
product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[402,400,355,353,349,344,341]) ).
tff(404,plain,
product(product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[403]) ).
tff(405,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[167]) ).
tff(406,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[149]) ).
tff(407,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[147]) ).
tff(408,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[98]) ).
tff(409,plain,
product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[96]) ).
tff(410,plain,
product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[99,18,376,375,409,408,407,406,405]) ).
tff(411,plain,
product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[402]) ).
tff(412,plain,
product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)),a3) = product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[400]) ).
tff(413,plain,
product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),a3)) = product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)),a3),
inference(symmetry,[status(thm)],[355]) ).
tff(414,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))) = product(product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),a3)),
inference(symmetry,[status(thm)],[353]) ).
tff(415,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[414,413,412,411]) ).
tff(416,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[415,410]) ).
tff(417,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[333,295,291,416,404,339,336,309,308,304]) ).
tff(418,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[417]) ).
tff(419,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(420,plain,
product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),
inference(unit_resolution,[status(thm)],[419,79]) ).
tff(421,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,a4),a6),a3),
inference(monotonicity,[status(thm)],[335,70]) ).
tff(422,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(423,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[422,7]) ).
tff(424,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(a3,a4),a6),a3),
inference(transitivity,[status(thm)],[423,421]) ).
tff(425,plain,
product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[424,68]) ).
tff(426,plain,
product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[425]) ).
tff(427,plain,
product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),
inference(transitivity,[status(thm)],[426,420]) ).
tff(428,plain,
product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),a1),
inference(monotonicity,[status(thm)],[427]) ).
tff(429,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),a1) = product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),
inference(symmetry,[status(thm)],[428]) ).
tff(430,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),a1) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(431,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),a1) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[430,79]) ).
tff(432,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),a1),
inference(symmetry,[status(thm)],[431]) ).
tff(433,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),
inference(transitivity,[status(thm)],[432,429]) ).
tff(434,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),
inference(monotonicity,[status(thm)],[433]) ).
tff(435,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(436,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),
inference(unit_resolution,[status(thm)],[435,79]) ).
tff(437,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(a3,a4),a6),a3),
inference(transitivity,[status(thm)],[205,208]) ).
tff(438,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[437,68]) ).
tff(439,plain,
product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[438]) ).
tff(440,plain,
product(a6,product(product(a3,a4),a6)) = product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[275]) ).
tff(441,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(442,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(unit_resolution,[status(thm)],[441,7]) ).
tff(443,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[442]) ).
tff(444,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[51]) ).
tff(445,plain,
product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[239]) ).
tff(446,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))) = product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,a4),a6)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(448,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,a4),a6)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[447,7]) ).
tff(449,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[51]) ).
tff(450,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[449,448,446]) ).
tff(451,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[450,444]) ).
tff(452,plain,
product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(symmetry,[status(thm)],[451]) ).
tff(453,plain,
product(product(product(a3,a4),a6),a3) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(transitivity,[status(thm)],[198,85,452,443]) ).
tff(454,plain,
product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(monotonicity,[status(thm)],[453,440]) ).
tff(455,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),
inference(transitivity,[status(thm)],[455,439,436]) ).
tff(457,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[456]) ).
tff(458,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[457,434,189,187,173,177,180,161,158,149,147,98,96,57,55,19,9]) ).
tff(459,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[458]) ).
tff(460,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(461,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[460,16]) ).
tff(462,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(monotonicity,[status(thm)],[461]) ).
tff(463,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(464,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(unit_resolution,[status(thm)],[463,7]) ).
tff(465,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),
inference(transitivity,[status(thm)],[455,426,420]) ).
tff(466,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a1) = product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),
inference(monotonicity,[status(thm)],[455]) ).
tff(467,plain,
product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a1),
inference(symmetry,[status(thm)],[466]) ).
tff(468,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a1),
inference(transitivity,[status(thm)],[432,429,467]) ).
tff(469,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a1),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1)),
inference(monotonicity,[status(thm)],[468,465]) ).
tff(470,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a1),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1)) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),
inference(symmetry,[status(thm)],[469]) ).
tff(471,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a1) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a1),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(472,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a1) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a1),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1)),
inference(unit_resolution,[status(thm)],[471,7]) ).
tff(473,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[457]) ).
tff(474,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[434]) ).
tff(475,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(a1,product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),
inference(symmetry,[status(thm)],[189]) ).
tff(476,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(a1,product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1))),
inference(symmetry,[status(thm)],[187]) ).
tff(477,plain,
product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1) = product(a4,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[106,119,122]) ).
tff(478,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1)) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[477]) ).
tff(479,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),a1) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(480,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),a1) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1)),
inference(unit_resolution,[status(thm)],[479,7]) ).
tff(481,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),a1) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(transitivity,[status(thm)],[480,478,181,178,174,476,475,474,473]) ).
tff(482,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),a1),a1) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a1),
inference(monotonicity,[status(thm)],[481]) ).
tff(483,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),a1),a1) = product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(484,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),a1),a1) = product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[483,79]) ).
tff(485,plain,
product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),a1),a1),
inference(symmetry,[status(thm)],[484]) ).
tff(486,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[455]) ).
tff(487,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),
inference(transitivity,[status(thm)],[486,485,482,472,470]) ).
tff(488,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[487]) ).
tff(489,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = 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) ),
inference(quant_inst,[status(thm)],]) ).
tff(490,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(unit_resolution,[status(thm)],[489,7]) ).
tff(491,plain,
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inference(symmetry,[status(thm)],[490]) ).
tff(492,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[158]) ).
tff(493,plain,
product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),
inference(transitivity,[status(thm)],[142,139,123,120,107]) ).
tff(494,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[493]) ).
tff(495,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(a3,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[494,98,96,57,55]) ).
tff(496,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[495,100]) ).
tff(497,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(498,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[497,7]) ).
tff(499,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[498]) ).
tff(500,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)),product(product(a3,a4),a6)) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(501,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)),product(product(a3,a4),a6)) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),
inference(unit_resolution,[status(thm)],[500,79]) ).
tff(502,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(503,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[502,7]) ).
tff(504,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[503]) ).
tff(505,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[504]) ).
tff(506,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[51]) ).
tff(507,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),
inference(transitivity,[status(thm)],[506,505,501]) ).
tff(508,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),a3),
inference(monotonicity,[status(thm)],[507]) ).
tff(509,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(510,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),
inference(unit_resolution,[status(thm)],[509,7]) ).
tff(511,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3),
inference(symmetry,[status(thm)],[510]) ).
tff(512,plain,
product(product(product(a3,a4),a6),a3) = product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3),
inference(symmetry,[status(thm)],[210]) ).
tff(513,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[100]) ).
tff(514,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[513]) ).
tff(515,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3),
inference(monotonicity,[status(thm)],[514]) ).
tff(516,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),
inference(symmetry,[status(thm)],[515]) ).
tff(517,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[54]) ).
tff(518,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(519,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)),
inference(unit_resolution,[status(thm)],[518,7]) ).
tff(520,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[519,517,503,514]) ).
tff(521,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3),
inference(monotonicity,[status(thm)],[520]) ).
tff(522,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(523,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(unit_resolution,[status(thm)],[522,79]) ).
tff(524,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3),
inference(symmetry,[status(thm)],[523]) ).
tff(525,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),
inference(transitivity,[status(thm)],[524,521,516]) ).
tff(526,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),
inference(monotonicity,[status(thm)],[525,512]) ).
tff(527,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a3,product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(528,plain,
product(product(a3,product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(unit_resolution,[status(thm)],[527,7]) ).
tff(529,plain,
product(product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(a3,product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[528]) ).
tff(530,plain,
product(product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[216,251]) ).
tff(531,plain,
product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)) = product(product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(symmetry,[status(thm)],[530]) ).
tff(532,plain,
a3 = product(product(a3,product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(transitivity,[status(thm)],[238,531,529]) ).
tff(533,plain,
product(product(product(a3,a4),a6),a3) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(a3,product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(monotonicity,[status(thm)],[265,532]) ).
tff(534,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(a3,product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(a3,a4),a6),a3),
inference(symmetry,[status(thm)],[533]) ).
tff(535,plain,
product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[252]) ).
tff(536,plain,
product(product(a3,product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(transitivity,[status(thm)],[528,530,535]) ).
tff(537,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(a3,product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(monotonicity,[status(thm)],[536]) ).
tff(538,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(a3,product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(symmetry,[status(thm)],[537]) ).
tff(539,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(540,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(unit_resolution,[status(thm)],[539,7]) ).
tff(541,plain,
product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[309,308,304]) ).
tff(542,plain,
product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[541]) ).
tff(543,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[542]) ).
tff(544,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[300]) ).
tff(545,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)) = product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[264,270,273,284,297,544,543]) ).
tff(546,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[545]) ).
tff(547,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[546]) ).
tff(548,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(549,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[548,7]) ).
tff(550,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,a4),a6),a3),
inference(transitivity,[status(thm)],[549,547,540,538,534]) ).
tff(551,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3),
inference(symmetry,[status(thm)],[521]) ).
tff(552,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(553,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(unit_resolution,[status(thm)],[552,7]) ).
tff(554,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3),
inference(symmetry,[status(thm)],[553]) ).
tff(555,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(a4,product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(monotonicity,[status(thm)],[44]) ).
tff(556,plain,
product(a4,product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(symmetry,[status(thm)],[555]) ).
tff(557,plain,
product(a3,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(a3,product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[100]) ).
tff(558,plain,
product(a3,product(a3,product(product(a3,a4),a6))) = product(a3,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[557]) ).
tff(559,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(a3,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[311,558]) ).
tff(560,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)) = product(product(a3,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[559]) ).
tff(561,plain,
product(product(a3,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[560]) ).
tff(562,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a3,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)) = product(product(a3,product(product(a3,a4),a6)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(563,plain,
product(product(a3,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)) = product(product(a3,product(product(a3,a4),a6)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[562,7]) ).
tff(564,plain,
product(product(a3,product(product(a3,a4),a6)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6))) = product(product(a3,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[563]) ).
tff(565,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = a3,
inference(transitivity,[status(thm)],[234,237]) ).
tff(566,plain,
product(product(a3,product(product(a3,a4),a6)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),
inference(monotonicity,[status(thm)],[278,565]) ).
tff(567,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3) = product(product(a3,product(product(a3,a4),a6)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[566]) ).
tff(568,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[567,564,561]) ).
tff(569,plain,
product(a4,product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[241,568]) ).
tff(570,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(a4,product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(symmetry,[status(thm)],[569]) ).
tff(571,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(572,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[571,7]) ).
tff(573,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[311]) ).
tff(574,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[573]) ).
tff(575,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(576,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[575,7]) ).
tff(577,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)) = product(a3,product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[576,311]) ).
tff(578,plain,
product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[277,577]) ).
tff(579,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a4,product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(a3,a4),a6)) = product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(580,plain,
product(product(a4,product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(a3,a4),a6)) = product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[579,7]) ).
tff(581,plain,
product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[578,574]) ).
tff(582,plain,
product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[581,51]) ).
tff(583,plain,
product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(a4,product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(transitivity,[status(thm)],[582,572,570]) ).
tff(584,plain,
product(product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(a4,product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[583,251]) ).
tff(585,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(586,plain,
product(product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(unit_resolution,[status(thm)],[585,7]) ).
tff(587,plain,
product(product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[586,584,580,578,574]) ).
tff(588,plain,
product(product(product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[587,51]) ).
tff(589,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(590,plain,
product(product(product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[589,79]) ).
tff(591,plain,
product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[590]) ).
tff(592,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))) = product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[578]) ).
tff(593,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[145,144]) ).
tff(594,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(a3,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[593,557]) ).
tff(595,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(a3,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(596,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(a3,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[595,7]) ).
tff(597,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[596,594,592]) ).
tff(598,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[597,301]) ).
tff(599,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(600,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[599,7]) ).
tff(601,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[600,598,591,588,572,570,556,554,551,523]) ).
tff(602,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)),
inference(monotonicity,[status(thm)],[601,550]) ).
tff(603,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(604,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[603,7]) ).
tff(605,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[604,602,526,511,508,351,347,346]) ).
tff(606,plain,
product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[605]) ).
tff(607,plain,
product(a3,product(product(a3,a4),a6)) = product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[376,375,409,408,407,406,405]) ).
tff(608,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[604]) ).
tff(609,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[602]) ).
tff(610,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[526]) ).
tff(611,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),a3) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3),
inference(symmetry,[status(thm)],[508]) ).
tff(612,plain,
product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),a3),
inference(symmetry,[status(thm)],[351]) ).
tff(613,plain,
product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[612,611,510,610,609,608]) ).
tff(614,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[613,607]) ).
tff(615,plain,
product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(transitivity,[status(thm)],[143,614,606,499,496,18,376,375,409,408,407,406,492,160,181,178,174,476,475,474,473]) ).
tff(616,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(monotonicity,[status(thm)],[615]) ).
tff(617,plain,
a1 = product(a1,a1),
inference(symmetry,[status(thm)],[117]) ).
tff(618,plain,
product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))) = product(product(a1,a1),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1)),
inference(monotonicity,[status(thm)],[617,427]) ).
tff(619,plain,
product(product(a1,a1),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1)) = product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[618]) ).
tff(620,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a1) = product(product(a1,a1),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(621,plain,
product(product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a1) = product(product(a1,a1),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1)),
inference(unit_resolution,[status(thm)],[620,7]) ).
tff(622,plain,
product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),
inference(monotonicity,[status(thm)],[115,433]) ).
tff(623,plain,
product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[622,122,138,141]) ).
tff(624,plain,
product(product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a1) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1),
inference(monotonicity,[status(thm)],[623]) ).
tff(625,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1) = product(product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a1),
inference(symmetry,[status(thm)],[624]) ).
tff(626,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1) = product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[625,621,619]) ).
tff(627,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[626]) ).
tff(628,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(629,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(unit_resolution,[status(thm)],[628,7]) ).
tff(630,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[629]) ).
tff(631,plain,
product(product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[622]) ).
tff(632,plain,
product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(transitivity,[status(thm)],[142,139,123,631]) ).
tff(633,plain,
product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[428,431]) ).
tff(634,plain,
product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[277,633]) ).
tff(635,plain,
a1 = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(transitivity,[status(thm)],[115,634]) ).
tff(636,plain,
product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(monotonicity,[status(thm)],[635,632]) ).
tff(637,plain,
product(a1,product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[623]) ).
tff(638,plain,
product(a1,product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(transitivity,[status(thm)],[637,636,630,627]) ).
tff(639,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a1,product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(monotonicity,[status(thm)],[638]) ).
tff(640,plain,
product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(a1,product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(symmetry,[status(thm)],[637]) ).
tff(641,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(642,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[641,16]) ).
tff(643,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a1,product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))))),
inference(monotonicity,[status(thm)],[642,640]) ).
tff(644,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(645,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[644,7]) ).
tff(646,plain,
product(product(a1,a1),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1)) = product(product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a1),
inference(symmetry,[status(thm)],[621]) ).
tff(647,plain,
product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1),
inference(transitivity,[status(thm)],[618,646,624]) ).
tff(648,plain,
product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[647]) ).
tff(649,plain,
product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[614]) ).
tff(650,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[606]) ).
tff(651,plain,
product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[496]) ).
tff(652,plain,
product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(a3,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[167,149,147,98,96,57,55]) ).
tff(653,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[652,100]) ).
tff(654,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(655,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[654,79]) ).
tff(656,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[655]) ).
tff(657,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[656,653,651,498,650,649,144]) ).
tff(658,plain,
product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[657]) ).
tff(659,plain,
product(product(a1,product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[94]) ).
tff(660,plain,
product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[164,149,147,98,96,57,55,19,9]) ).
tff(661,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),
inference(monotonicity,[status(thm)],[660]) ).
tff(662,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3) = product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[661,378,381,91,659,658,648,645,643,639,616,491,488,464,462,459,418,307,171,169,165]) ).
tff(663,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3) = product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[378,381]) ).
tff(664,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3)) = product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)),
inference(monotonicity,[status(thm)],[663]) ).
tff(665,plain,
product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[664]) ).
tff(666,plain,
product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),
inference(monotonicity,[status(thm)],[383,512]) ).
tff(667,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)) = product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[666]) ).
tff(668,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(669,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),
inference(unit_resolution,[status(thm)],[668,7]) ).
tff(670,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3) = product(a3,a3),
inference(monotonicity,[status(thm)],[253]) ).
tff(671,plain,
product(a3,a3) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3),
inference(symmetry,[status(thm)],[670]) ).
tff(672,plain,
a3 = product(a3,a3),
inference(symmetry,[status(thm)],[46]) ).
tff(673,plain,
a3 = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3)),
inference(transitivity,[status(thm)],[672,671,669,667,665]) ).
tff(674,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[442,451]) ).
tff(675,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[444,251]) ).
tff(676,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(677,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(unit_resolution,[status(thm)],[676,7]) ).
tff(678,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[677,675,102]) ).
tff(679,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[678,674]) ).
tff(680,plain,
product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)),
inference(monotonicity,[status(thm)],[679]) ).
tff(681,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[680]) ).
tff(682,plain,
product(product(product(a3,a4),a6),a3) = product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[198,85]) ).
tff(683,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[682]) ).
tff(684,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[683]) ).
tff(685,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,a4),a6),a3)),
inference(monotonicity,[status(thm)],[684]) ).
tff(686,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[685]) ).
tff(687,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(688,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),
inference(unit_resolution,[status(thm)],[687,79]) ).
tff(689,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[688]) ).
tff(690,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3)),
inference(transitivity,[status(thm)],[689,686,681]) ).
tff(691,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3))),
inference(monotonicity,[status(thm)],[690,673]) ).
tff(692,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),
inference(symmetry,[status(thm)],[691]) ).
tff(693,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(694,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3))),
inference(unit_resolution,[status(thm)],[693,7]) ).
tff(695,plain,
product(product(product(product(a3,a4),a6),a3),a3) = product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3),
inference(monotonicity,[status(thm)],[682]) ).
tff(696,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3) = product(product(product(product(a3,a4),a6),a3),a3),
inference(symmetry,[status(thm)],[695]) ).
tff(697,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a3,a4),a6),a3),a3),
inference(transitivity,[status(thm)],[298,285,274,271,263,202,696]) ).
tff(698,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),
inference(monotonicity,[status(thm)],[697,512]) ).
tff(699,plain,
product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[698]) ).
tff(700,plain,
product(product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(monotonicity,[status(thm)],[699]) ).
tff(701,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(symmetry,[status(thm)],[700]) ).
tff(702,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3),a3) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(703,plain,
product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3),a3) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(unit_resolution,[status(thm)],[702,79]) ).
tff(704,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),a3) = product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),
inference(monotonicity,[status(thm)],[663]) ).
tff(705,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),a3) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[704,57,55,19,9]) ).
tff(706,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[251,216]) ).
tff(707,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(708,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(unit_resolution,[status(thm)],[707,7]) ).
tff(709,plain,
product(product(product(product(a3,a4),a6),a3),a3) = product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),
inference(transitivity,[status(thm)],[695,53]) ).
tff(710,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a3) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),a3),
inference(monotonicity,[status(thm)],[298]) ).
tff(711,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a3),product(product(product(product(a3,a4),a6),a3),a3)) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(monotonicity,[status(thm)],[710,709]) ).
tff(712,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),a3) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a3),product(product(product(product(a3,a4),a6),a3),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(713,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),a3) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),a3),product(product(product(product(a3,a4),a6),a3),a3)),
inference(unit_resolution,[status(thm)],[712,7]) ).
tff(714,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),a3) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[713,711,708,706,309,308,304]) ).
tff(715,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),a3)) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[714,705]) ).
tff(716,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(717,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),a3),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),a3)),
inference(unit_resolution,[status(thm)],[716,7]) ).
tff(718,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3) = product(product(a3,a4),a6),
inference(transitivity,[status(thm)],[717,715,300,298,285,274,271,263,51]) ).
tff(719,plain,
product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3),a3) = product(product(product(a3,a4),a6),a3),
inference(monotonicity,[status(thm)],[718]) ).
tff(720,plain,
product(product(product(a3,a4),a6),a3) = product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3),a3),
inference(symmetry,[status(thm)],[719]) ).
tff(721,plain,
product(product(product(a3,a4),a6),a3) = product(product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(transitivity,[status(thm)],[720,703,701]) ).
tff(722,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3))),
inference(monotonicity,[status(thm)],[721]) ).
tff(723,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3))) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[722]) ).
tff(724,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(725,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3))),
inference(unit_resolution,[status(thm)],[724,7]) ).
tff(726,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[444,674]) ).
tff(727,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(symmetry,[status(thm)],[726]) ).
tff(728,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[444,682]) ).
tff(729,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(730,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),a3))),
inference(unit_resolution,[status(thm)],[729,7]) ).
tff(731,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),a3))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[730]) ).
tff(732,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(transitivity,[status(thm)],[264,270,273,284,297]) ).
tff(733,plain,
product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)),
inference(monotonicity,[status(thm)],[732]) ).
tff(734,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[733]) ).
tff(735,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),
inference(transitivity,[status(thm)],[679,684]) ).
tff(736,plain,
product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),a3))),
inference(monotonicity,[status(thm)],[735,734]) ).
tff(737,plain,
product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3))) = product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(a3,a4),a6),a3))),
inference(monotonicity,[status(thm)],[699]) ).
tff(738,plain,
product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(transitivity,[status(thm)],[737,736,731,728,727]) ).
tff(739,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(monotonicity,[status(thm)],[738]) ).
tff(740,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(symmetry,[status(thm)],[739]) ).
tff(741,plain,
product(a3,product(product(product(a3,a4),a6),a3)) = product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[682]) ).
tff(742,plain,
product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) = product(a3,product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[741]) ).
tff(743,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3) = product(a3,product(product(product(a3,a4),a6),a3)),
inference(transitivity,[status(thm)],[378,381,742]) ).
tff(744,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[682]) ).
tff(745,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[744]) ).
tff(746,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),
inference(transitivity,[status(thm)],[726,745]) ).
tff(747,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(a3,product(product(product(a3,a4),a6),a3))),
inference(monotonicity,[status(thm)],[746,743]) ).
tff(748,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(a3,product(product(product(a3,a4),a6),a3))) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(symmetry,[status(thm)],[747]) ).
tff(749,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(a3,product(product(product(a3,a4),a6),a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(750,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(a3,product(product(product(a3,a4),a6),a3))),
inference(unit_resolution,[status(thm)],[749,7]) ).
tff(751,plain,
product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[222]) ).
tff(752,plain,
a6 = product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[219]) ).
tff(753,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[21,29,752,751]) ).
tff(754,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),
inference(monotonicity,[status(thm)],[753]) ).
tff(755,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[754]) ).
tff(756,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(757,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3))),
inference(unit_resolution,[status(thm)],[756,7]) ).
tff(758,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3))) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[757]) ).
tff(759,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(transitivity,[status(thm)],[744,727]) ).
tff(760,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(761,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(unit_resolution,[status(thm)],[760,7]) ).
tff(762,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),
inference(monotonicity,[status(thm)],[593]) ).
tff(763,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3),
inference(symmetry,[status(thm)],[762]) ).
tff(764,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)) = product(a4,product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[44,54]) ).
tff(765,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(766,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)),
inference(unit_resolution,[status(thm)],[765,7]) ).
tff(767,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[766,764,138,141]) ).
tff(768,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),
inference(monotonicity,[status(thm)],[767]) ).
tff(769,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(770,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(unit_resolution,[status(thm)],[769,79]) ).
tff(771,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3),
inference(symmetry,[status(thm)],[770]) ).
tff(772,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[682]) ).
tff(773,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(transitivity,[status(thm)],[772,771,768,763,761]) ).
tff(774,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3))) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),
inference(monotonicity,[status(thm)],[773,759]) ).
tff(775,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3))),
inference(symmetry,[status(thm)],[774]) ).
tff(776,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),a3),a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(777,plain,
product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),a3),a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),
inference(unit_resolution,[status(thm)],[776,79]) ).
tff(778,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3) = a6,
inference(transitivity,[status(thm)],[21,29]) ).
tff(779,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)) = product(a6,product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[778,54]) ).
tff(780,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(781,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),a3)),
inference(unit_resolution,[status(thm)],[780,7]) ).
tff(782,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a3) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),
inference(monotonicity,[status(thm)],[726]) ).
tff(783,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a3) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[782,781,779,63,66]) ).
tff(784,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),a3),
inference(symmetry,[status(thm)],[768]) ).
tff(785,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a3),
inference(symmetry,[status(thm)],[761]) ).
tff(786,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[785,762,784,770]) ).
tff(787,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),a3),
inference(monotonicity,[status(thm)],[786]) ).
tff(788,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),
inference(transitivity,[status(thm)],[787,766,764,123,120,107]) ).
tff(789,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a3)) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[788,783]) ).
tff(790,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),a3) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(791,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),a3) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),a3),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),a3)),
inference(unit_resolution,[status(thm)],[790,7]) ).
tff(792,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),a3) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[791,789,98,96,57,55,19,9]) ).
tff(793,plain,
product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),a3),a3) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),
inference(monotonicity,[status(thm)],[792]) ).
tff(794,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3) = product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),a3),a3),
inference(symmetry,[status(thm)],[793]) ).
tff(795,plain,
product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[658]) ).
tff(796,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[648]) ).
tff(797,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[645]) ).
tff(798,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a1,product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[643]) ).
tff(799,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a1,product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))))),
inference(symmetry,[status(thm)],[639]) ).
tff(800,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(symmetry,[status(thm)],[616]) ).
tff(801,plain,
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= 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inference(symmetry,[status(thm)],[488]) ).
tff(802,plain,
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inference(symmetry,[status(thm)],[464]) ).
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= product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(symmetry,[status(thm)],[462]) ).
tff(804,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(symmetry,[status(thm)],[459]) ).
tff(805,plain,
product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[418]) ).
tff(806,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[307]) ).
tff(807,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[171]) ).
tff(808,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[169]) ).
tff(809,plain,
product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),
inference(transitivity,[status(thm)],[164,808,807,806,805,804,803,802,801,490,800,799,798,797,796,795,94,92,382,379,794,777,775,758,755,750,748,740,725,723,694,692]) ).
tff(810,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) = product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),a3),a3),
inference(symmetry,[status(thm)],[777]) ).
tff(811,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(a3,product(product(product(a3,a4),a6),a3))) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[750]) ).
tff(812,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3))) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(a3,a4),a6),a3),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),
inference(symmetry,[status(thm)],[725]) ).
tff(813,plain,
product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3)),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(a3,a4),a6),a3))) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[694]) ).
tff(814,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[691,813,722,812,739,747,811,754,757,774,810,793,378,381,91,659,658,648,645,643,639,616,491,488,464,462,459,418,307,171,169,492,160]) ).
tff(815,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) = product(a4,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[161,158,149,147,98,96,57,55,19,651,498,650,649,144,142,139]) ).
tff(816,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[295]) ).
tff(817,plain,
product(product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[416]) ).
tff(818,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[404]) ).
tff(819,plain,
product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[336]) ).
tff(820,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[266]) ).
tff(821,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a3,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(symmetry,[status(thm)],[258]) ).
tff(822,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[212]) ).
tff(823,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[191]) ).
tff(824,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[173,177,180,161,158,149,147,98,96,57,55,19,9]) ).
tff(825,plain,
product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[824]) ).
tff(826,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[825]) ).
tff(827,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(a3,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[656,653,18]) ).
tff(828,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[100,827]) ).
tff(829,plain,
product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[828]) ).
tff(830,plain,
product(a4,product(product(a3,a4),a6)) = product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),
inference(transitivity,[status(thm)],[138,141,143,614,606,499,496,829,826,823,193,822,214,821,820,819,338,818,817,290,816,340,432,429]) ).
tff(831,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(832,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(unit_resolution,[status(thm)],[831,79]) ).
tff(833,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[457,434,189,187,173,177,180]) ).
tff(834,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[833]) ).
tff(835,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[834]) ).
tff(836,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[162]) ).
tff(837,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[836]) ).
tff(838,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[417]) ).
tff(839,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[838]) ).
tff(840,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[334]) ).
tff(841,plain,
product(product(a3,a4),a6) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[50,264,270,273,284,840]) ).
tff(842,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[378,381,91,659]) ).
tff(843,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[842,841]) ).
tff(844,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[843]) ).
tff(845,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(846,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[845,7]) ).
tff(847,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(transitivity,[status(thm)],[656,653,18,376,375,409,408,407,406,492,160,181,178,174,476,475,474,473]) ).
tff(848,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(monotonicity,[status(thm)],[847]) ).
tff(849,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[848]) ).
tff(850,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(851,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(unit_resolution,[status(thm)],[850,7]) ).
tff(852,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))) = a1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(853,plain,
product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))) = a1,
inference(unit_resolution,[status(thm)],[852,79]) ).
tff(854,plain,
product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[455]) ).
tff(855,plain,
product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) = a1,
inference(transitivity,[status(thm)],[854,853]) ).
tff(856,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[855]) ).
tff(857,plain,
product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[856]) ).
tff(858,plain,
product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1) = product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[428,431,333,295,291,416,404,339,336,266,258,215,212,194,191,825,828,651,498,650,649,144,142,139,123,631,857,851,849,846,844,576,371,368,839,837,835,832,455]) ).
tff(859,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(860,plain,
product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(unit_resolution,[status(thm)],[859,7]) ).
tff(861,plain,
product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[860]) ).
tff(862,plain,
product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[51,100]) ).
tff(863,plain,
product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))) = product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[862]) ).
tff(864,plain,
product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(monotonicity,[status(thm)],[863]) ).
tff(865,plain,
product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(a3,a4),a6),a3),
inference(transitivity,[status(thm)],[864,540,538,534]) ).
tff(866,plain,
product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(a3,a4),a6),a3),product(product(product(a3,a4),a6),a3)),
inference(monotonicity,[status(thm)],[865,865]) ).
tff(867,plain,
product(product(product(product(a3,a4),a6),a3),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(symmetry,[status(thm)],[866]) ).
tff(868,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(product(product(a3,a4),a6),a3),product(product(product(a3,a4),a6),a3)) = product(product(product(a3,a4),a6),a3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(869,plain,
product(product(product(product(a3,a4),a6),a3),product(product(product(a3,a4),a6),a3)) = product(product(product(a3,a4),a6),a3),
inference(unit_resolution,[status(thm)],[868,16]) ).
tff(870,plain,
product(product(product(a3,a4),a6),a3) = product(product(product(product(a3,a4),a6),a3),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[869]) ).
tff(871,plain,
product(product(product(a3,a4),a6),a3) = product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(transitivity,[status(thm)],[870,867,861]) ).
tff(872,plain,
product(product(product(product(a3,a4),a6),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[871]) ).
tff(873,plain,
product(product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(a3,a4),a6),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[872]) ).
tff(874,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(875,plain,
product(product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[874,7]) ).
tff(876,plain,
product(product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[875]) ).
tff(877,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(878,plain,
product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[877,7]) ).
tff(879,plain,
product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[878]) ).
tff(880,plain,
product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),
inference(transitivity,[status(thm)],[542,300,298,285,274,271,263]) ).
tff(881,plain,
product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),a6),
inference(transitivity,[status(thm)],[542,300,298,285,274,271,263,51,268]) ).
tff(882,plain,
product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),a6),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(monotonicity,[status(thm)],[881,880]) ).
tff(883,plain,
product(product(product(product(a3,a3),product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3)),a6),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[882]) ).
tff(884,plain,
product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)) = product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[264,270,883,879]) ).
tff(885,plain,
product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[884,863]) ).
tff(886,plain,
product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a3,a4),a6),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[885,876,873]) ).
tff(887,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,a4),a6),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[886,410]) ).
tff(888,plain,
product(product(product(product(product(a3,a4),a6),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[887]) ).
tff(889,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a3,a4),a6),a3),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,a4),a6),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(890,plain,
product(product(product(product(product(a3,a4),a6),a3),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(a3,a4),a6),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(unit_resolution,[status(thm)],[889,7]) ).
tff(891,plain,
product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[99,651,498,650,649,144]) ).
tff(892,plain,
product(product(product(product(a3,a4),a6),a3),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[68]) ).
tff(893,plain,
product(product(product(product(a3,a4),a6),a3),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),
inference(transitivity,[status(thm)],[892,454]) ).
tff(894,plain,
product(product(product(product(product(a3,a4),a6),a3),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[893,891]) ).
tff(895,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(a3,a4),a6),a3),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[894]) ).
tff(896,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[465]) ).
tff(897,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[896]) ).
tff(898,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(899,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(unit_resolution,[status(thm)],[898,7]) ).
tff(900,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),a1),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[899]) ).
tff(901,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),
inference(monotonicity,[status(thm)],[433,175]) ).
tff(902,plain,
product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(transitivity,[status(thm)],[901,181,178,174,476,475,474,473]) ).
tff(903,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(a1,product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))))),
inference(monotonicity,[status(thm)],[902,640]) ).
tff(904,plain,
product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(a1,product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(a1,product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[903]) ).
tff(905,plain,
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inference(monotonicity,[status(thm)],[638]) ).
tff(906,plain,
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inference(symmetry,[status(thm)],[905]) ).
tff(907,plain,
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= product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[851]) ).
tff(908,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[846]) ).
tff(909,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[576]) ).
tff(910,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[832]) ).
tff(911,plain,
product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))) = product(product(product(a3,a4),a6),a3),
inference(transitivity,[status(thm)],[454,910,834,836,838,367,370,909,843,908,848,907,856,622,122,138,141,143,614,606,499,496,18,376,375,409,408,407,406,808,807,806,805,804,803,802,801,490,906,904,900,897,895,890,888,549,547,540,538,534]) ).
tff(912,plain,
product(product(product(product(product(a3,a4),a6),a3),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a3,a4),a6),a3),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[890]) ).
tff(913,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[549]) ).
tff(914,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(symmetry,[status(thm)],[540]) ).
tff(915,plain,
product(product(product(a3,a4),a6),a3) = product(product(a3,a4),a6),
inference(transitivity,[status(thm)],[533,537,914,546,913,887,912,894,896,899,903,905,491,488,464,462,459,418,300,298,285,274,271,263,51]) ).
tff(916,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)),
inference(monotonicity,[status(thm)],[726]) ).
tff(917,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[916]) ).
tff(918,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(product(product(a3,a4),a6),a3)),
inference(monotonicity,[status(thm)],[745]) ).
tff(919,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[918]) ).
tff(920,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(921,plain,
product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),
inference(unit_resolution,[status(thm)],[920,79]) ).
tff(922,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(product(a3,a4),a6),a3)),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[921]) ).
tff(923,plain,
product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)) = product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3)),
inference(transitivity,[status(thm)],[922,919,917]) ).
tff(924,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)),
inference(monotonicity,[status(thm)],[786]) ).
tff(925,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[924]) ).
tff(926,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),
inference(transitivity,[status(thm)],[771,768]) ).
tff(927,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),
inference(monotonicity,[status(thm)],[926,512]) ).
tff(928,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[927]) ).
tff(929,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(930,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)),
inference(unit_resolution,[status(thm)],[929,7]) ).
tff(931,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),
inference(symmetry,[status(thm)],[240]) ).
tff(932,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[228,51]) ).
tff(933,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = a4,
inference(transitivity,[status(thm)],[932,232,931,43,41]) ).
tff(934,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3) = product(a4,a3),
inference(monotonicity,[status(thm)],[933]) ).
tff(935,plain,
product(a4,a3) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3),
inference(symmetry,[status(thm)],[934]) ).
tff(936,plain,
a4 = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),
inference(transitivity,[status(thm)],[136,135]) ).
tff(937,plain,
product(a4,a3) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),a3),
inference(monotonicity,[status(thm)],[936]) ).
tff(938,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),a3) = product(a4,a3),
inference(symmetry,[status(thm)],[937]) ).
tff(939,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),a3) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(940,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),a3) = product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),
inference(unit_resolution,[status(thm)],[939,79]) ).
tff(941,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),a3),a3),
inference(symmetry,[status(thm)],[940]) ).
tff(942,plain,
product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)),
inference(transitivity,[status(thm)],[131,128,941,938,935,930,928,925]) ).
tff(943,plain,
product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3))),
inference(monotonicity,[status(thm)],[942,923]) ).
tff(944,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3))) = product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[943]) ).
tff(945,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(946,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3))),
inference(unit_resolution,[status(thm)],[945,7]) ).
tff(947,plain,
product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) = product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[810,793,378,381]) ).
tff(948,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(a3,a4),a6),a3)) = product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)),
inference(monotonicity,[status(thm)],[947]) ).
tff(949,plain,
product(product(a3,product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),a3)) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[948]) ).
tff(950,plain,
product(a6,product(product(a3,a4),a6)) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[63,66,656,653,9]) ).
tff(951,plain,
product(a1,product(a6,product(product(a3,a4),a6))) = product(a1,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[950]) ).
tff(952,plain,
product(a1,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(a1,product(a6,product(product(a3,a4),a6))),
inference(symmetry,[status(thm)],[951]) ).
tff(953,plain,
product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[99,18,376,375,409,408,407,406,492,160]) ).
tff(954,plain,
product(a1,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(a1,product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[953]) ).
tff(955,plain,
product(a1,product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(a1,product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[954]) ).
tff(956,plain,
product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(transitivity,[status(thm)],[181,178,174,476,475,474,473]) ).
tff(957,plain,
product(a1,product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(monotonicity,[status(thm)],[635,956]) ).
tff(958,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(a1,product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[957]) ).
tff(959,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(960,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(unit_resolution,[status(thm)],[959,7]) ).
tff(961,plain,
product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) = product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[455]) ).
tff(962,plain,
product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))) = product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),
inference(symmetry,[status(thm)],[961]) ).
tff(963,plain,
product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))) = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),
inference(symmetry,[status(thm)],[854]) ).
tff(964,plain,
a1 = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[853]) ).
tff(965,plain,
a1 = product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),
inference(transitivity,[status(thm)],[964,963]) ).
tff(966,plain,
product(a1,product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))))),
inference(monotonicity,[status(thm)],[965,962]) ).
tff(967,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))))) = product(a1,product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[966]) ).
tff(968,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(969,plain,
product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))))),
inference(unit_resolution,[status(thm)],[968,7]) ).
tff(970,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) = product(product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),a1),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),
inference(monotonicity,[status(thm)],[493]) ).
tff(971,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))) = product(a1,product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[970,969,967]) ).
tff(972,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(a1,product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(monotonicity,[status(thm)],[971]) ).
tff(973,plain,
product(product(a1,product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[972]) ).
tff(974,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(975,plain,
product(product(a1,product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(unit_resolution,[status(thm)],[974,7]) ).
tff(976,plain,
product(product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(a1,product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[975]) ).
tff(977,plain,
product(product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(monotonicity,[status(thm)],[623]) ).
tff(978,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(a1,product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(a1,product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))),
inference(symmetry,[status(thm)],[977]) ).
tff(979,plain,
product(product(a3,a4),a6) = a6,
inference(transitivity,[status(thm)],[50,264,270,273,284,297,544,805,804,803,802,801,490,800,978,976,973,960,958,955,952,62,672,671,669,667,949,946,944,219]) ).
tff(980,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(transitivity,[status(thm)],[295,291,416,404,339,336,863]) ).
tff(981,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)) = product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),
inference(monotonicity,[status(thm)],[980,50]) ).
tff(982,plain,
product(product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[981]) ).
tff(983,plain,
product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),product(product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))))) = product(product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(a6,product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[960]) ).
tff(984,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3),product(product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)),a3)) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),a3),
inference(symmetry,[status(thm)],[669]) ).
tff(985,plain,
product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(a3,a4),a6),a3)),product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3)))),product(product(product(a3,a4),a6),a3))) = product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3),product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),a3)),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))),product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a3,product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6))),a3),product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),a3))))),product(product(product(a3,a4),a6),a3)),
inference(symmetry,[status(thm)],[946]) ).
tff(986,plain,
a6 = product(a3,a4),
inference(transitivity,[status(thm)],[752,943,985,948,666,984,670,46,89,951,954,957,983,972,975,977,616,906,904,900,897,895,890,888,549,547,982,245,243]) ).
tff(987,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(a3,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[145,614,606,499,496,18]) ).
tff(988,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)) = product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)),
inference(monotonicity,[status(thm)],[987]) ).
tff(989,plain,
product(product(a3,product(product(a3,a4),a6)),product(product(a3,a4),a6)) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[988]) ).
tff(990,plain,
product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,a4),a6))) = product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),
inference(symmetry,[status(thm)],[245]) ).
tff(991,plain,
product(a3,a4) = a4,
inference(transitivity,[status(thm)],[242,990,981,546,913,887,912,894,896,899,903,905,800,978,976,973,960,958,955,952,62,238,989,232,931,43,41]) ).
tff(992,plain,
a4 = a3,
inference(transitivity,[status(thm)],[136,135,240,233,988,237]) ).
tff(993,plain,
product(product(a3,product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))) = product(product(product(product(product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))),
inference(symmetry,[status(thm)],[653]) ).
tff(994,plain,
a3 = product(a6,product(product(a3,a4),a6)),
inference(transitivity,[status(thm)],[89,951,954,957,983,972,975,977,616,491,488,464,462,459,418,307,171,169,149,147,98,96,57,55,19,993,655,67,64]) ).
tff(995,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(a4,product(product(a3,a4),a6)),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1)),
inference(symmetry,[status(thm)],[634]) ).
tff(996,plain,
product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))))) = product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6))),
inference(transitivity,[status(thm)],[333,295,291,416,404,339,336]) ).
tff(997,plain,
product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(monotonicity,[status(thm)],[143,996]) ).
tff(998,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(product(a6,product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(a3,a4),a6))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6))),product(a3,product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a3,a4),a6)),product(a3,product(product(a3,a4),a6)))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))))),
inference(symmetry,[status(thm)],[997]) ).
tff(999,plain,
product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))) = product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(transitivity,[status(thm)],[614,606,499,496,9]) ).
tff(1000,plain,
product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))) = product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[999,541]) ).
tff(1001,plain,
product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(product(product(a3,product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))) = product(product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(a3,product(product(a3,a4),a6))),product(product(product(a3,a4),a6),product(a3,product(product(a3,a4),a6)))),
inference(symmetry,[status(thm)],[1000]) ).
tff(1002,plain,
product(a6,product(product(a3,a4),a6)) = a1,
inference(transitivity,[status(thm)],[63,66,656,653,651,498,650,649,144,142,139,123,631,857,851,849,846,844,576,371,368,1001,998,995,114]) ).
tff(1003,plain,
tuple(product(a6,product(product(a3,a4),a6)),a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)) = tuple(a1,product(a6,product(product(a3,a4),a6)),a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))),
inference(monotonicity,[status(thm)],[1002,994,992,991,986,979,915,911,858,830,815,814,809,662]) ).
tff(1004,plain,
tuple(a1,product(a6,product(product(a3,a4),a6)),a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))) = tuple(product(a6,product(product(a3,a4),a6)),a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)),
inference(symmetry,[status(thm)],[1003]) ).
tff(1005,plain,
( ( tuple(a1,a2,a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),a2),product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),product(product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),a3),product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11))) != tuple(a2,a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),a2),product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),product(product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),a3),product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11)),product(product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11)),a3)) )
<=> ( tuple(a1,product(a6,product(product(a3,a4),a6)),a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))) != tuple(product(a6,product(product(a3,a4),a6)),a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1006,plain,
( ( tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15) )
<=> ( tuple(a1,a2,a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),a2),product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),product(product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),a3),product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11))) != tuple(a2,a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),a2),product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),product(product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),a3),product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11)),product(product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11)),a3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1007,plain,
( ( tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15) )
<=> ( tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1008,axiom,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(1009,plain,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(modus_ponens,[status(thm)],[1008,1007]) ).
tff(1010,plain,
tuple(a1,a2,a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),a2),product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),product(product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),a3),product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11))) != tuple(a2,a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),a2),product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),product(product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11),a3),product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11)),product(product(a2,product(product(product(product(product(product(a3,a4),a6),a3),a2),a1),a11)),a3)),
inference(modus_ponens,[status(thm)],[1009,1006]) ).
tff(1011,plain,
tuple(a1,product(a6,product(product(a3,a4),a6)),a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))))) != tuple(product(a6,product(product(a3,a4),a6)),a3,a4,product(a3,a4),a6,product(product(a3,a4),a6),product(product(product(a3,a4),a6),a3),product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),product(product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6))),a3),product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),product(product(product(a6,product(product(a3,a4),a6)),product(product(product(product(product(product(a3,a4),a6),a3),product(a6,product(product(a3,a4),a6))),a1),product(a4,product(product(a3,a4),a6)))),a3)),
inference(modus_ponens,[status(thm)],[1010,1005]) ).
tff(1012,plain,
$false,
inference(unit_resolution,[status(thm)],[1011,1004]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : TOP053-1 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 12:20:35 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.22/1.00 % SZS status Unsatisfiable
% 1.22/1.00 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------