%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP051-1 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:42:45 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 117
% Syntax : Number of formulae : 838 ( 735 unt; 0 typ; 0 def)
% Number of atoms : 947 ( 943 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 196 ( 90 ~; 86 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-10 aty)
% Number of variables : 277 ( 271 !; 0 ?; 277 :)
% Comments :
%------------------------------------------------------------------------------
tff(tuple_type,type,
tuple: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(a9_type,type,
a9: $i ).
tff(a11_type,type,
a11: $i ).
tff(a10_type,type,
a10: $i ).
tff(a5_type,type,
a5: $i ).
tff(a4_type,type,
a4: $i ).
tff(a8_type,type,
a8: $i ).
tff(a3_type,type,
a3: $i ).
tff(a6_type,type,
a6: $i ).
tff(a7_type,type,
a7: $i ).
tff(a2_type,type,
a2: $i ).
tff(a1_type,type,
a1: $i ).
tff(product_type,type,
product: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( product(X,X) = X )
<=> ( product(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( product(X,X) = X )
<=> ! [X: $i] : ( product(X,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( product(X,X) = X )
<=> ! [X: $i] : ( product(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( product(X,X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle) ).
tff(5,plain,
! [X: $i] : ( product(X,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( product(X,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( product(X,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a8,a8) = a8 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
product(a8,a8) = a8,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( product(a7,a3) = a8 )
<=> ( product(a7,a3) = a8 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
product(a7,a3) = a8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_08) ).
tff(12,plain,
product(a7,a3) = a8,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
a8 = product(a7,a3),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
product(a8,a8) = product(product(a7,a3),product(a7,a3)),
inference(monotonicity,[status(thm)],[13,13]) ).
tff(15,plain,
product(product(a7,a3),product(a7,a3)) = product(a8,a8),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
^ [Y: $i,X: $i] :
refl(( ( product(product(X,Y),Y) = X )
<=> ( product(product(X,Y),Y) = X ) )),
inference(bind,[status(th)],[]) ).
tff(17,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)],[16]) ).
tff(18,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(19,axiom,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).
tff(20,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = product(product(a7,a3),product(a7,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = product(product(a7,a3),product(a7,a3)),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ( product(a5,a9) = a6 )
<=> ( product(a5,a9) = a6 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
product(a5,a9) = a6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_06) ).
tff(27,plain,
product(a5,a9) = a6,
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
a6 = product(a5,a9),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a6,a6) = a6 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
product(a6,a6) = a6,
inference(unit_resolution,[status(thm)],[29,7]) ).
tff(31,plain,
product(a6,a6) = product(product(a5,a9),product(a5,a9)),
inference(monotonicity,[status(thm)],[28,28]) ).
tff(32,plain,
product(product(a5,a9),product(a5,a9)) = product(a6,a6),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
product(product(a5,a9),product(a5,a9)) = product(a5,a9),
inference(transitivity,[status(thm)],[32,30,28]) ).
tff(34,plain,
( ( product(a8,a6) = a9 )
<=> ( product(a8,a6) = a9 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
product(a8,a6) = a9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_09) ).
tff(36,plain,
product(a8,a6) = a9,
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
a9 = product(a8,a6),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
product(a9,a9) = product(product(a8,a6),product(a8,a6)),
inference(monotonicity,[status(thm)],[37,37]) ).
tff(39,plain,
product(product(a8,a6),product(a8,a6)) = product(a9,a9),
inference(symmetry,[status(thm)],[38]) ).
tff(40,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(41,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)],[40]) ).
tff(42,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(43,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(44,plain,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a8,a8),a6) = product(product(a8,a6),product(a8,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
product(product(a8,a8),a6) = product(product(a8,a6),product(a8,a6)),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
product(product(a5,a9),product(a5,a9)) = a6,
inference(transitivity,[status(thm)],[32,30]) ).
tff(50,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))) = product(product(a8,a8),a6),
inference(monotonicity,[status(thm)],[15,49]) ).
tff(51,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))) = product(a9,a9),
inference(transitivity,[status(thm)],[50,48,39]) ).
tff(52,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = product(product(a9,a9),product(a5,a9)),
inference(monotonicity,[status(thm)],[51,33]) ).
tff(53,plain,
product(product(a9,a9),product(a5,a9)) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(a1,product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
product(product(a1,product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))) = a1,
inference(unit_resolution,[status(thm)],[54,22]) ).
tff(56,plain,
a8 = product(a8,a8),
inference(symmetry,[status(thm)],[9]) ).
tff(57,plain,
a8 = product(product(a7,a3),product(a7,a3)),
inference(transitivity,[status(thm)],[56,14]) ).
tff(58,plain,
product(a1,a8) = product(a1,product(product(a7,a3),product(a7,a3))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
product(a1,product(product(a7,a3),product(a7,a3))) = product(a1,a8),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
product(product(a1,product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))) = product(product(a1,a8),product(product(a7,a3),product(a7,a3))),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
product(product(a1,a8),product(product(a7,a3),product(a7,a3))) = product(product(a1,product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))) = product(product(a9,a9),product(a5,a9)),
inference(monotonicity,[status(thm)],[39,33]) ).
tff(63,plain,
product(product(a9,a9),product(a5,a9)) = product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
product(product(a7,a3),product(a7,a3)) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[24]) ).
tff(65,plain,
product(product(a7,a3),product(a7,a3)) = product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))),
inference(transitivity,[status(thm)],[64,52,63]) ).
tff(66,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,a8),a6) = product(product(a1,a6),product(a8,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
product(product(a1,a8),a6) = product(product(a1,a6),product(a8,a6)),
inference(unit_resolution,[status(thm)],[66,46]) ).
tff(68,plain,
product(product(a1,a6),product(a8,a6)) = product(product(a1,a8),a6),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,a1),a6) = product(product(a1,a6),product(a1,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
product(product(a1,a1),a6) = product(product(a1,a6),product(a1,a6)),
inference(unit_resolution,[status(thm)],[69,46]) ).
tff(71,plain,
product(product(a1,a6),product(a1,a6)) = product(product(a1,a1),a6),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ( product(a1,a6) = a2 )
<=> ( product(a1,a6) = a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
product(a1,a6) = a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot) ).
tff(74,plain,
product(a1,a6) = a2,
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
product(product(a1,a6),product(a1,a6)) = product(a2,a2),
inference(monotonicity,[status(thm)],[74,74]) ).
tff(76,plain,
product(a2,a2) = product(product(a1,a6),product(a1,a6)),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a2,a2) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
product(a2,a2) = a2,
inference(unit_resolution,[status(thm)],[77,7]) ).
tff(79,plain,
a2 = product(a2,a2),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
product(a1,a6) = product(product(a1,a1),a6),
inference(transitivity,[status(thm)],[74,79,76,71]) ).
tff(81,plain,
product(product(a1,a6),product(a8,a6)) = product(product(product(a1,a1),a6),product(a8,a6)),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
product(product(product(a1,a1),a6),product(a8,a6)) = product(product(a1,a6),product(a8,a6)),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
product(product(product(a1,a1),a6),product(a8,a6)) = product(product(a1,a8),a6),
inference(transitivity,[status(thm)],[82,68]) ).
tff(84,plain,
product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))) = product(product(product(a1,a8),a6),product(a6,a6)),
inference(monotonicity,[status(thm)],[83,32]) ).
tff(85,plain,
product(product(product(a1,a8),a6),product(a6,a6)) = product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
product(product(product(a1,a8),product(a1,a8)),product(product(a5,a9),product(a5,a9))) = product(product(product(a1,a8),product(a1,a8)),a6),
inference(monotonicity,[status(thm)],[49]) ).
tff(87,plain,
product(product(product(a1,a8),product(a1,a8)),a6) = product(product(product(a1,a8),product(a1,a8)),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,a1),a8) = product(product(a1,a8),product(a1,a8)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
product(product(a1,a1),a8) = product(product(a1,a8),product(a1,a8)),
inference(unit_resolution,[status(thm)],[88,46]) ).
tff(90,plain,
product(product(a1,a8),product(a1,a8)) = product(product(a1,a1),a8),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
product(product(product(a1,a8),product(a1,a8)),a6) = product(product(product(a1,a1),a8),a6),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
product(product(product(a1,a1),a8),a6) = product(product(product(a1,a8),product(a1,a8)),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(product(a1,a1),a8),a6) = product(product(product(a1,a1),a6),product(a8,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
product(product(product(a1,a1),a8),a6) = product(product(product(a1,a1),a6),product(a8,a6)),
inference(unit_resolution,[status(thm)],[93,46]) ).
tff(95,plain,
product(product(product(a1,a1),a6),product(a8,a6)) = product(product(product(a1,a1),a8),a6),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
product(product(a1,a8),a6) = product(product(product(a1,a8),product(a1,a8)),product(product(a5,a9),product(a5,a9))),
inference(transitivity,[status(thm)],[67,81,95,92,87]) ).
tff(97,plain,
product(product(product(a1,a8),a6),product(a6,a6)) = product(product(product(product(a1,a8),product(a1,a8)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))),
inference(monotonicity,[status(thm)],[96,31]) ).
tff(98,plain,
product(product(product(product(a1,a8),product(a1,a8)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = product(product(product(a1,a8),a6),product(a6,a6)),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a1,a8),product(a1,a8)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = product(product(a1,a8),product(a1,a8)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
product(product(product(product(a1,a8),product(a1,a8)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = product(product(a1,a8),product(a1,a8)),
inference(unit_resolution,[status(thm)],[99,22]) ).
tff(101,plain,
product(product(a1,a8),product(a1,a8)) = product(product(product(product(a1,a8),product(a1,a8)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a1,a1) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
product(a1,a1) = a1,
inference(unit_resolution,[status(thm)],[102,7]) ).
tff(104,plain,
product(product(a1,a1),a8) = product(a1,a8),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
product(a1,a8) = product(product(a1,a1),a8),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
product(a1,a8) = product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))),
inference(transitivity,[status(thm)],[105,89,101,98,85]) ).
tff(107,plain,
product(product(a1,a8),product(product(a7,a3),product(a7,a3))) = product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))),product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9)))),
inference(monotonicity,[status(thm)],[106,65]) ).
tff(108,plain,
product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))),product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9)))) = product(product(a1,a8),product(product(a7,a3),product(a7,a3))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a8,a6),product(a8,a6))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))),product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a8,a6),product(a8,a6))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))),product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9)))),
inference(unit_resolution,[status(thm)],[109,46]) ).
tff(111,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a9,a9) = a9 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
product(a9,a9) = a9,
inference(unit_resolution,[status(thm)],[111,7]) ).
tff(113,plain,
product(product(a8,a6),product(a8,a6)) = a9,
inference(transitivity,[status(thm)],[39,112]) ).
tff(114,plain,
( ( product(a4,a10) = a5 )
<=> ( product(a4,a10) = a5 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,axiom,
product(a4,a10) = a5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_05) ).
tff(116,plain,
product(a4,a10) = a5,
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
a5 = product(a4,a10),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
product(a5,a5) = product(product(a4,a10),product(a4,a10)),
inference(monotonicity,[status(thm)],[117,117]) ).
tff(119,plain,
product(product(a4,a10),product(a4,a10)) = product(a5,a5),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6))) = product(product(a5,a5),a9),
inference(monotonicity,[status(thm)],[119,113]) ).
tff(121,plain,
product(product(a5,a5),a9) = product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6))),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a5,a5),a9) = product(product(a5,a9),product(a5,a9)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
product(product(a5,a5),a9) = product(product(a5,a9),product(a5,a9)),
inference(unit_resolution,[status(thm)],[122,46]) ).
tff(124,plain,
product(product(a5,a9),product(a5,a9)) = product(product(a5,a5),a9),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
product(product(a5,a9),product(a5,a9)) = product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6))),
inference(transitivity,[status(thm)],[124,121]) ).
tff(126,plain,
product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a8,a6),product(a8,a6))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a8,a6),product(a8,a6))),product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6)))),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a8,a6),product(a8,a6))),product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6)))) = product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a8,a6),product(a8,a6))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a4,a10),product(a4,a10))),product(product(a8,a6),product(a8,a6))) = product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a8,a6),product(a8,a6))),product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a4,a10),product(a4,a10))),product(product(a8,a6),product(a8,a6))) = product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a8,a6),product(a8,a6))),product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6)))),
inference(unit_resolution,[status(thm)],[128,46]) ).
tff(130,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a4,a4),a10) = product(product(a4,a10),product(a4,a10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
product(product(a4,a4),a10) = product(product(a4,a10),product(a4,a10)),
inference(unit_resolution,[status(thm)],[130,46]) ).
tff(132,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a10,a10) = a10 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
product(a10,a10) = a10,
inference(unit_resolution,[status(thm)],[132,7]) ).
tff(134,plain,
( ( product(a9,a4) = a10 )
<=> ( product(a9,a4) = a10 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,axiom,
product(a9,a4) = a10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_10) ).
tff(136,plain,
product(a9,a4) = a10,
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
a10 = product(a9,a4),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
product(a10,a10) = product(product(a9,a4),product(a9,a4)),
inference(monotonicity,[status(thm)],[137,137]) ).
tff(139,plain,
product(product(a9,a4),product(a9,a4)) = product(a10,a10),
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(a9,a9),a4) = product(product(a9,a4),product(a9,a4)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
product(product(a9,a9),a4) = product(product(a9,a4),product(a9,a4)),
inference(unit_resolution,[status(thm)],[140,46]) ).
tff(142,plain,
( ( product(a3,a1) = a4 )
<=> ( product(a3,a1) = a4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,axiom,
product(a3,a1) = a4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_04) ).
tff(144,plain,
product(a3,a1) = a4,
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
a4 = product(a3,a1),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
product(a4,a4) = product(product(a3,a1),product(a3,a1)),
inference(monotonicity,[status(thm)],[145,145]) ).
tff(147,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a4,a4) = a4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
product(a4,a4) = a4,
inference(unit_resolution,[status(thm)],[147,7]) ).
tff(149,plain,
a4 = product(a4,a4),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
a4 = product(product(a3,a1),product(a3,a1)),
inference(transitivity,[status(thm)],[149,146]) ).
tff(151,plain,
product(product(a3,a1),product(a3,a1)) = product(a4,a4),
inference(symmetry,[status(thm)],[146]) ).
tff(152,plain,
product(product(a3,a1),product(a3,a1)) = product(a3,a1),
inference(transitivity,[status(thm)],[151,148,145]) ).
tff(153,plain,
product(a8,a1) = product(product(a8,a8),a1),
inference(monotonicity,[status(thm)],[56]) ).
tff(154,plain,
product(product(a8,a8),a1) = product(a8,a1),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a8,a8),a1) = product(product(a8,a1),product(a8,a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
product(product(a8,a8),a1) = product(product(a8,a1),product(a8,a1)),
inference(unit_resolution,[status(thm)],[155,46]) ).
tff(157,plain,
product(product(a8,a1),product(a8,a1)) = product(product(a8,a8),a1),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
product(product(a8,a1),product(a8,a1)) = product(a8,a1),
inference(transitivity,[status(thm)],[157,154]) ).
tff(159,plain,
product(product(product(a8,a1),product(a8,a1)),product(product(a3,a1),product(a3,a1))) = product(product(a8,a1),product(a3,a1)),
inference(monotonicity,[status(thm)],[158,152]) ).
tff(160,plain,
product(product(a8,a1),product(a3,a1)) = product(product(product(a8,a1),product(a8,a1)),product(product(a3,a1),product(a3,a1))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ( product(a2,a7) = a3 )
<=> ( product(a2,a7) = a3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,axiom,
product(a2,a7) = a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_03) ).
tff(163,plain,
product(a2,a7) = a3,
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
a3 = product(a2,a7),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
product(a3,a3) = product(product(a2,a7),product(a2,a7)),
inference(monotonicity,[status(thm)],[164,164]) ).
tff(166,plain,
product(product(a2,a7),product(a2,a7)) = product(a3,a3),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
product(product(product(a2,a7),product(a2,a7)),a1) = product(product(a3,a3),a1),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
product(product(a3,a3),a1) = product(product(product(a2,a7),product(a2,a7)),a1),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a3,a3),a1) = product(product(a3,a1),product(a3,a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
product(product(a3,a3),a1) = product(product(a3,a1),product(a3,a1)),
inference(unit_resolution,[status(thm)],[169,46]) ).
tff(171,plain,
product(product(a3,a1),product(a3,a1)) = product(product(a3,a3),a1),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
product(a3,a1) = product(product(product(a2,a7),product(a2,a7)),a1),
inference(transitivity,[status(thm)],[144,149,146,171,168]) ).
tff(173,plain,
product(product(a8,a1),product(a3,a1)) = product(product(a8,a1),product(product(product(a2,a7),product(a2,a7)),a1)),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
product(product(a8,a1),product(product(product(a2,a7),product(a2,a7)),a1)) = product(product(a8,a1),product(a3,a1)),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a8,product(product(a2,a7),product(a2,a7))),a1) = product(product(a8,a1),product(product(product(a2,a7),product(a2,a7)),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
product(product(a8,product(product(a2,a7),product(a2,a7))),a1) = product(product(a8,a1),product(product(product(a2,a7),product(a2,a7)),a1)),
inference(unit_resolution,[status(thm)],[175,46]) ).
tff(177,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))),product(product(a2,a7),product(a2,a7))) = product(product(a6,a2),product(a6,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(178,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))),product(product(a2,a7),product(a2,a7))) = product(product(a6,a2),product(a6,a2)),
inference(unit_resolution,[status(thm)],[177,22]) ).
tff(179,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a3,a3) = a3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
product(a3,a3) = a3,
inference(unit_resolution,[status(thm)],[179,7]) ).
tff(181,plain,
product(product(a2,a7),product(a2,a7)) = a3,
inference(transitivity,[status(thm)],[166,180]) ).
tff(182,plain,
( ( product(a6,a2) = a7 )
<=> ( product(a6,a2) = a7 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(183,axiom,
product(a6,a2) = a7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_07) ).
tff(184,plain,
product(a6,a2) = a7,
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
a7 = product(a6,a2),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
product(a7,a7) = product(product(a6,a2),product(a6,a2)),
inference(monotonicity,[status(thm)],[185,185]) ).
tff(187,plain,
product(product(a6,a2),product(a6,a2)) = product(a7,a7),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))) = product(product(a7,a7),a3),
inference(monotonicity,[status(thm)],[187,181]) ).
tff(189,plain,
product(product(a7,a7),a3) = product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a7,a7),a3) = product(product(a7,a3),product(a7,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(191,plain,
product(product(a7,a7),a3) = product(product(a7,a3),product(a7,a3)),
inference(unit_resolution,[status(thm)],[190,46]) ).
tff(192,plain,
product(product(a7,a3),product(a7,a3)) = product(product(a7,a7),a3),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
product(a7,a3) = product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))),
inference(transitivity,[status(thm)],[12,56,14,192,189]) ).
tff(194,plain,
product(product(a7,a3),product(a3,a3)) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))),product(product(a2,a7),product(a2,a7))),
inference(monotonicity,[status(thm)],[193,165]) ).
tff(195,plain,
product(a8,product(product(a2,a7),product(a2,a7))) = product(product(a7,a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[13,166]) ).
tff(196,plain,
product(a8,product(product(a2,a7),product(a2,a7))) = product(product(a6,a2),product(a6,a2)),
inference(transitivity,[status(thm)],[195,194,178]) ).
tff(197,plain,
product(product(a8,product(product(a2,a7),product(a2,a7))),a1) = product(product(product(a6,a2),product(a6,a2)),a1),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
product(product(product(a6,a2),product(a6,a2)),a1) = product(product(a8,product(product(a2,a7),product(a2,a7))),a1),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(a1,product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(200,plain,
product(product(a1,product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = a1,
inference(unit_resolution,[status(thm)],[199,22]) ).
tff(201,plain,
product(a1,product(product(a5,a9),product(a5,a9))) = product(a1,a6),
inference(monotonicity,[status(thm)],[49]) ).
tff(202,plain,
product(a1,a6) = product(a1,product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
a2 = product(a1,a6),
inference(symmetry,[status(thm)],[74]) ).
tff(204,plain,
product(product(a1,a1),a6) = product(a1,product(product(a5,a9),product(a5,a9))),
inference(transitivity,[status(thm)],[70,75,78,203,202]) ).
tff(205,plain,
product(product(product(a1,a1),a6),product(a6,a6)) = product(product(a1,product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))),
inference(monotonicity,[status(thm)],[204,31]) ).
tff(206,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a1,a1),a6),a6) = product(product(product(a1,a1),a6),product(a6,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(207,plain,
product(product(product(a1,a1),a6),a6) = product(product(product(a1,a1),a6),product(a6,a6)),
inference(unit_resolution,[status(thm)],[206,46]) ).
tff(208,plain,
a2 = product(product(a1,a1),a6),
inference(transitivity,[status(thm)],[79,76,71]) ).
tff(209,plain,
product(a2,a6) = product(product(product(a1,a1),a6),a6),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,plain,
product(product(a1,a6),a6) = product(a2,a6),
inference(monotonicity,[status(thm)],[74]) ).
tff(211,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,a6),a6) = product(product(a1,a6),product(a6,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(212,plain,
product(product(a1,a6),a6) = product(product(a1,a6),product(a6,a6)),
inference(unit_resolution,[status(thm)],[211,46]) ).
tff(213,plain,
product(product(a1,a6),product(a6,a6)) = product(product(a1,a6),a6),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
product(product(a1,a6),product(a6,a6)) = a1,
inference(transitivity,[status(thm)],[213,210,209,207,205,200]) ).
tff(215,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a1,a6),product(a6,a6))) = product(product(product(a6,a2),product(a6,a2)),a1),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
product(a2,a6) = product(product(a1,a6),a6),
inference(symmetry,[status(thm)],[210]) ).
tff(217,plain,
product(product(product(a1,a1),a6),a6) = product(a2,a6),
inference(symmetry,[status(thm)],[209]) ).
tff(218,plain,
product(product(product(a1,a1),a6),product(a6,a6)) = product(product(product(a1,a1),a6),a6),
inference(symmetry,[status(thm)],[207]) ).
tff(219,plain,
product(a2,a2) = product(a1,a6),
inference(transitivity,[status(thm)],[78,203]) ).
tff(220,plain,
product(product(a2,a2),product(a2,a2)) = product(product(a1,a6),product(a1,a6)),
inference(monotonicity,[status(thm)],[219,219]) ).
tff(221,plain,
product(product(a2,a2),product(a2,a2)) = product(product(a1,a1),a6),
inference(transitivity,[status(thm)],[220,71]) ).
tff(222,plain,
product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9))) = product(product(product(a1,a1),a6),product(a6,a6)),
inference(monotonicity,[status(thm)],[221,32]) ).
tff(223,plain,
product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9))) = product(product(a1,a6),product(a6,a6)),
inference(transitivity,[status(thm)],[222,218,217,216,212]) ).
tff(224,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,a6),a2) = product(product(a6,a2),product(a6,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(225,plain,
product(product(a6,a6),a2) = product(product(a6,a2),product(a6,a2)),
inference(unit_resolution,[status(thm)],[224,46]) ).
tff(226,plain,
product(product(a6,a6),product(a1,a6)) = product(product(a6,a6),a2),
inference(monotonicity,[status(thm)],[74]) ).
tff(227,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,a1),a6) = product(product(a6,a6),product(a1,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(228,plain,
product(product(a6,a1),a6) = product(product(a6,a6),product(a1,a6)),
inference(unit_resolution,[status(thm)],[227,46]) ).
tff(229,plain,
product(product(a6,a1),product(product(a5,a9),product(a5,a9))) = product(product(a6,a1),a6),
inference(monotonicity,[status(thm)],[49]) ).
tff(230,plain,
product(product(a6,a1),product(product(a5,a9),product(a5,a9))) = product(product(a6,a2),product(a6,a2)),
inference(transitivity,[status(thm)],[229,228,226,225]) ).
tff(231,plain,
product(product(product(a6,a1),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) = product(product(product(a6,a2),product(a6,a2)),product(product(a1,a6),product(a6,a6))),
inference(monotonicity,[status(thm)],[230,223]) ).
tff(232,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a6,a1),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(a6,a1),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(233,plain,
product(product(product(a6,a1),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(a6,a1),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))),
inference(unit_resolution,[status(thm)],[232,46]) ).
tff(234,plain,
a6 = product(a6,a6),
inference(symmetry,[status(thm)],[30]) ).
tff(235,plain,
a6 = product(product(a5,a9),product(a5,a9)),
inference(transitivity,[status(thm)],[234,31]) ).
tff(236,plain,
product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))) = product(product(a6,a6),product(product(a1,a1),a6)),
inference(monotonicity,[status(thm)],[32,221]) ).
tff(237,plain,
product(product(a6,a6),product(product(a1,a1),a6)) = product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
product(product(a6,a6),a2) = product(product(a6,a6),product(product(a1,a1),a6)),
inference(monotonicity,[status(thm)],[208]) ).
tff(239,plain,
product(product(a6,a2),product(a6,a2)) = product(product(a6,a6),a2),
inference(symmetry,[status(thm)],[225]) ).
tff(240,plain,
product(product(a6,a2),product(a6,a2)) = product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[239,238,237]) ).
tff(241,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(244,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))),
inference(unit_resolution,[status(thm)],[243,46]) ).
tff(245,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
product(a6,a6) = product(a5,a9),
inference(transitivity,[status(thm)],[30,28]) ).
tff(247,plain,
product(product(a6,a6),product(a6,a6)) = product(product(a5,a9),product(a5,a9)),
inference(monotonicity,[status(thm)],[246,246]) ).
tff(248,plain,
product(product(product(a5,a9),product(a5,a9)),product(product(a5,a9),product(a5,a9))) = product(product(a6,a6),product(a6,a6)),
inference(monotonicity,[status(thm)],[32,32]) ).
tff(249,plain,
product(product(product(a5,a9),product(a5,a9)),product(product(a5,a9),product(a5,a9))) = product(product(a5,a9),product(a5,a9)),
inference(transitivity,[status(thm)],[248,247]) ).
tff(250,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) = product(product(product(a5,a9),product(a5,a9)),product(product(a1,a6),product(a6,a6))),
inference(monotonicity,[status(thm)],[249,223]) ).
tff(251,plain,
product(product(product(a5,a9),product(a5,a9)),product(product(a1,a6),product(a6,a6))) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
product(product(product(a5,a9),product(a5,a9)),product(product(a1,a6),product(a6,a6))) = product(a6,a1),
inference(monotonicity,[status(thm)],[49,214]) ).
tff(253,plain,
product(a6,a1) = product(product(product(a5,a9),product(a5,a9)),product(product(a1,a6),product(a6,a6))),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
product(a6,a1) = product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))),
inference(transitivity,[status(thm)],[253,251,245,242]) ).
tff(255,plain,
product(product(a6,a1),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))) = product(product(a6,a1),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(258,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))),
inference(unit_resolution,[status(thm)],[257,46]) ).
tff(259,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a7,a7) = a7 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(261,plain,
product(a7,a7) = a7,
inference(unit_resolution,[status(thm)],[260,7]) ).
tff(262,plain,
product(product(a6,a6),product(product(a1,a1),a6)) = product(product(a6,a6),a2),
inference(symmetry,[status(thm)],[238]) ).
tff(263,plain,
product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))) = a7,
inference(transitivity,[status(thm)],[236,262,225,187,261]) ).
tff(264,plain,
product(a7,product(product(a1,a6),product(a1,a6))) = product(product(a6,a2),product(a2,a2)),
inference(monotonicity,[status(thm)],[185,75]) ).
tff(265,plain,
product(product(a6,a2),product(a2,a2)) = product(a7,product(product(a1,a6),product(a1,a6))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
product(product(a2,a2),product(a2,a2)) = product(a2,a2),
inference(transitivity,[status(thm)],[220,75]) ).
tff(267,plain,
product(product(a6,a2),product(a6,a2)) = product(a6,a2),
inference(transitivity,[status(thm)],[187,261,185]) ).
tff(268,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2))) = product(product(a6,a2),product(a2,a2)),
inference(monotonicity,[status(thm)],[267,266]) ).
tff(269,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2))) = product(a7,product(product(a1,a6),product(a1,a6))),
inference(transitivity,[status(thm)],[268,265]) ).
tff(270,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))) = product(product(a7,product(product(a1,a6),product(a1,a6))),a7),
inference(monotonicity,[status(thm)],[269,263]) ).
tff(271,plain,
product(product(a7,product(product(a1,a6),product(a1,a6))),a7) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))),
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(a7,product(product(a1,a6),product(a1,a6))),a7) = product(product(a7,a7),product(product(product(a1,a6),product(a1,a6)),a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(273,plain,
product(product(a7,product(product(a1,a6),product(a1,a6))),a7) = product(product(a7,a7),product(product(product(a1,a6),product(a1,a6)),a7)),
inference(unit_resolution,[status(thm)],[272,46]) ).
tff(274,plain,
product(product(a7,a7),product(product(product(a1,a6),product(a1,a6)),a7)) = product(product(a7,product(product(a1,a6),product(a1,a6))),a7),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a2,a2),a7) = product(product(a2,a7),product(a2,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(276,plain,
product(product(a2,a2),a7) = product(product(a2,a7),product(a2,a7)),
inference(unit_resolution,[status(thm)],[275,46]) ).
tff(277,plain,
product(product(product(a1,a6),product(a1,a6)),a7) = product(product(a2,a2),a7),
inference(monotonicity,[status(thm)],[75]) ).
tff(278,plain,
product(product(product(a1,a6),product(a1,a6)),a7) = a3,
inference(transitivity,[status(thm)],[277,276,166,180]) ).
tff(279,plain,
product(product(a7,a7),product(product(product(a1,a6),product(a1,a6)),a7)) = product(product(a7,a7),a3),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
product(product(a7,a7),a3) = product(product(a7,a7),product(product(product(a1,a6),product(a1,a6)),a7)),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
product(a8,a8) = product(product(a6,a1),product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[14,192,280,274,271,259,256]) ).
tff(282,plain,
product(product(a8,a8),a6) = product(product(product(a6,a1),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))),
inference(monotonicity,[status(thm)],[281,235]) ).
tff(283,plain,
product(product(a8,a6),product(a8,a6)) = product(product(a8,a8),a6),
inference(symmetry,[status(thm)],[48]) ).
tff(284,plain,
product(a9,a9) = product(product(product(a8,a1),product(a8,a1)),product(product(a3,a1),product(a3,a1))),
inference(transitivity,[status(thm)],[38,283,282,233,231,215,198,176,174,160]) ).
tff(285,plain,
product(product(a9,a9),a4) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a3,a1),product(a3,a1))),product(product(a3,a1),product(a3,a1))),
inference(monotonicity,[status(thm)],[284,150]) ).
tff(286,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a3,a1),product(a3,a1))),product(product(a3,a1),product(a3,a1))) = product(product(a9,a9),a4),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
product(product(a3,a1),product(a3,a1)) = product(product(product(a2,a7),product(a2,a7)),a1),
inference(transitivity,[status(thm)],[171,168]) ).
tff(288,plain,
product(product(a7,a3),product(a3,a3)) = product(a8,product(product(a2,a7),product(a2,a7))),
inference(symmetry,[status(thm)],[195]) ).
tff(289,plain,
product(product(product(a7,a3),product(a3,a3)),a1) = product(product(a8,product(product(a2,a7),product(a2,a7))),a1),
inference(monotonicity,[status(thm)],[288]) ).
tff(290,plain,
product(product(a8,product(product(a2,a7),product(a2,a7))),a1) = product(product(product(a7,a3),product(a3,a3)),a1),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
product(product(a8,a1),product(product(product(a2,a7),product(a2,a7)),a1)) = product(product(a8,product(product(a2,a7),product(a2,a7))),a1),
inference(symmetry,[status(thm)],[176]) ).
tff(292,plain,
product(product(product(a8,a1),product(a8,a1)),product(product(a3,a1),product(a3,a1))) = product(product(product(a7,a3),product(a3,a3)),a1),
inference(transitivity,[status(thm)],[159,173,291,290]) ).
tff(293,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a3,a1),product(a3,a1))),product(product(a3,a1),product(a3,a1))) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a2,a7),product(a2,a7)),a1)),
inference(monotonicity,[status(thm)],[292,287]) ).
tff(294,plain,
product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a2,a7),product(a2,a7)),a1)) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a3,a1),product(a3,a1))),product(product(a3,a1),product(a3,a1))),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a7,a3),product(a3,a3)),product(product(a2,a7),product(a2,a7))),a1) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a2,a7),product(a2,a7)),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(296,plain,
product(product(product(product(a7,a3),product(a3,a3)),product(product(a2,a7),product(a2,a7))),a1) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a2,a7),product(a2,a7)),a1)),
inference(unit_resolution,[status(thm)],[295,46]) ).
tff(297,plain,
product(product(a7,a3),product(a3,a3)) = product(a7,a7),
inference(transitivity,[status(thm)],[194,178,187]) ).
tff(298,plain,
product(product(product(a7,a3),product(a3,a3)),product(product(a2,a7),product(a2,a7))) = product(product(a7,a7),a3),
inference(monotonicity,[status(thm)],[297,181]) ).
tff(299,plain,
product(product(product(a7,a3),product(a3,a3)),product(product(a2,a7),product(a2,a7))) = product(a8,a8),
inference(transitivity,[status(thm)],[298,191,15]) ).
tff(300,plain,
product(product(product(product(a7,a3),product(a3,a3)),product(product(a2,a7),product(a2,a7))),a1) = product(product(a8,a8),a1),
inference(monotonicity,[status(thm)],[299]) ).
tff(301,plain,
product(product(a8,a8),a1) = product(product(product(product(a7,a3),product(a3,a3)),product(product(a2,a7),product(a2,a7))),a1),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
product(a8,a1) = a10,
inference(transitivity,[status(thm)],[153,301,296,294,286,141,139,133]) ).
tff(303,plain,
product(a3,a1) = product(a4,a4),
inference(transitivity,[status(thm)],[144,149]) ).
tff(304,plain,
product(product(a3,a1),product(a8,a1)) = product(product(a4,a4),a10),
inference(monotonicity,[status(thm)],[303,302]) ).
tff(305,plain,
product(product(product(a2,a7),product(a2,a7)),a1) = product(a3,a1),
inference(transitivity,[status(thm)],[167,170,151,148,145]) ).
tff(306,plain,
product(product(product(product(a2,a7),product(a2,a7)),a1),product(a8,a1)) = product(product(a3,a1),product(a8,a1)),
inference(monotonicity,[status(thm)],[305]) ).
tff(307,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a2,a7),product(a2,a7)),a8),a1) = product(product(product(product(a2,a7),product(a2,a7)),a1),product(a8,a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(308,plain,
product(product(product(product(a2,a7),product(a2,a7)),a8),a1) = product(product(product(product(a2,a7),product(a2,a7)),a1),product(a8,a1)),
inference(unit_resolution,[status(thm)],[307,46]) ).
tff(309,plain,
product(product(product(a2,a7),product(a2,a7)),a8) = product(product(a3,a3),product(a7,a3)),
inference(monotonicity,[status(thm)],[166,13]) ).
tff(310,plain,
product(product(a3,a3),product(a7,a3)) = product(product(product(a2,a7),product(a2,a7)),a8),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a3,a7),a3) = product(product(a3,a3),product(a7,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(312,plain,
product(product(a3,a7),a3) = product(product(a3,a3),product(a7,a3)),
inference(unit_resolution,[status(thm)],[311,46]) ).
tff(313,plain,
product(product(a6,a2),product(a6,a2)) = a7,
inference(transitivity,[status(thm)],[187,261]) ).
tff(314,plain,
product(product(product(a1,a6),product(a1,a6)),product(product(a1,a6),product(a1,a6))) = product(product(a2,a2),product(a2,a2)),
inference(monotonicity,[status(thm)],[75,75]) ).
tff(315,plain,
product(product(a2,a2),product(a2,a2)) = product(product(product(a1,a6),product(a1,a6)),product(product(a1,a6),product(a1,a6))),
inference(symmetry,[status(thm)],[314]) ).
tff(316,plain,
product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a1,a6),product(a1,a6)),product(product(a1,a6),product(a1,a6))),a7),
inference(monotonicity,[status(thm)],[315,313]) ).
tff(317,plain,
product(product(product(product(a1,a6),product(a1,a6)),product(product(a1,a6),product(a1,a6))),a7) = product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[316]) ).
tff(318,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a1,a6),product(a1,a6)),product(product(a1,a6),product(a1,a6))),a7) = product(product(product(product(a1,a6),product(a1,a6)),a7),product(product(product(a1,a6),product(a1,a6)),a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(319,plain,
product(product(product(product(a1,a6),product(a1,a6)),product(product(a1,a6),product(a1,a6))),a7) = product(product(product(product(a1,a6),product(a1,a6)),a7),product(product(product(a1,a6),product(a1,a6)),a7)),
inference(unit_resolution,[status(thm)],[318,46]) ).
tff(320,plain,
product(product(product(product(a1,a6),product(a1,a6)),a7),product(product(product(a1,a6),product(a1,a6)),a7)) = product(product(product(product(a1,a6),product(a1,a6)),product(product(a1,a6),product(a1,a6))),a7),
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
product(product(product(a1,a6),product(a1,a6)),a7) = product(a3,a3),
inference(transitivity,[status(thm)],[277,276,166]) ).
tff(322,plain,
product(product(product(product(a1,a6),product(a1,a6)),a7),product(product(product(a1,a6),product(a1,a6)),a7)) = product(product(a3,a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[321,321]) ).
tff(323,plain,
product(product(a3,a3),product(a3,a3)) = product(product(product(product(a1,a6),product(a1,a6)),a7),product(product(product(a1,a6),product(a1,a6)),a7)),
inference(symmetry,[status(thm)],[322]) ).
tff(324,plain,
product(a3,a3) = product(a2,a7),
inference(transitivity,[status(thm)],[180,164]) ).
tff(325,plain,
product(product(a3,a3),product(a3,a3)) = product(product(a2,a7),product(a2,a7)),
inference(monotonicity,[status(thm)],[324,324]) ).
tff(326,plain,
product(product(a2,a7),product(a2,a7)) = product(product(a3,a3),product(a3,a3)),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
a3 = product(a3,a3),
inference(symmetry,[status(thm)],[180]) ).
tff(328,plain,
a3 = product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))),
inference(transitivity,[status(thm)],[327,165,326,323,320,317]) ).
tff(329,plain,
product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2))) = product(a3,product(product(a6,a2),product(a6,a2))),
inference(monotonicity,[status(thm)],[181]) ).
tff(330,plain,
product(a3,product(product(a6,a2),product(a6,a2))) = product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[329]) ).
tff(331,plain,
product(product(a2,a7),product(a7,a7)) = product(a3,product(product(a6,a2),product(a6,a2))),
inference(monotonicity,[status(thm)],[163,186]) ).
tff(332,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a2,a7),a7) = product(product(a2,a7),product(a7,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
product(product(a2,a7),a7) = product(product(a2,a7),product(a7,a7)),
inference(unit_resolution,[status(thm)],[332,46]) ).
tff(334,plain,
product(a3,a7) = product(product(a2,a7),a7),
inference(monotonicity,[status(thm)],[164]) ).
tff(335,plain,
product(a3,a7) = product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2))),
inference(transitivity,[status(thm)],[334,333,331,330]) ).
tff(336,plain,
product(product(a3,a7),a3) = product(product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))),
inference(monotonicity,[status(thm)],[335,328]) ).
tff(337,plain,
product(product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))) = product(product(a3,a7),a3),
inference(symmetry,[status(thm)],[336]) ).
tff(338,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a2,a7),product(a2,a7)),product(product(a2,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(339,plain,
product(product(product(product(a2,a7),product(a2,a7)),product(product(a2,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))),
inference(unit_resolution,[status(thm)],[338,46]) ).
tff(340,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(a2,a2),product(a2,a2))) = product(product(a5,a9),product(a5,a9)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(341,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(a2,a2),product(a2,a2))) = product(product(a5,a9),product(a5,a9)),
inference(unit_resolution,[status(thm)],[340,22]) ).
tff(342,plain,
product(product(a1,a6),product(a1,a6)) = product(product(a2,a2),product(a2,a2)),
inference(symmetry,[status(thm)],[220]) ).
tff(343,plain,
product(a2,a2) = product(product(a2,a2),product(a2,a2)),
inference(transitivity,[status(thm)],[76,342]) ).
tff(344,plain,
a7 = product(a7,a7),
inference(symmetry,[status(thm)],[261]) ).
tff(345,plain,
product(a6,a2) = product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[184,344,186,239,238,237]) ).
tff(346,plain,
product(product(a6,a2),product(a2,a2)) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(a2,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[345,343]) ).
tff(347,plain,
product(product(a6,a2),product(a2,a2)) = product(a6,a6),
inference(transitivity,[status(thm)],[346,341,32]) ).
tff(348,plain,
product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a2,a2))) = product(product(product(a1,a1),a6),product(a6,a6)),
inference(monotonicity,[status(thm)],[221,347]) ).
tff(349,plain,
product(product(product(a2,a2),product(a2,a2)),product(product(a2,a2),product(a2,a2))) = product(product(a2,a2),product(a2,a2)),
inference(monotonicity,[status(thm)],[266,266]) ).
tff(350,plain,
product(product(product(product(a2,a2),product(a2,a2)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))) = product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[349,268]) ).
tff(351,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a2,a2),product(a2,a2)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(352,plain,
product(product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a2,a2),product(a2,a2)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))),
inference(unit_resolution,[status(thm)],[351,46]) ).
tff(353,plain,
product(product(a2,a7),product(a2,a7)) = product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))),
inference(transitivity,[status(thm)],[326,323,320,317]) ).
tff(354,plain,
product(product(product(a2,a7),product(a2,a7)),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[353]) ).
tff(355,plain,
product(product(product(a2,a7),product(a2,a7)),product(product(a2,a2),product(a2,a2))) = a1,
inference(transitivity,[status(thm)],[354,352,350,348,205,200]) ).
tff(356,plain,
product(product(product(product(a2,a7),product(a2,a7)),product(product(a2,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))) = product(a1,product(product(a6,a2),product(a6,a2))),
inference(monotonicity,[status(thm)],[355]) ).
tff(357,plain,
product(a1,product(product(a6,a2),product(a6,a2))) = product(product(product(product(a2,a7),product(a2,a7)),product(product(a2,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
product(product(a7,a3),product(a3,a3)) = product(product(a6,a2),product(a6,a2)),
inference(transitivity,[status(thm)],[194,178]) ).
tff(359,plain,
product(a1,product(product(a7,a3),product(a3,a3))) = product(a1,product(product(a6,a2),product(a6,a2))),
inference(monotonicity,[status(thm)],[358]) ).
tff(360,plain,
product(a1,product(product(a7,a3),product(a3,a3))) = product(product(product(a2,a7),product(a2,a7)),a8),
inference(transitivity,[status(thm)],[359,357,339,337,312,310]) ).
tff(361,plain,
product(product(a1,product(product(a7,a3),product(a3,a3))),a1) = product(product(product(product(a2,a7),product(a2,a7)),a8),a1),
inference(monotonicity,[status(thm)],[360]) ).
tff(362,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,product(product(a7,a3),product(a3,a3))),a1) = product(product(a1,a1),product(product(product(a7,a3),product(a3,a3)),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(363,plain,
product(product(a1,product(product(a7,a3),product(a3,a3))),a1) = product(product(a1,a1),product(product(product(a7,a3),product(a3,a3)),a1)),
inference(unit_resolution,[status(thm)],[362,46]) ).
tff(364,plain,
product(product(a1,a1),product(product(product(a7,a3),product(a3,a3)),a1)) = product(product(a1,product(product(a7,a3),product(a3,a3))),a1),
inference(symmetry,[status(thm)],[363]) ).
tff(365,plain,
product(product(a8,a6),product(a8,a6)) = product(product(product(a7,a3),product(a3,a3)),a1),
inference(transitivity,[status(thm)],[283,282,233,231,215,198,290]) ).
tff(366,plain,
a1 = product(a1,a1),
inference(symmetry,[status(thm)],[103]) ).
tff(367,plain,
product(a1,product(product(a8,a6),product(a8,a6))) = product(product(a1,a1),product(product(product(a7,a3),product(a3,a3)),a1)),
inference(monotonicity,[status(thm)],[366,365]) ).
tff(368,plain,
product(product(product(a1,a6),product(a6,a6)),product(product(a8,a6),product(a8,a6))) = product(a1,product(product(a8,a6),product(a8,a6))),
inference(monotonicity,[status(thm)],[214]) ).
tff(369,plain,
product(product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9))),product(product(a8,a6),product(a8,a6))) = product(product(product(a1,a6),product(a6,a6)),product(product(a8,a6),product(a8,a6))),
inference(monotonicity,[status(thm)],[223]) ).
tff(370,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9))),product(product(a8,a6),product(a8,a6))) = product(product(product(product(a2,a2),product(a2,a2)),product(product(a8,a6),product(a8,a6))),product(product(product(a5,a9),product(a5,a9)),product(product(a8,a6),product(a8,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(371,plain,
product(product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9))),product(product(a8,a6),product(a8,a6))) = product(product(product(product(a2,a2),product(a2,a2)),product(product(a8,a6),product(a8,a6))),product(product(product(a5,a9),product(a5,a9)),product(product(a8,a6),product(a8,a6)))),
inference(unit_resolution,[status(thm)],[370,46]) ).
tff(372,plain,
product(product(product(product(a2,a2),product(a2,a2)),product(product(a8,a6),product(a8,a6))),product(product(product(a5,a9),product(a5,a9)),product(product(a8,a6),product(a8,a6)))) = product(product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9))),product(product(a8,a6),product(a8,a6))),
inference(symmetry,[status(thm)],[371]) ).
tff(373,plain,
product(product(product(a5,a9),product(a5,a9)),product(product(a8,a6),product(a8,a6))) = product(product(a5,a9),product(a9,a9)),
inference(monotonicity,[status(thm)],[33,39]) ).
tff(374,plain,
product(product(a5,a9),product(a9,a9)) = product(product(product(a5,a9),product(a5,a9)),product(product(a8,a6),product(a8,a6))),
inference(symmetry,[status(thm)],[373]) ).
tff(375,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a5,a9),a9) = product(product(a5,a9),product(a9,a9)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(376,plain,
product(product(a5,a9),a9) = product(product(a5,a9),product(a9,a9)),
inference(unit_resolution,[status(thm)],[375,46]) ).
tff(377,plain,
product(a6,a9) = product(product(a5,a9),a9),
inference(monotonicity,[status(thm)],[28]) ).
tff(378,plain,
product(product(a6,a6),product(a8,a6)) = product(a6,a9),
inference(monotonicity,[status(thm)],[30,36]) ).
tff(379,plain,
product(product(a6,a6),product(a8,a6)) = product(product(product(a5,a9),product(a5,a9)),product(product(a8,a6),product(a8,a6))),
inference(transitivity,[status(thm)],[378,377,376,374]) ).
tff(380,plain,
product(product(a8,a6),product(a8,a6)) = product(a8,a6),
inference(transitivity,[status(thm)],[39,112,37]) ).
tff(381,plain,
product(product(product(a2,a2),product(a2,a2)),product(product(a8,a6),product(a8,a6))) = product(product(product(a1,a1),a6),product(a8,a6)),
inference(monotonicity,[status(thm)],[221,380]) ).
tff(382,plain,
product(product(product(a1,a1),a6),product(a8,a6)) = product(product(product(a2,a2),product(a2,a2)),product(product(a8,a6),product(a8,a6))),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a6,a6),product(a8,a6))) = product(product(product(product(a2,a2),product(a2,a2)),product(product(a8,a6),product(a8,a6))),product(product(product(a5,a9),product(a5,a9)),product(product(a8,a6),product(a8,a6)))),
inference(monotonicity,[status(thm)],[382,379]) ).
tff(384,plain,
product(a6,a9) = product(product(a6,a6),product(a8,a6)),
inference(symmetry,[status(thm)],[378]) ).
tff(385,plain,
product(product(a5,a9),a9) = product(a6,a9),
inference(symmetry,[status(thm)],[377]) ).
tff(386,plain,
product(product(a5,a9),product(a9,a9)) = product(product(a5,a9),a9),
inference(symmetry,[status(thm)],[376]) ).
tff(387,plain,
product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6))) = product(a5,a9),
inference(transitivity,[status(thm)],[120,123,32,30,28]) ).
tff(388,plain,
product(product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6))),product(product(a8,a6),product(a8,a6))) = product(product(a5,a9),product(a9,a9)),
inference(monotonicity,[status(thm)],[387,39]) ).
tff(389,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6))),product(product(a8,a6),product(a8,a6))) = product(product(a4,a10),product(a4,a10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(390,plain,
product(product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6))),product(product(a8,a6),product(a8,a6))) = product(product(a4,a10),product(a4,a10)),
inference(unit_resolution,[status(thm)],[389,22]) ).
tff(391,plain,
product(product(a4,a10),product(a4,a10)) = product(product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6))),product(product(a8,a6),product(a8,a6))),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
product(product(a4,a10),product(a4,a10)) = product(product(a6,a6),product(a8,a6)),
inference(transitivity,[status(thm)],[391,388,386,385,384]) ).
tff(393,plain,
product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a4,a10),product(a4,a10))) = product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a6,a6),product(a8,a6))),
inference(monotonicity,[status(thm)],[392]) ).
tff(394,plain,
product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a4,a10),product(a4,a10))) = product(a5,a5),
inference(transitivity,[status(thm)],[393,383,372,369,368,367,364,361,308,306,304,131,119]) ).
tff(395,plain,
product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a4,a10),product(a4,a10))),product(product(a8,a6),product(a8,a6))) = product(product(a5,a5),a9),
inference(monotonicity,[status(thm)],[394,113]) ).
tff(396,plain,
product(product(a5,a5),a9) = product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a4,a10),product(a4,a10))),product(product(a8,a6),product(a8,a6))),
inference(symmetry,[status(thm)],[395]) ).
tff(397,plain,
product(a5,a9) = a1,
inference(transitivity,[status(thm)],[27,234,31,124,396,129,127,110,108,61,55]) ).
tff(398,plain,
product(product(a9,a9),product(a5,a9)) = product(product(product(a8,a6),product(a8,a6)),a1),
inference(monotonicity,[status(thm)],[38,397]) ).
tff(399,plain,
product(product(product(a8,a6),product(a8,a6)),a1) = product(product(a9,a9),product(a5,a9)),
inference(symmetry,[status(thm)],[398]) ).
tff(400,plain,
product(product(a1,product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = product(product(product(a1,a1),a6),product(a6,a6)),
inference(symmetry,[status(thm)],[205]) ).
tff(401,plain,
a1 = product(product(a1,product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[200]) ).
tff(402,plain,
a1 = product(product(a1,a6),product(a6,a6)),
inference(transitivity,[status(thm)],[401,400,218,217,216,212]) ).
tff(403,plain,
product(product(product(a8,a6),product(a8,a6)),a1) = product(product(product(a8,a6),product(a8,a6)),product(product(a1,a6),product(a6,a6))),
inference(monotonicity,[status(thm)],[402]) ).
tff(404,plain,
product(product(product(a8,a6),product(a8,a6)),product(product(a1,a6),product(a6,a6))) = product(product(product(a8,a6),product(a8,a6)),a1),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
product(product(product(a1,a1),a6),product(a6,a6)) = product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[222]) ).
tff(406,plain,
product(product(a1,a6),product(a6,a6)) = product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9))),
inference(transitivity,[status(thm)],[213,210,209,207,405]) ).
tff(407,plain,
product(product(a8,a8),a6) = product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[50]) ).
tff(408,plain,
product(product(a8,a6),product(a8,a6)) = product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),
inference(transitivity,[status(thm)],[283,407]) ).
tff(409,plain,
product(product(product(a8,a6),product(a8,a6)),product(product(a1,a6),product(a6,a6))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))),
inference(monotonicity,[status(thm)],[408,406]) ).
tff(410,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) = product(product(product(a8,a6),product(a8,a6)),product(product(a1,a6),product(a6,a6))),
inference(symmetry,[status(thm)],[409]) ).
tff(411,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(412,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))),
inference(unit_resolution,[status(thm)],[411,46]) ).
tff(413,plain,
product(product(a6,a2),product(a2,a2)) = product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[268]) ).
tff(414,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(a2,a2),product(a2,a2))) = product(product(a6,a2),product(a2,a2)),
inference(symmetry,[status(thm)],[346]) ).
tff(415,plain,
product(product(a5,a9),product(a5,a9)) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[341]) ).
tff(416,plain,
product(product(a5,a9),product(a5,a9)) = product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[415,414,413]) ).
tff(417,plain,
product(product(a2,a2),product(a2,a2)) = a2,
inference(transitivity,[status(thm)],[220,75,78]) ).
tff(418,plain,
product(a9,product(product(a5,a9),product(a5,a9))) = product(product(a8,a6),product(a6,a6)),
inference(monotonicity,[status(thm)],[37,32]) ).
tff(419,plain,
product(product(a8,a6),product(a6,a6)) = product(a9,product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[418]) ).
tff(420,plain,
product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))) = product(product(a9,product(product(a5,a9),product(a5,a9))),a2),
inference(monotonicity,[status(thm)],[419,417]) ).
tff(421,plain,
product(product(a9,product(product(a5,a9),product(a5,a9))),a2) = product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
a2 = product(product(a2,a2),product(a2,a2)),
inference(transitivity,[status(thm)],[79,76,342]) ).
tff(423,plain,
a9 = product(a9,a9),
inference(symmetry,[status(thm)],[112]) ).
tff(424,plain,
product(a8,a6) = product(a9,a9),
inference(transitivity,[status(thm)],[36,423]) ).
tff(425,plain,
product(product(a8,a6),product(a6,a6)) = product(product(a9,a9),product(a5,a9)),
inference(monotonicity,[status(thm)],[424,246]) ).
tff(426,plain,
product(a9,product(product(a5,a9),product(a5,a9))) = product(product(a7,a3),product(a7,a3)),
inference(transitivity,[status(thm)],[418,425,53,24]) ).
tff(427,plain,
product(product(a9,product(product(a5,a9),product(a5,a9))),a2) = product(product(product(a7,a3),product(a7,a3)),product(product(a2,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[426,422]) ).
tff(428,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a2,a2),product(a2,a2))) = product(product(a9,product(product(a5,a9),product(a5,a9))),a2),
inference(symmetry,[status(thm)],[427]) ).
tff(429,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a2,a2),product(a2,a2))) = product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[428,421]) ).
tff(430,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))),
inference(monotonicity,[status(thm)],[429,416]) ).
tff(431,plain,
product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[430]) ).
tff(432,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2))) = a1,
inference(transitivity,[status(thm)],[268,346,341,124,396,129,127,110,108,61,55]) ).
tff(433,plain,
product(product(a6,a2),product(a2,a2)) = product(product(a5,a9),product(a5,a9)),
inference(transitivity,[status(thm)],[346,341]) ).
tff(434,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a2,a2))) = product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))),
inference(monotonicity,[status(thm)],[433]) ).
tff(435,plain,
product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))) = product(product(a6,a2),product(a6,a2)),
inference(transitivity,[status(thm)],[236,262,225]) ).
tff(436,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))) = product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[435,268]) ).
tff(437,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a5,a9),product(a5,a9)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(438,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))),
inference(unit_resolution,[status(thm)],[437,46]) ).
tff(439,plain,
product(product(a5,a9),product(a5,a9)) = product(a7,product(product(a1,a6),product(a1,a6))),
inference(transitivity,[status(thm)],[415,414,265]) ).
tff(440,plain,
product(product(product(a5,a9),product(a5,a9)),product(product(a6,a2),product(a6,a2))) = product(product(a7,product(product(a1,a6),product(a1,a6))),a7),
inference(monotonicity,[status(thm)],[439,313]) ).
tff(441,plain,
product(product(a7,product(product(a1,a6),product(a1,a6))),a7) = product(product(product(a5,a9),product(a5,a9)),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[440]) ).
tff(442,plain,
product(product(a7,a3),product(a7,a3)) = product(product(product(a5,a9),product(a5,a9)),product(product(a6,a2),product(a6,a2))),
inference(transitivity,[status(thm)],[192,280,274,441]) ).
tff(443,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[442]) ).
tff(444,plain,
product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))) = product(a6,a1),
inference(transitivity,[status(thm)],[420,427,443,438,436,434,241,244,250,252]) ).
tff(445,plain,
product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))) = product(product(a6,a1),a1),
inference(monotonicity,[status(thm)],[444,432]) ).
tff(446,plain,
product(product(a6,a1),a1) = product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
product(product(product(a7,a3),product(a3,a3)),product(product(a5,a9),product(a5,a9))) = product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))),
inference(monotonicity,[status(thm)],[358]) ).
tff(448,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))) = product(product(product(a7,a3),product(a3,a3)),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[447]) ).
tff(449,plain,
product(a6,a1) = product(product(product(a7,a3),product(a3,a3)),product(product(a5,a9),product(a5,a9))),
inference(transitivity,[status(thm)],[253,251,245,242,448]) ).
tff(450,plain,
product(product(a6,a1),a1) = product(product(product(product(a7,a3),product(a3,a3)),product(product(a5,a9),product(a5,a9))),a1),
inference(monotonicity,[status(thm)],[449]) ).
tff(451,plain,
product(product(product(product(a7,a3),product(a3,a3)),product(product(a5,a9),product(a5,a9))),a1) = product(product(a6,a1),a1),
inference(symmetry,[status(thm)],[450]) ).
tff(452,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a7,a3),product(a3,a3)),product(product(a5,a9),product(a5,a9))),a1) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a5,a9),product(a5,a9)),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(453,plain,
product(product(product(product(a7,a3),product(a3,a3)),product(product(a5,a9),product(a5,a9))),a1) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a5,a9),product(a5,a9)),a1)),
inference(unit_resolution,[status(thm)],[452,46]) ).
tff(454,plain,
product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a5,a9),product(a5,a9)),a1)) = product(product(product(product(a7,a3),product(a3,a3)),product(product(a5,a9),product(a5,a9))),a1),
inference(symmetry,[status(thm)],[453]) ).
tff(455,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))) = product(product(product(a7,a3),product(a7,a3)),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[443]) ).
tff(456,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[438]) ).
tff(457,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a2,a2))) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))),
inference(symmetry,[status(thm)],[436]) ).
tff(458,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))) = product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[434]) ).
tff(459,plain,
product(product(product(a5,a9),product(a5,a9)),a1) = product(a6,a1),
inference(monotonicity,[status(thm)],[49]) ).
tff(460,plain,
product(product(product(a5,a9),product(a5,a9)),a1) = product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[459,253,251,245,242,458,457,456,455,428,421]) ).
tff(461,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a8,a1),a6) = product(product(a8,a6),product(a1,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(462,plain,
product(product(a8,a1),a6) = product(product(a8,a6),product(a1,a6)),
inference(unit_resolution,[status(thm)],[461,46]) ).
tff(463,plain,
product(product(a8,a6),product(a1,a6)) = product(product(a8,a1),a6),
inference(symmetry,[status(thm)],[462]) ).
tff(464,plain,
product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))) = product(product(product(a8,a1),a6),product(product(a1,a1),a6)),
inference(monotonicity,[status(thm)],[463,221]) ).
tff(465,plain,
product(product(product(a8,a1),a6),product(product(a1,a1),a6)) = product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[464]) ).
tff(466,plain,
product(product(a1,a1),a6) = product(product(a2,a2),product(a2,a2)),
inference(transitivity,[status(thm)],[70,342]) ).
tff(467,plain,
product(product(product(a8,a6),product(a8,a6)),product(product(a2,a2),product(a2,a2))) = product(product(a9,a9),a2),
inference(monotonicity,[status(thm)],[39,417]) ).
tff(468,plain,
product(product(a9,a9),a2) = product(product(product(a8,a6),product(a8,a6)),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[467]) ).
tff(469,plain,
product(product(a1,a1),a6) = a2,
inference(transitivity,[status(thm)],[70,75,78]) ).
tff(470,plain,
product(product(a8,a6),product(product(a1,a1),a6)) = product(product(a9,a9),a2),
inference(monotonicity,[status(thm)],[424,469]) ).
tff(471,plain,
product(product(a8,a6),product(a1,a6)) = product(product(a8,a6),product(product(a1,a1),a6)),
inference(monotonicity,[status(thm)],[80]) ).
tff(472,plain,
product(product(a8,a1),a6) = product(product(product(a8,a6),product(a8,a6)),product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[462,471,470,468]) ).
tff(473,plain,
product(product(product(a8,a1),a6),product(product(a1,a1),a6)) = product(product(product(product(a8,a6),product(a8,a6)),product(product(a2,a2),product(a2,a2))),product(product(a2,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[472,466]) ).
tff(474,plain,
product(product(product(product(a8,a6),product(a8,a6)),product(product(a2,a2),product(a2,a2))),product(product(a2,a2),product(a2,a2))) = product(product(product(a8,a1),a6),product(product(a1,a1),a6)),
inference(symmetry,[status(thm)],[473]) ).
tff(475,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a8,a6),product(a8,a6)),product(product(a2,a2),product(a2,a2))),product(product(a2,a2),product(a2,a2))) = product(product(a8,a6),product(a8,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(476,plain,
product(product(product(product(a8,a6),product(a8,a6)),product(product(a2,a2),product(a2,a2))),product(product(a2,a2),product(a2,a2))) = product(product(a8,a6),product(a8,a6)),
inference(unit_resolution,[status(thm)],[475,22]) ).
tff(477,plain,
product(product(a8,a6),product(a8,a6)) = product(product(product(product(a8,a6),product(a8,a6)),product(product(a2,a2),product(a2,a2))),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[476]) ).
tff(478,plain,
product(product(product(a6,a1),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(a8,a8),a6),
inference(symmetry,[status(thm)],[282]) ).
tff(479,plain,
product(product(product(a6,a1),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) = product(product(product(a6,a1),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[233]) ).
tff(480,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a1,a6),product(a6,a6))) = product(product(product(a6,a1),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))),
inference(symmetry,[status(thm)],[231]) ).
tff(481,plain,
product(product(product(a6,a2),product(a6,a2)),a1) = product(product(product(a6,a2),product(a6,a2)),product(product(a1,a6),product(a6,a6))),
inference(symmetry,[status(thm)],[215]) ).
tff(482,plain,
product(product(product(a7,a3),product(a3,a3)),a1) = product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[289,197,481,480,479,478,48,477,474,465]) ).
tff(483,plain,
product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a5,a9),product(a5,a9)),a1)) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2)))),
inference(monotonicity,[status(thm)],[482,460]) ).
tff(484,plain,
product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2)))) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a5,a9),product(a5,a9)),a1)),
inference(symmetry,[status(thm)],[483]) ).
tff(485,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a8,a6),product(a1,a6)),product(product(a8,a6),product(a6,a6))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(486,plain,
product(product(product(product(a8,a6),product(a1,a6)),product(product(a8,a6),product(a6,a6))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2)))),
inference(unit_resolution,[status(thm)],[485,46]) ).
tff(487,plain,
product(product(a8,a6),product(a6,a6)) = product(product(a7,a3),product(a7,a3)),
inference(transitivity,[status(thm)],[425,53,24]) ).
tff(488,plain,
product(product(product(a8,a6),product(a6,a6)),product(product(a6,a2),product(a6,a2))) = product(product(product(a7,a3),product(a7,a3)),product(product(a6,a2),product(a6,a2))),
inference(monotonicity,[status(thm)],[487]) ).
tff(489,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a6,a2),product(a6,a2))) = product(product(product(a8,a6),product(a6,a6)),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[488]) ).
tff(490,plain,
product(product(a7,a3),product(a7,a3)) = product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))),
inference(transitivity,[status(thm)],[192,189]) ).
tff(491,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))),product(product(a6,a2),product(a6,a2))),
inference(monotonicity,[status(thm)],[490]) ).
tff(492,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))),product(product(a6,a2),product(a6,a2))) = product(product(product(a7,a3),product(a7,a3)),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[491]) ).
tff(493,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(494,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2)))),
inference(unit_resolution,[status(thm)],[493,46]) ).
tff(495,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2)))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a2,a7))),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[494]) ).
tff(496,plain,
product(a3,product(product(a6,a2),product(a6,a2))) = product(product(a2,a7),product(a7,a7)),
inference(symmetry,[status(thm)],[331]) ).
tff(497,plain,
product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2))) = product(product(a2,a7),product(a7,a7)),
inference(transitivity,[status(thm)],[329,496]) ).
tff(498,plain,
product(a7,a7) = product(a6,a2),
inference(transitivity,[status(thm)],[261,185]) ).
tff(499,plain,
product(product(a7,a7),product(a7,a7)) = product(product(a6,a2),product(a6,a2)),
inference(monotonicity,[status(thm)],[498,498]) ).
tff(500,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))) = product(product(a7,a7),product(a7,a7)),
inference(monotonicity,[status(thm)],[187,187]) ).
tff(501,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))) = product(product(a6,a2),product(a6,a2)),
inference(transitivity,[status(thm)],[500,499]) ).
tff(502,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2)))) = product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a7,a7))),
inference(monotonicity,[status(thm)],[501,497]) ).
tff(503,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a7,a7))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a7),product(a2,a7)),product(product(a6,a2),product(a6,a2)))),
inference(symmetry,[status(thm)],[502]) ).
tff(504,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))),product(product(a6,a2),product(a6,a2))) = product(product(a2,a2),product(a2,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(505,plain,
product(product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))),product(product(a6,a2),product(a6,a2))) = product(product(a2,a2),product(a2,a2)),
inference(unit_resolution,[status(thm)],[504,22]) ).
tff(506,plain,
product(a3,product(product(a6,a2),product(a6,a2))) = product(product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))),product(product(a6,a2),product(a6,a2))),
inference(monotonicity,[status(thm)],[328]) ).
tff(507,plain,
product(product(a2,a7),product(a7,a7)) = product(a2,a2),
inference(transitivity,[status(thm)],[331,506,505,220,75]) ).
tff(508,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a7,a7))) = product(product(a6,a2),product(a2,a2)),
inference(monotonicity,[status(thm)],[267,507]) ).
tff(509,plain,
product(product(a6,a2),product(a2,a2)) = product(product(product(a6,a2),product(a6,a2)),product(product(a2,a7),product(a7,a7))),
inference(symmetry,[status(thm)],[508]) ).
tff(510,plain,
product(a6,a6) = product(product(product(a8,a6),product(a6,a6)),product(product(a6,a2),product(a6,a2))),
inference(transitivity,[status(thm)],[31,415,414,509,503,495,492,489]) ).
tff(511,plain,
product(product(a6,a6),product(product(a1,a1),a6)) = product(product(product(product(a8,a6),product(a6,a6)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[510,466]) ).
tff(512,plain,
product(product(product(product(a8,a6),product(a6,a6)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))) = product(product(a6,a6),product(product(a1,a1),a6)),
inference(symmetry,[status(thm)],[511]) ).
tff(513,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a8,a6),product(a6,a6)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(514,plain,
product(product(product(product(a8,a6),product(a6,a6)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))),
inference(unit_resolution,[status(thm)],[513,46]) ).
tff(515,plain,
product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))) = product(product(product(product(a8,a6),product(a6,a6)),product(product(a6,a2),product(a6,a2))),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[514]) ).
tff(516,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a7,a3),product(a3,a3))) = product(product(product(a7,a3),product(a7,a3)),product(product(a6,a2),product(a6,a2))),
inference(monotonicity,[status(thm)],[358]) ).
tff(517,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a7,a3),product(a3,a3))) = a6,
inference(transitivity,[status(thm)],[516,491,494,502,508,346,341,32,30]) ).
tff(518,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a7,a3),product(a3,a3))),a1) = product(a6,a1),
inference(monotonicity,[status(thm)],[517]) ).
tff(519,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a7,a3),product(a7,a3)),product(product(a7,a3),product(a3,a3))),a1) = product(product(product(product(a7,a3),product(a7,a3)),a1),product(product(product(a7,a3),product(a3,a3)),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(520,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a7,a3),product(a3,a3))),a1) = product(product(product(product(a7,a3),product(a7,a3)),a1),product(product(product(a7,a3),product(a3,a3)),a1)),
inference(unit_resolution,[status(thm)],[519,46]) ).
tff(521,plain,
product(product(product(product(a7,a3),product(a7,a3)),a1),product(product(product(a7,a3),product(a3,a3)),a1)) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a7,a3),product(a3,a3))),a1),
inference(symmetry,[status(thm)],[520]) ).
tff(522,plain,
product(product(product(a7,a3),product(a7,a3)),a1) = product(product(a8,a8),a1),
inference(monotonicity,[status(thm)],[15]) ).
tff(523,plain,
product(product(a8,a8),a1) = product(product(product(a7,a3),product(a7,a3)),a1),
inference(symmetry,[status(thm)],[522]) ).
tff(524,plain,
product(product(a8,a1),product(a8,a1)) = product(product(product(a7,a3),product(a7,a3)),a1),
inference(transitivity,[status(thm)],[157,523]) ).
tff(525,plain,
product(product(product(a8,a1),product(a8,a1)),product(product(a8,a6),product(a8,a6))) = product(product(product(product(a7,a3),product(a7,a3)),a1),product(product(product(a7,a3),product(a3,a3)),a1)),
inference(monotonicity,[status(thm)],[524,365]) ).
tff(526,plain,
product(product(product(a8,a1),product(a8,a1)),product(product(a8,a6),product(a8,a6))) = product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[525,521,518,253,251,245,242,458,457,456,455,428,421]) ).
tff(527,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a8,a6),product(a8,a6))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a6,a2),product(a6,a2)),product(product(a2,a2),product(a2,a2)))),
inference(monotonicity,[status(thm)],[526,416]) ).
tff(528,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a8,a1),product(a8,a1)),product(product(a8,a6),product(a8,a6))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(529,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a8,a6),product(a8,a6))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9)))),
inference(unit_resolution,[status(thm)],[528,46]) ).
tff(530,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9)))) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a8,a6),product(a8,a6))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[529]) ).
tff(531,plain,
product(product(a8,a6),product(a6,a6)) = product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))),
inference(transitivity,[status(thm)],[425,63]) ).
tff(532,plain,
product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))) = product(product(product(a8,a1),product(a8,a1)),a6),
inference(monotonicity,[status(thm)],[49]) ).
tff(533,plain,
product(product(product(a8,a1),product(a8,a1)),a6) = product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[532]) ).
tff(534,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a8,a1),product(a8,a1)),a6) = product(product(product(a8,a1),a6),product(product(a8,a1),a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(535,plain,
product(product(product(a8,a1),product(a8,a1)),a6) = product(product(product(a8,a1),a6),product(product(a8,a1),a6)),
inference(unit_resolution,[status(thm)],[534,46]) ).
tff(536,plain,
product(product(product(a8,a1),a6),product(product(a8,a1),a6)) = product(product(product(a8,a1),product(a8,a1)),a6),
inference(symmetry,[status(thm)],[535]) ).
tff(537,plain,
product(a9,a2) = product(product(a8,a6),product(a1,a6)),
inference(monotonicity,[status(thm)],[37,203]) ).
tff(538,plain,
product(a9,a2) = product(product(a8,a1),a6),
inference(transitivity,[status(thm)],[537,463]) ).
tff(539,plain,
product(product(a9,a2),product(a9,a2)) = product(product(product(a8,a1),a6),product(product(a8,a1),a6)),
inference(monotonicity,[status(thm)],[538,538]) ).
tff(540,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a9,a9),a2) = product(product(a9,a2),product(a9,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(541,plain,
product(product(a9,a9),a2) = product(product(a9,a2),product(a9,a2)),
inference(unit_resolution,[status(thm)],[540,46]) ).
tff(542,plain,
product(product(a8,a6),product(a1,a6)) = product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),
inference(transitivity,[status(thm)],[471,470,541,539,536,533]) ).
tff(543,plain,
product(product(product(a8,a6),product(a1,a6)),product(product(a8,a6),product(a6,a6))) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9)))),
inference(monotonicity,[status(thm)],[542,531]) ).
tff(544,plain,
product(product(product(a8,a6),product(a1,a6)),product(product(a8,a6),product(a6,a6))) = product(a6,a2),
inference(transitivity,[status(thm)],[543,530,527,515,512,262,225,187,261,185]) ).
tff(545,plain,
product(product(product(product(a8,a6),product(a1,a6)),product(product(a8,a6),product(a6,a6))),product(product(a2,a2),product(a2,a2))) = product(product(a6,a2),product(a2,a2)),
inference(monotonicity,[status(thm)],[544,266]) ).
tff(546,plain,
product(product(a6,a2),product(a2,a2)) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a8,a6),product(a6,a6))),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[545]) ).
tff(547,plain,
product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a8,a6),product(a8,a6))),product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6)))) = product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a4,a10),product(a4,a10))),product(product(a8,a6),product(a8,a6))),
inference(symmetry,[status(thm)],[129]) ).
tff(548,plain,
product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a5,a9),product(a5,a9))),product(product(product(a8,a6),product(a8,a6)),product(product(a5,a9),product(a5,a9)))) = product(product(product(product(product(a1,a1),a6),product(a8,a6)),product(product(a8,a6),product(a8,a6))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[110]) ).
tff(549,plain,
a1 = product(product(a1,product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))),
inference(symmetry,[status(thm)],[55]) ).
tff(550,plain,
a1 = product(a6,a6),
inference(transitivity,[status(thm)],[549,60,107,548,126,547,395,123,32]) ).
tff(551,plain,
product(a6,a1) = product(product(a6,a6),product(a6,a6)),
inference(monotonicity,[status(thm)],[234,550]) ).
tff(552,plain,
a1 = product(product(a5,a9),product(a5,a9)),
inference(transitivity,[status(thm)],[549,60,107,548,126,547,395,123]) ).
tff(553,plain,
product(product(product(a6,a2),product(a6,a2)),a1) = product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))),
inference(monotonicity,[status(thm)],[552]) ).
tff(554,plain,
a9 = a8,
inference(transitivity,[status(thm)],[423,38,283,282,233,231,215,553,241,244,250,252,551,247,415,414,546,486,484,454,451,446,431,412,410,404,399,53,24,15,9]) ).
tff(555,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = product(product(a8,a1),product(a8,a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(556,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = product(product(a8,a1),product(a8,a1)),
inference(unit_resolution,[status(thm)],[555,22]) ).
tff(557,plain,
product(product(a8,a1),a6) = product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),
inference(transitivity,[status(thm)],[462,471,470,541,539,536,533]) ).
tff(558,plain,
product(product(product(a8,a1),a6),product(a6,a6)) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))),
inference(monotonicity,[status(thm)],[557,31]) ).
tff(559,plain,
product(product(product(a8,a6),product(a1,a6)),a1) = product(product(product(a8,a1),a6),product(a6,a6)),
inference(monotonicity,[status(thm)],[463,550]) ).
tff(560,plain,
product(product(a8,a6),product(product(a1,a1),a6)) = product(product(a8,a6),product(a1,a6)),
inference(symmetry,[status(thm)],[471]) ).
tff(561,plain,
product(product(a9,a9),a2) = product(product(a8,a6),product(product(a1,a1),a6)),
inference(symmetry,[status(thm)],[470]) ).
tff(562,plain,
product(product(a8,a6),product(a6,a6)) = product(a8,a8),
inference(transitivity,[status(thm)],[425,53,24,15]) ).
tff(563,plain,
product(product(product(a8,a6),product(a6,a6)),product(product(a5,a9),product(a5,a9))) = product(product(a8,a8),a6),
inference(monotonicity,[status(thm)],[562,49]) ).
tff(564,plain,
product(product(product(a8,a6),product(a6,a6)),product(product(a5,a9),product(a5,a9))) = product(a9,a9),
inference(transitivity,[status(thm)],[563,48,39]) ).
tff(565,plain,
product(product(product(product(a8,a6),product(a6,a6)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))) = product(product(a9,a9),a2),
inference(monotonicity,[status(thm)],[564,417]) ).
tff(566,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a8,a6),product(a6,a6)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(567,plain,
product(product(product(product(a8,a6),product(a6,a6)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))),
inference(unit_resolution,[status(thm)],[566,46]) ).
tff(568,plain,
product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))) = product(product(product(product(a8,a6),product(a6,a6)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[567]) ).
tff(569,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a9,product(product(a5,a9),product(a5,a9))),a2) = product(product(a9,a2),product(product(product(a5,a9),product(a5,a9)),a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(570,plain,
product(product(a9,product(product(a5,a9),product(a5,a9))),a2) = product(product(a9,a2),product(product(product(a5,a9),product(a5,a9)),a2)),
inference(unit_resolution,[status(thm)],[569,46]) ).
tff(571,plain,
product(product(a9,a2),product(product(product(a5,a9),product(a5,a9)),a2)) = product(product(a9,product(product(a5,a9),product(a5,a9))),a2),
inference(symmetry,[status(thm)],[570]) ).
tff(572,plain,
product(product(product(a5,a9),product(a5,a9)),a2) = product(product(a6,a6),a2),
inference(monotonicity,[status(thm)],[32]) ).
tff(573,plain,
product(product(a6,a6),a2) = product(product(product(a5,a9),product(a5,a9)),a2),
inference(symmetry,[status(thm)],[572]) ).
tff(574,plain,
product(a6,a2) = product(product(product(a5,a9),product(a5,a9)),a2),
inference(transitivity,[status(thm)],[184,344,186,239,573]) ).
tff(575,plain,
product(product(a9,a2),product(a6,a2)) = product(product(a9,a2),product(product(product(a5,a9),product(a5,a9)),a2)),
inference(monotonicity,[status(thm)],[574]) ).
tff(576,plain,
product(product(a8,a6),product(a1,a6)) = product(a9,a2),
inference(symmetry,[status(thm)],[537]) ).
tff(577,plain,
product(product(product(a8,a6),product(a1,a6)),product(product(a6,a2),product(a6,a2))) = product(product(a9,a2),product(a6,a2)),
inference(monotonicity,[status(thm)],[576,267]) ).
tff(578,plain,
product(product(product(a8,a6),product(a1,a6)),product(product(a6,a2),product(a6,a2))) = product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[577,575,571,421]) ).
tff(579,plain,
product(product(product(product(a8,a6),product(a1,a6)),product(product(a6,a2),product(a6,a2))),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))),
inference(monotonicity,[status(thm)],[578,240]) ).
tff(580,plain,
product(product(a9,a2),product(a6,a2)) = product(product(product(a8,a6),product(a1,a6)),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[577]) ).
tff(581,plain,
product(product(a9,a2),product(product(product(a5,a9),product(a5,a9)),a2)) = product(product(a9,a2),product(a6,a2)),
inference(symmetry,[status(thm)],[575]) ).
tff(582,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a2,a2))) = product(product(product(a8,a6),product(a1,a6)),product(product(a6,a2),product(a6,a2))),
inference(transitivity,[status(thm)],[457,456,455,428,570,581,580]) ).
tff(583,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a6,a2),product(a6,a2))),product(product(a6,a2),product(a6,a2))),
inference(monotonicity,[status(thm)],[582]) ).
tff(584,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))),product(product(product(a6,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(585,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))),product(product(product(a6,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))),
inference(unit_resolution,[status(thm)],[584,46]) ).
tff(586,plain,
product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))),product(product(product(a6,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[585]) ).
tff(587,plain,
product(product(product(a6,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))) = product(product(a7,product(product(a1,a6),product(a1,a6))),a7),
inference(monotonicity,[status(thm)],[265,313]) ).
tff(588,plain,
product(product(a7,product(product(a1,a6),product(a1,a6))),a7) = product(product(product(a6,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[587]) ).
tff(589,plain,
product(product(a7,a3),product(a7,a3)) = product(product(product(a6,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2))),
inference(transitivity,[status(thm)],[192,280,274,588]) ).
tff(590,plain,
product(product(a7,a7),product(a7,a7)) = product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[500]) ).
tff(591,plain,
product(product(a6,a2),product(a6,a2)) = product(product(a7,a7),product(a7,a7)),
inference(symmetry,[status(thm)],[499]) ).
tff(592,plain,
product(product(a6,a2),product(a6,a2)) = product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))),
inference(transitivity,[status(thm)],[591,590]) ).
tff(593,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a7,a3),product(a7,a3))) = product(product(product(product(a6,a2),product(a6,a2)),product(product(a6,a2),product(a6,a2))),product(product(product(a6,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))),
inference(monotonicity,[status(thm)],[592,589]) ).
tff(594,plain,
product(product(product(a7,a3),product(a3,a3)),product(product(a7,a3),product(a7,a3))) = product(product(product(a6,a2),product(a6,a2)),product(product(a7,a3),product(a7,a3))),
inference(monotonicity,[status(thm)],[358]) ).
tff(595,plain,
product(product(product(a7,a3),product(a3,a3)),product(product(a7,a3),product(a7,a3))) = product(product(a8,a6),product(a1,a6)),
inference(transitivity,[status(thm)],[594,593,586,583,579,568,565,561,560]) ).
tff(596,plain,
product(product(product(product(a7,a3),product(a3,a3)),product(product(a7,a3),product(a7,a3))),a1) = product(product(product(a8,a6),product(a1,a6)),a1),
inference(monotonicity,[status(thm)],[595]) ).
tff(597,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a7,a3),product(a3,a3)),product(product(a7,a3),product(a7,a3))),a1) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a7,a3),product(a7,a3)),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(598,plain,
product(product(product(product(a7,a3),product(a3,a3)),product(product(a7,a3),product(a7,a3))),a1) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a7,a3),product(a7,a3)),a1)),
inference(unit_resolution,[status(thm)],[597,46]) ).
tff(599,plain,
product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a7,a3),product(a7,a3)),a1)) = product(product(product(product(a7,a3),product(a3,a3)),product(product(a7,a3),product(a7,a3))),a1),
inference(symmetry,[status(thm)],[598]) ).
tff(600,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a3,a1),product(a3,a1))),product(product(a8,a1),product(a8,a1))) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a7,a3),product(a7,a3)),a1)),
inference(monotonicity,[status(thm)],[292,524]) ).
tff(601,plain,
product(product(a8,a6),product(a8,a6)) = product(product(product(a8,a1),product(a8,a1)),product(product(a3,a1),product(a3,a1))),
inference(transitivity,[status(thm)],[283,282,233,231,215,198,176,174,160]) ).
tff(602,plain,
product(product(product(a8,a6),product(a8,a6)),product(product(a8,a1),product(a8,a1))) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a3,a1),product(a3,a1))),product(product(a8,a1),product(a8,a1))),
inference(monotonicity,[status(thm)],[601]) ).
tff(603,plain,
product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a2,a7),product(a2,a7)),a1)) = product(product(product(product(a7,a3),product(a3,a3)),product(product(a2,a7),product(a2,a7))),a1),
inference(symmetry,[status(thm)],[296]) ).
tff(604,plain,
product(product(a9,a4),product(a9,a4)) = product(product(a9,a9),a4),
inference(symmetry,[status(thm)],[141]) ).
tff(605,plain,
product(product(a9,a4),product(a9,a4)) = product(product(a8,a1),product(a8,a1)),
inference(transitivity,[status(thm)],[604,285,293,603,300,156]) ).
tff(606,plain,
product(product(product(a8,a6),product(a8,a6)),product(product(a9,a4),product(a9,a4))) = product(product(product(a8,a6),product(a8,a6)),product(product(a8,a1),product(a8,a1))),
inference(monotonicity,[status(thm)],[605]) ).
tff(607,plain,
a10 = product(a10,a10),
inference(symmetry,[status(thm)],[133]) ).
tff(608,plain,
a10 = product(product(a9,a4),product(a9,a4)),
inference(transitivity,[status(thm)],[607,138]) ).
tff(609,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a8,a6),product(a8,a6)),product(product(a3,a1),product(a3,a1))),product(product(a3,a1),product(a3,a1))) = product(product(a8,a6),product(a8,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(610,plain,
product(product(product(product(a8,a6),product(a8,a6)),product(product(a3,a1),product(a3,a1))),product(product(a3,a1),product(a3,a1))) = product(product(a8,a6),product(a8,a6)),
inference(unit_resolution,[status(thm)],[609,22]) ).
tff(611,plain,
product(product(a3,a1),product(a3,a1)) = a4,
inference(transitivity,[status(thm)],[151,148]) ).
tff(612,plain,
product(product(product(a8,a6),product(a8,a6)),product(product(a3,a1),product(a3,a1))) = product(product(a9,a9),a4),
inference(monotonicity,[status(thm)],[39,611]) ).
tff(613,plain,
product(product(a9,a9),a4) = product(product(product(a8,a6),product(a8,a6)),product(product(a3,a1),product(a3,a1))),
inference(symmetry,[status(thm)],[612]) ).
tff(614,plain,
product(a9,a4) = product(product(product(a8,a6),product(a8,a6)),product(product(a3,a1),product(a3,a1))),
inference(transitivity,[status(thm)],[136,607,138,604,613]) ).
tff(615,plain,
product(product(a9,a4),product(a4,a4)) = product(product(product(product(a8,a6),product(a8,a6)),product(product(a3,a1),product(a3,a1))),product(product(a3,a1),product(a3,a1))),
inference(monotonicity,[status(thm)],[614,146]) ).
tff(616,plain,
product(a10,product(product(a3,a1),product(a3,a1))) = product(product(a9,a4),product(a4,a4)),
inference(monotonicity,[status(thm)],[137,151]) ).
tff(617,plain,
product(a10,product(product(a3,a1),product(a3,a1))) = product(product(a8,a6),product(a8,a6)),
inference(transitivity,[status(thm)],[616,615,610]) ).
tff(618,plain,
product(product(a10,product(product(a3,a1),product(a3,a1))),a10) = product(product(product(a8,a6),product(a8,a6)),product(product(a9,a4),product(a9,a4))),
inference(monotonicity,[status(thm)],[617,608]) ).
tff(619,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a10,product(product(a3,a1),product(a3,a1))),a10) = product(product(a10,a10),product(product(product(a3,a1),product(a3,a1)),a10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(620,plain,
product(product(a10,product(product(a3,a1),product(a3,a1))),a10) = product(product(a10,a10),product(product(product(a3,a1),product(a3,a1)),a10)),
inference(unit_resolution,[status(thm)],[619,46]) ).
tff(621,plain,
product(product(a10,a10),product(product(product(a3,a1),product(a3,a1)),a10)) = product(product(a10,product(product(a3,a1),product(a3,a1))),a10),
inference(symmetry,[status(thm)],[620]) ).
tff(622,plain,
product(product(product(a3,a1),product(a3,a1)),a10) = product(product(a4,a4),a10),
inference(monotonicity,[status(thm)],[151]) ).
tff(623,plain,
product(product(a4,a4),a10) = product(product(product(a3,a1),product(a3,a1)),a10),
inference(symmetry,[status(thm)],[622]) ).
tff(624,plain,
product(product(a4,a10),product(a4,a10)) = product(product(a4,a4),a10),
inference(symmetry,[status(thm)],[131]) ).
tff(625,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a5,a5) = a5 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(626,plain,
product(a5,a5) = a5,
inference(unit_resolution,[status(thm)],[625,7]) ).
tff(627,plain,
a5 = product(a5,a5),
inference(symmetry,[status(thm)],[626]) ).
tff(628,plain,
a5 = product(product(product(a3,a1),product(a3,a1)),a10),
inference(transitivity,[status(thm)],[627,118,624,623]) ).
tff(629,plain,
product(product(a10,a10),a5) = product(product(a10,a10),product(product(product(a3,a1),product(a3,a1)),a10)),
inference(monotonicity,[status(thm)],[628]) ).
tff(630,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a10,a10),a5) = product(product(a10,a5),product(a10,a5)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(631,plain,
product(product(a10,a10),a5) = product(product(a10,a5),product(a10,a5)),
inference(unit_resolution,[status(thm)],[630,46]) ).
tff(632,plain,
product(product(a10,a5),product(a10,a5)) = product(product(a10,a10),a5),
inference(symmetry,[status(thm)],[631]) ).
tff(633,plain,
( ( product(a10,a5) = a11 )
<=> ( product(a10,a5) = a11 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(634,axiom,
product(a10,a5) = a11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_11) ).
tff(635,plain,
product(a10,a5) = a11,
inference(modus_ponens,[status(thm)],[634,633]) ).
tff(636,plain,
a11 = product(a10,a5),
inference(symmetry,[status(thm)],[635]) ).
tff(637,plain,
product(a11,a11) = product(product(a10,a5),product(a10,a5)),
inference(monotonicity,[status(thm)],[636,636]) ).
tff(638,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a11,a11) = a11 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(639,plain,
product(a11,a11) = a11,
inference(unit_resolution,[status(thm)],[638,7]) ).
tff(640,plain,
a11 = product(a11,a11),
inference(symmetry,[status(thm)],[639]) ).
tff(641,plain,
a11 = a10,
inference(transitivity,[status(thm)],[640,637,632,629,621,618,606,602,600,599,596,559,558,556,157,301,296,294,286,141,139,133]) ).
tff(642,plain,
a1 = a6,
inference(transitivity,[status(thm)],[549,60,107,548,126,547,395,123,32,30]) ).
tff(643,plain,
product(product(a8,a8),a1) = product(product(a8,a8),a6),
inference(monotonicity,[status(thm)],[642]) ).
tff(644,plain,
a10 = a9,
inference(transitivity,[status(thm)],[607,138,604,285,293,603,300,643,48,39,112]) ).
tff(645,plain,
product(product(a3,a3),a1) = product(product(product(a2,a7),product(a2,a7)),product(product(a5,a9),product(a5,a9))),
inference(monotonicity,[status(thm)],[165,552]) ).
tff(646,plain,
product(product(product(a2,a7),product(a2,a7)),product(product(a5,a9),product(a5,a9))) = product(product(a3,a3),a1),
inference(symmetry,[status(thm)],[645]) ).
tff(647,plain,
product(a2,a6) = a1,
inference(transitivity,[status(thm)],[209,207,205,200]) ).
tff(648,plain,
product(product(a2,a6),a2) = product(a1,product(product(a2,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[647,422]) ).
tff(649,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a2,a6),a2) = product(product(a2,a2),product(a6,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(650,plain,
product(product(a2,a6),a2) = product(product(a2,a2),product(a6,a2)),
inference(unit_resolution,[status(thm)],[649,46]) ).
tff(651,plain,
product(product(a2,a2),product(a6,a2)) = product(product(a2,a6),a2),
inference(symmetry,[status(thm)],[650]) ).
tff(652,plain,
product(product(a2,a2),a7) = product(product(a2,a2),product(a6,a2)),
inference(monotonicity,[status(thm)],[185]) ).
tff(653,plain,
product(product(a2,a7),product(a2,a7)) = product(product(a2,a2),a7),
inference(symmetry,[status(thm)],[276]) ).
tff(654,plain,
product(product(a2,a7),product(a2,a7)) = product(a1,product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[653,652,651,648]) ).
tff(655,plain,
product(product(product(a2,a7),product(a2,a7)),product(product(a5,a9),product(a5,a9))) = product(product(a1,product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))),
inference(monotonicity,[status(thm)],[654]) ).
tff(656,plain,
product(product(a1,product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(a2,a7),product(a2,a7)),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[655]) ).
tff(657,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(a1,product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(658,plain,
product(product(a1,product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(a1,product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))),
inference(unit_resolution,[status(thm)],[657,46]) ).
tff(659,plain,
product(product(a1,product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) = product(product(a1,product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[658]) ).
tff(660,plain,
product(a1,product(product(a5,a9),product(a5,a9))) = product(product(a2,a2),product(a2,a2)),
inference(transitivity,[status(thm)],[201,74,79,76,342]) ).
tff(661,plain,
product(product(a1,product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) = product(product(product(a2,a2),product(a2,a2)),product(product(a1,a6),product(a6,a6))),
inference(monotonicity,[status(thm)],[660,223]) ).
tff(662,plain,
product(product(product(a2,a2),product(a2,a2)),product(product(a1,a6),product(a6,a6))) = product(product(a1,product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))),
inference(symmetry,[status(thm)],[661]) ).
tff(663,plain,
product(product(product(a2,a2),product(a2,a2)),product(product(a1,a6),product(a6,a6))) = product(product(product(a2,a2),product(a2,a2)),a1),
inference(monotonicity,[status(thm)],[214]) ).
tff(664,plain,
product(product(product(a2,a2),product(a2,a2)),a1) = product(product(product(a2,a2),product(a2,a2)),product(product(a1,a6),product(a6,a6))),
inference(symmetry,[status(thm)],[663]) ).
tff(665,plain,
product(product(product(a2,a2),product(a2,a2)),a1) = product(product(product(a1,a1),a6),product(a6,a6)),
inference(monotonicity,[status(thm)],[221,550]) ).
tff(666,plain,
product(product(product(a1,a1),a6),product(a6,a6)) = product(product(product(a2,a2),product(a2,a2)),a1),
inference(symmetry,[status(thm)],[665]) ).
tff(667,plain,
product(product(product(a8,a6),product(a1,a6)),product(product(a1,a6),product(a6,a6))) = product(product(product(a8,a6),product(a1,a6)),a1),
inference(monotonicity,[status(thm)],[214]) ).
tff(668,plain,
product(product(a9,a2),product(a9,a2)) = product(product(a9,a9),a2),
inference(symmetry,[status(thm)],[541]) ).
tff(669,plain,
product(product(product(a8,a1),a6),product(product(a8,a1),a6)) = product(product(a9,a2),product(a9,a2)),
inference(symmetry,[status(thm)],[539]) ).
tff(670,plain,
product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))) = product(product(a8,a6),product(a1,a6)),
inference(transitivity,[status(thm)],[532,535,669,668,561,560]) ).
tff(671,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) = product(product(product(a8,a6),product(a1,a6)),product(product(a1,a6),product(a6,a6))),
inference(monotonicity,[status(thm)],[670,223]) ).
tff(672,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a8,a1),product(a8,a1)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(673,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))),
inference(unit_resolution,[status(thm)],[672,46]) ).
tff(674,plain,
product(product(product(a8,a6),product(a1,a6)),product(product(a5,a9),product(a5,a9))) = product(product(product(a8,a1),a6),product(a6,a6)),
inference(monotonicity,[status(thm)],[463,32]) ).
tff(675,plain,
product(product(product(a8,a6),product(a1,a6)),product(product(a5,a9),product(a5,a9))) = product(product(a8,a1),product(a8,a1)),
inference(transitivity,[status(thm)],[674,558,556]) ).
tff(676,plain,
product(product(product(product(a8,a6),product(a1,a6)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))) = product(product(product(a8,a1),product(a8,a1)),product(product(a2,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[675]) ).
tff(677,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a8,a6),product(a1,a6)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(678,plain,
product(product(product(product(a8,a6),product(a1,a6)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))),
inference(unit_resolution,[status(thm)],[677,46]) ).
tff(679,plain,
product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a5,a9),product(a5,a9))),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[678]) ).
tff(680,plain,
product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a5,a9),product(a5,a9)),product(product(a2,a2),product(a2,a2)))),
inference(monotonicity,[status(thm)],[240]) ).
tff(681,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(682,plain,
product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))),
inference(unit_resolution,[status(thm)],[681,46]) ).
tff(683,plain,
product(product(product(product(a8,a6),product(a1,a6)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(a6,a2),product(a6,a2))),
inference(symmetry,[status(thm)],[682]) ).
tff(684,plain,
product(product(a2,a7),product(a7,a7)) = product(product(a2,a2),product(a2,a2)),
inference(transitivity,[status(thm)],[331,506,505]) ).
tff(685,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a7,a7))) = product(product(product(a7,a3),product(a7,a3)),product(product(a2,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[684]) ).
tff(686,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a7,a7))) = product(product(product(a8,a6),product(a1,a6)),product(product(a6,a2),product(a6,a2))),
inference(transitivity,[status(thm)],[685,428,570,581,580]) ).
tff(687,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a7,a7))),product(product(a2,a7),product(a2,a7))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a6,a2),product(a6,a2))),product(product(product(a2,a2),product(a2,a2)),product(product(a6,a2),product(a6,a2)))),
inference(monotonicity,[status(thm)],[686,353]) ).
tff(688,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a7,a7))),product(product(a2,a7),product(a2,a7))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a2,a7))),product(product(product(a2,a7),product(a7,a7)),product(product(a2,a7),product(a2,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(689,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a7,a7))),product(product(a2,a7),product(a2,a7))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a2,a7))),product(product(product(a2,a7),product(a7,a7)),product(product(a2,a7),product(a2,a7)))),
inference(unit_resolution,[status(thm)],[688,46]) ).
tff(690,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a2,a7))),product(product(product(a2,a7),product(a7,a7)),product(product(a2,a7),product(a2,a7)))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a7,a7))),product(product(a2,a7),product(a2,a7))),
inference(symmetry,[status(thm)],[689]) ).
tff(691,plain,
product(product(a2,a7),a7) = product(a3,a7),
inference(symmetry,[status(thm)],[334]) ).
tff(692,plain,
product(product(a2,a7),product(a7,a7)) = product(product(a2,a7),a7),
inference(symmetry,[status(thm)],[333]) ).
tff(693,plain,
product(product(a2,a7),product(a7,a7)) = product(a3,a7),
inference(transitivity,[status(thm)],[692,691]) ).
tff(694,plain,
product(product(product(a2,a7),product(a7,a7)),product(product(a2,a7),product(a2,a7))) = product(product(a3,a7),a3),
inference(monotonicity,[status(thm)],[693,181]) ).
tff(695,plain,
product(product(a3,a7),a3) = product(product(product(a2,a7),product(a7,a7)),product(product(a2,a7),product(a2,a7))),
inference(symmetry,[status(thm)],[694]) ).
tff(696,plain,
product(product(a3,a3),product(a7,a3)) = product(product(a3,a7),a3),
inference(symmetry,[status(thm)],[312]) ).
tff(697,plain,
product(product(a3,a3),product(a7,a3)) = product(product(product(a2,a7),product(a7,a7)),product(product(a2,a7),product(a2,a7))),
inference(transitivity,[status(thm)],[696,695]) ).
tff(698,plain,
product(product(a7,a3),product(a7,a3)) = product(a7,a3),
inference(transitivity,[status(thm)],[15,9,13]) ).
tff(699,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a2,a7))) = product(product(a7,a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[698,166]) ).
tff(700,plain,
product(product(a7,a3),product(a3,a3)) = product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a2,a7))),
inference(symmetry,[status(thm)],[699]) ).
tff(701,plain,
product(product(product(a7,a3),product(a3,a3)),product(product(a3,a3),product(a7,a3))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a7),product(a2,a7))),product(product(product(a2,a7),product(a7,a7)),product(product(a2,a7),product(a2,a7)))),
inference(monotonicity,[status(thm)],[700,697]) ).
tff(702,plain,
product(product(product(a7,a3),product(a3,a3)),product(product(a3,a3),product(a7,a3))) = product(product(product(a8,a1),product(a8,a1)),product(product(a2,a2),product(a2,a2))),
inference(transitivity,[status(thm)],[701,690,687,683,680,679,676]) ).
tff(703,plain,
product(product(product(product(a7,a3),product(a3,a3)),product(product(a3,a3),product(a7,a3))),a1) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))),
inference(monotonicity,[status(thm)],[702,552]) ).
tff(704,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a7,a3),product(a3,a3)),product(product(a3,a3),product(a7,a3))),a1) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a3,a3),product(a7,a3)),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(705,plain,
product(product(product(product(a7,a3),product(a3,a3)),product(product(a3,a3),product(a7,a3))),a1) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a3,a3),product(a7,a3)),a1)),
inference(unit_resolution,[status(thm)],[704,46]) ).
tff(706,plain,
product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a3,a3),product(a7,a3)),a1)) = product(product(product(product(a7,a3),product(a3,a3)),product(product(a3,a3),product(a7,a3))),a1),
inference(symmetry,[status(thm)],[705]) ).
tff(707,plain,
product(product(product(a3,a3),product(a7,a3)),a1) = product(product(product(product(a2,a7),product(a2,a7)),a8),a1),
inference(monotonicity,[status(thm)],[310]) ).
tff(708,plain,
product(product(product(product(a2,a7),product(a2,a7)),a8),a1) = product(product(product(a3,a3),product(a7,a3)),a1),
inference(symmetry,[status(thm)],[707]) ).
tff(709,plain,
product(product(product(product(a2,a7),product(a2,a7)),a1),product(a8,a1)) = product(product(product(product(a2,a7),product(a2,a7)),a8),a1),
inference(symmetry,[status(thm)],[308]) ).
tff(710,plain,
product(product(a3,a1),product(a8,a1)) = product(product(product(product(a2,a7),product(a2,a7)),a1),product(a8,a1)),
inference(symmetry,[status(thm)],[306]) ).
tff(711,plain,
product(product(a4,a4),a10) = product(product(a3,a1),product(a8,a1)),
inference(symmetry,[status(thm)],[304]) ).
tff(712,plain,
product(product(a4,a10),product(a4,a10)) = product(product(product(a3,a3),product(a7,a3)),a1),
inference(transitivity,[status(thm)],[624,711,710,709,708]) ).
tff(713,plain,
a9 = product(product(product(a7,a3),product(a3,a3)),a1),
inference(transitivity,[status(thm)],[423,38,283,282,233,231,215,198,290]) ).
tff(714,plain,
product(a9,product(product(a4,a10),product(a4,a10))) = product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a3,a3),product(a7,a3)),a1)),
inference(monotonicity,[status(thm)],[713,712]) ).
tff(715,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a3,a1),product(a3,a1)),product(product(a9,a4),product(a9,a4))),product(product(a9,a4),product(a9,a4))) = product(product(a3,a1),product(a3,a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(716,plain,
product(product(product(product(a3,a1),product(a3,a1)),product(product(a9,a4),product(a9,a4))),product(product(a9,a4),product(a9,a4))) = product(product(a3,a1),product(a3,a1)),
inference(unit_resolution,[status(thm)],[715,22]) ).
tff(717,plain,
product(product(a9,a4),product(a9,a4)) = a10,
inference(transitivity,[status(thm)],[139,133]) ).
tff(718,plain,
product(product(product(a3,a1),product(a3,a1)),product(product(a9,a4),product(a9,a4))) = product(product(a4,a4),a10),
inference(monotonicity,[status(thm)],[151,717]) ).
tff(719,plain,
product(product(a4,a4),a10) = product(product(product(a3,a1),product(a3,a1)),product(product(a9,a4),product(a9,a4))),
inference(symmetry,[status(thm)],[718]) ).
tff(720,plain,
a5 = product(product(product(a3,a1),product(a3,a1)),product(product(a9,a4),product(a9,a4))),
inference(transitivity,[status(thm)],[627,118,624,719]) ).
tff(721,plain,
product(a5,product(product(a9,a4),product(a9,a4))) = product(product(product(product(a3,a1),product(a3,a1)),product(product(a9,a4),product(a9,a4))),product(product(a9,a4),product(a9,a4))),
inference(monotonicity,[status(thm)],[720]) ).
tff(722,plain,
product(product(a4,a10),product(a10,a10)) = product(a5,product(product(a9,a4),product(a9,a4))),
inference(monotonicity,[status(thm)],[116,138]) ).
tff(723,plain,
product(product(a4,a10),product(a10,a10)) = product(a4,a4),
inference(transitivity,[status(thm)],[722,721,716,151]) ).
tff(724,plain,
product(product(a9,a4),product(a9,a4)) = product(a9,a4),
inference(transitivity,[status(thm)],[139,133,137]) ).
tff(725,plain,
product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a10,a10))) = product(product(a9,a4),product(a4,a4)),
inference(monotonicity,[status(thm)],[724,723]) ).
tff(726,plain,
product(a5,product(product(a9,a4),product(a9,a4))) = product(product(a4,a10),product(a10,a10)),
inference(symmetry,[status(thm)],[722]) ).
tff(727,plain,
product(product(a4,a10),product(a4,a10)) = a5,
inference(transitivity,[status(thm)],[119,626]) ).
tff(728,plain,
product(product(product(a4,a10),product(a4,a10)),product(product(a9,a4),product(a9,a4))) = product(a5,product(product(a9,a4),product(a9,a4))),
inference(monotonicity,[status(thm)],[727]) ).
tff(729,plain,
product(product(product(a4,a10),product(a4,a10)),product(product(a9,a4),product(a9,a4))) = product(product(a4,a10),product(a10,a10)),
inference(transitivity,[status(thm)],[728,726]) ).
tff(730,plain,
product(a10,a10) = product(a9,a4),
inference(transitivity,[status(thm)],[133,137]) ).
tff(731,plain,
product(product(a10,a10),product(a10,a10)) = product(product(a9,a4),product(a9,a4)),
inference(monotonicity,[status(thm)],[730,730]) ).
tff(732,plain,
product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a9,a4))) = product(product(a10,a10),product(a10,a10)),
inference(monotonicity,[status(thm)],[139,139]) ).
tff(733,plain,
product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a9,a4))) = product(product(a9,a4),product(a9,a4)),
inference(transitivity,[status(thm)],[732,731]) ).
tff(734,plain,
product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a9,a4))),product(product(product(a4,a10),product(a4,a10)),product(product(a9,a4),product(a9,a4)))) = product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a10,a10))),
inference(monotonicity,[status(thm)],[733,729]) ).
tff(735,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))),product(product(a9,a4),product(a9,a4))) = product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a9,a4))),product(product(product(a4,a10),product(a4,a10)),product(product(a9,a4),product(a9,a4)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(736,plain,
product(product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))),product(product(a9,a4),product(a9,a4))) = product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a9,a4))),product(product(product(a4,a10),product(a4,a10)),product(product(a9,a4),product(a9,a4)))),
inference(unit_resolution,[status(thm)],[735,46]) ).
tff(737,plain,
product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))) = product(product(a10,a10),a5),
inference(monotonicity,[status(thm)],[139,727]) ).
tff(738,plain,
product(product(a10,a10),a5) = product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))),
inference(symmetry,[status(thm)],[737]) ).
tff(739,plain,
product(product(a10,a5),product(a10,a5)) = product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))),
inference(transitivity,[status(thm)],[632,738]) ).
tff(740,plain,
product(product(product(a10,a5),product(a10,a5)),product(product(a9,a4),product(a9,a4))) = product(product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))),product(product(a9,a4),product(a9,a4))),
inference(monotonicity,[status(thm)],[739]) ).
tff(741,plain,
product(product(product(a10,a5),product(a10,a5)),product(product(a9,a4),product(a9,a4))) = a9,
inference(transitivity,[status(thm)],[740,736,734,725,615,610,39,112]) ).
tff(742,plain,
product(product(product(product(a10,a5),product(a10,a5)),product(product(a9,a4),product(a9,a4))),product(product(a4,a10),product(a4,a10))) = product(a9,product(product(a4,a10),product(a4,a10))),
inference(monotonicity,[status(thm)],[741]) ).
tff(743,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a10,a5),product(a10,a5)),product(product(a9,a4),product(a9,a4))),product(product(a4,a10),product(a4,a10))) = product(product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))),product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(744,plain,
product(product(product(product(a10,a5),product(a10,a5)),product(product(a9,a4),product(a9,a4))),product(product(a4,a10),product(a4,a10))) = product(product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))),product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10)))),
inference(unit_resolution,[status(thm)],[743,46]) ).
tff(745,plain,
product(product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))),product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10)))) = product(product(product(product(a10,a5),product(a10,a5)),product(product(a9,a4),product(a9,a4))),product(product(a4,a10),product(a4,a10))),
inference(symmetry,[status(thm)],[744]) ).
tff(746,plain,
product(product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))),product(product(a10,a5),product(a10,a5))) = product(product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))),product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10)))),
inference(monotonicity,[status(thm)],[739]) ).
tff(747,plain,
product(product(product(a9,a4),product(a9,a4)),a5) = product(product(a10,a10),a5),
inference(monotonicity,[status(thm)],[139]) ).
tff(748,plain,
product(product(a10,a10),a5) = product(product(product(a9,a4),product(a9,a4)),a5),
inference(symmetry,[status(thm)],[747]) ).
tff(749,plain,
product(product(a10,a5),product(a10,a5)) = product(product(product(a9,a4),product(a9,a4)),a5),
inference(transitivity,[status(thm)],[632,748]) ).
tff(750,plain,
product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))) = product(product(product(product(a9,a4),product(a9,a4)),a5),product(a5,a5)),
inference(monotonicity,[status(thm)],[749,119]) ).
tff(751,plain,
product(product(product(product(a9,a4),product(a9,a4)),a5),product(a5,a5)) = product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))),
inference(symmetry,[status(thm)],[750]) ).
tff(752,plain,
product(product(product(a9,a4),product(a9,a4)),a5) = product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))),
inference(transitivity,[status(thm)],[747,738]) ).
tff(753,plain,
product(product(product(product(a9,a4),product(a9,a4)),a5),product(a5,a5)) = product(product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))),product(product(a4,a10),product(a4,a10))),
inference(monotonicity,[status(thm)],[752,118]) ).
tff(754,plain,
product(product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))),product(product(a4,a10),product(a4,a10))) = product(product(product(product(a9,a4),product(a9,a4)),a5),product(a5,a5)),
inference(symmetry,[status(thm)],[753]) ).
tff(755,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))),product(product(a4,a10),product(a4,a10))) = product(product(a9,a4),product(a9,a4)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(756,plain,
product(product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))),product(product(a4,a10),product(a4,a10))) = product(product(a9,a4),product(a9,a4)),
inference(unit_resolution,[status(thm)],[755,22]) ).
tff(757,plain,
product(product(a9,a4),product(a9,a4)) = product(product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10))),product(product(a4,a10),product(a4,a10))),
inference(symmetry,[status(thm)],[756]) ).
tff(758,plain,
product(product(a9,a4),product(a9,a4)) = product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))),
inference(transitivity,[status(thm)],[757,754,751]) ).
tff(759,plain,
product(product(product(a9,a4),product(a9,a4)),product(product(a10,a5),product(a10,a5))) = product(product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))),product(product(a10,a5),product(a10,a5))),
inference(monotonicity,[status(thm)],[758]) ).
tff(760,plain,
product(product(a10,a10),product(product(product(a3,a1),product(a3,a1)),a10)) = product(product(a10,a10),a5),
inference(symmetry,[status(thm)],[629]) ).
tff(761,plain,
product(product(a9,a4),product(a4,a4)) = product(a10,product(product(a3,a1),product(a3,a1))),
inference(symmetry,[status(thm)],[616]) ).
tff(762,plain,
product(product(product(a9,a4),product(a4,a4)),product(product(a9,a4),product(a9,a4))) = product(product(a10,product(product(a3,a1),product(a3,a1))),a10),
inference(monotonicity,[status(thm)],[761,717]) ).
tff(763,plain,
product(product(product(a9,a4),product(a4,a4)),product(product(a9,a4),product(a9,a4))) = product(product(a10,a5),product(a10,a5)),
inference(transitivity,[status(thm)],[762,620,760,631]) ).
tff(764,plain,
product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a9,a4))),product(product(product(a9,a4),product(a4,a4)),product(product(a9,a4),product(a9,a4)))) = product(product(product(a9,a4),product(a9,a4)),product(product(a10,a5),product(a10,a5))),
inference(monotonicity,[status(thm)],[733,763]) ).
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(a9,a4),product(a9,a4)),product(product(a9,a4),product(a4,a4))),product(product(a9,a4),product(a9,a4))) = product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a9,a4))),product(product(product(a9,a4),product(a4,a4)),product(product(a9,a4),product(a9,a4)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(766,plain,
product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a4,a4))),product(product(a9,a4),product(a9,a4))) = product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a9,a4))),product(product(product(a9,a4),product(a4,a4)),product(product(a9,a4),product(a9,a4)))),
inference(unit_resolution,[status(thm)],[765,46]) ).
tff(767,plain,
product(product(a8,a1),product(a8,a1)) = product(product(a9,a4),product(a9,a4)),
inference(transitivity,[status(thm)],[157,301,296,294,286,141]) ).
tff(768,plain,
product(product(a9,a4),product(a4,a4)) = product(product(a8,a6),product(a8,a6)),
inference(transitivity,[status(thm)],[615,610]) ).
tff(769,plain,
product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a4,a4))) = product(product(product(a9,a4),product(a9,a4)),product(product(a8,a6),product(a8,a6))),
inference(monotonicity,[status(thm)],[768]) ).
tff(770,plain,
product(product(product(a9,a4),product(a9,a4)),product(product(a8,a6),product(a8,a6))) = product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a4,a4))),
inference(symmetry,[status(thm)],[769]) ).
tff(771,plain,
product(product(product(a9,a4),product(a9,a4)),product(product(a8,a6),product(a8,a6))) = product(product(product(a8,a1),product(a8,a1)),product(product(a8,a6),product(a8,a6))),
inference(monotonicity,[status(thm)],[605]) ).
tff(772,plain,
product(product(product(a8,a1),product(a8,a1)),product(product(a8,a6),product(a8,a6))) = product(product(product(a9,a4),product(a9,a4)),product(product(a8,a6),product(a8,a6))),
inference(symmetry,[status(thm)],[771]) ).
tff(773,plain,
product(product(product(product(a7,a3),product(a7,a3)),a1),product(product(product(a7,a3),product(a3,a3)),a1)) = product(product(product(a8,a1),product(a8,a1)),product(product(a8,a6),product(a8,a6))),
inference(symmetry,[status(thm)],[525]) ).
tff(774,plain,
product(a6,a1) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a7,a3),product(a3,a3))),a1),
inference(symmetry,[status(thm)],[518]) ).
tff(775,plain,
product(a6,a1) = product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a4,a4))),
inference(transitivity,[status(thm)],[774,520,773,772,770]) ).
tff(776,plain,
product(product(a6,a1),product(product(a8,a1),product(a8,a1))) = product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a4,a4))),product(product(a9,a4),product(a9,a4))),
inference(monotonicity,[status(thm)],[775,767]) ).
tff(777,plain,
product(product(product(a7,a3),product(a7,a3)),a1) = product(product(a8,a1),product(a8,a1)),
inference(transitivity,[status(thm)],[522,156]) ).
tff(778,plain,
product(product(product(product(a5,a9),product(a5,a9)),a1),product(product(product(a7,a3),product(a7,a3)),a1)) = product(product(a6,a1),product(product(a8,a1),product(a8,a1))),
inference(monotonicity,[status(thm)],[459,777]) ).
tff(779,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a5,a9),product(a5,a9)),product(product(a7,a3),product(a7,a3))),a1) = product(product(product(product(a5,a9),product(a5,a9)),a1),product(product(product(a7,a3),product(a7,a3)),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(780,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a7,a3),product(a7,a3))),a1) = product(product(product(product(a5,a9),product(a5,a9)),a1),product(product(product(a7,a3),product(a7,a3)),a1)),
inference(unit_resolution,[status(thm)],[779,46]) ).
tff(781,plain,
product(product(product(a5,a9),product(a5,a9)),product(product(a7,a3),product(a7,a3))) = product(a6,product(product(a7,a3),product(a7,a3))),
inference(monotonicity,[status(thm)],[49]) ).
tff(782,plain,
product(a6,product(product(a7,a3),product(a7,a3))) = product(product(product(a5,a9),product(a5,a9)),product(product(a7,a3),product(a7,a3))),
inference(symmetry,[status(thm)],[781]) ).
tff(783,plain,
product(product(a6,product(product(a7,a3),product(a7,a3))),a1) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a7,a3),product(a7,a3))),a1),
inference(monotonicity,[status(thm)],[782]) ).
tff(784,plain,
a6 = a1,
inference(transitivity,[status(thm)],[234,31,124,396,129,127,110,108,61,55]) ).
tff(785,plain,
product(product(a6,product(product(a7,a3),product(a7,a3))),a6) = product(product(a6,product(product(a7,a3),product(a7,a3))),a1),
inference(monotonicity,[status(thm)],[784]) ).
tff(786,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,product(product(a7,a3),product(a7,a3))),a6) = product(product(a6,a6),product(product(product(a7,a3),product(a7,a3)),a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(787,plain,
product(product(a6,product(product(a7,a3),product(a7,a3))),a6) = product(product(a6,a6),product(product(product(a7,a3),product(a7,a3)),a6)),
inference(unit_resolution,[status(thm)],[786,46]) ).
tff(788,plain,
product(product(a6,a6),product(product(product(a7,a3),product(a7,a3)),a6)) = product(product(a6,product(product(a7,a3),product(a7,a3))),a6),
inference(symmetry,[status(thm)],[787]) ).
tff(789,plain,
product(product(product(a7,a3),product(a7,a3)),a6) = product(product(a8,a8),a6),
inference(monotonicity,[status(thm)],[15]) ).
tff(790,plain,
product(product(a8,a8),a6) = product(product(product(a7,a3),product(a7,a3)),a6),
inference(symmetry,[status(thm)],[789]) ).
tff(791,plain,
product(a9,a9) = product(product(product(a7,a3),product(a7,a3)),a6),
inference(transitivity,[status(thm)],[38,283,790]) ).
tff(792,plain,
product(a5,a9) = product(a6,a6),
inference(transitivity,[status(thm)],[27,234]) ).
tff(793,plain,
product(product(a5,a9),product(a9,a9)) = product(product(a6,a6),product(product(product(a7,a3),product(a7,a3)),a6)),
inference(monotonicity,[status(thm)],[792,791]) ).
tff(794,plain,
a5 = a4,
inference(transitivity,[status(thm)],[627,118,391,388,793,788,785,783,780,778,776,766,764,759,746,745,742,714,706,703,673,671,667,559,558,556,157,643,282,233,231,215,553,241,244,250,252,551,247,124,396,129,127,110,108,61,55,401,400,666,664,662,659,656,646,170,151,148]) ).
tff(795,plain,
product(product(a2,a2),product(a6,a2)) = product(product(a2,a2),a7),
inference(symmetry,[status(thm)],[652]) ).
tff(796,plain,
product(a1,product(product(a2,a2),product(a2,a2))) = product(product(a2,a6),a2),
inference(symmetry,[status(thm)],[648]) ).
tff(797,plain,
product(a1,product(product(a2,a2),product(a2,a2))) = product(product(a6,a6),product(product(a1,a1),a6)),
inference(monotonicity,[status(thm)],[550,221]) ).
tff(798,plain,
product(product(a6,a6),product(product(a1,a1),a6)) = product(a1,product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[797]) ).
tff(799,plain,
a4 = a3,
inference(transitivity,[status(thm)],[149,146,171,645,655,658,661,663,665,205,200,549,60,107,548,126,547,395,123,415,414,546,486,484,454,451,446,515,512,798,796,650,795,276,166,180]) ).
tff(800,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[412]) ).
tff(801,plain,
a8 = a7,
inference(transitivity,[status(thm)],[56,14,64,52,398,403,409,800,430,515,512,262,225,187,261]) ).
tff(802,plain,
product(a1,a6) = product(product(a6,a6),product(a6,a6)),
inference(monotonicity,[status(thm)],[550,234]) ).
tff(803,plain,
product(product(a6,a6),product(a6,a6)) = product(a1,a6),
inference(symmetry,[status(thm)],[802]) ).
tff(804,plain,
product(product(a5,a9),product(a5,a9)) = product(product(a6,a6),product(a6,a6)),
inference(symmetry,[status(thm)],[247]) ).
tff(805,plain,
product(product(product(product(a8,a6),product(a1,a6)),product(product(a2,a2),product(a2,a2))),product(product(product(a8,a6),product(a6,a6)),product(product(a2,a2),product(a2,a2)))) = product(product(product(product(a8,a6),product(a1,a6)),product(product(a8,a6),product(a6,a6))),product(product(a2,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[486]) ).
tff(806,plain,
a3 = a2,
inference(transitivity,[status(thm)],[327,165,653,652,651,648,797,511,514,445,450,453,483,805,545,346,341,804,803,74]) ).
tff(807,plain,
product(product(a5,a9),product(a9,a9)) = product(product(product(product(a4,a10),product(a4,a10)),product(product(a8,a6),product(a8,a6))),product(product(a8,a6),product(a8,a6))),
inference(symmetry,[status(thm)],[388]) ).
tff(808,plain,
product(product(a6,a6),product(product(product(a7,a3),product(a7,a3)),a6)) = product(product(a5,a9),product(a9,a9)),
inference(symmetry,[status(thm)],[793]) ).
tff(809,plain,
product(product(a6,product(product(a7,a3),product(a7,a3))),a1) = product(product(a6,product(product(a7,a3),product(a7,a3))),a6),
inference(symmetry,[status(thm)],[785]) ).
tff(810,plain,
product(product(product(product(a5,a9),product(a5,a9)),product(product(a7,a3),product(a7,a3))),a1) = product(product(a6,product(product(a7,a3),product(a7,a3))),a1),
inference(symmetry,[status(thm)],[783]) ).
tff(811,plain,
product(product(product(product(a5,a9),product(a5,a9)),a1),product(product(product(a7,a3),product(a7,a3)),a1)) = product(product(product(product(a5,a9),product(a5,a9)),product(product(a7,a3),product(a7,a3))),a1),
inference(symmetry,[status(thm)],[780]) ).
tff(812,plain,
product(product(a6,a1),product(product(a8,a1),product(a8,a1))) = product(product(product(product(a5,a9),product(a5,a9)),a1),product(product(product(a7,a3),product(a7,a3)),a1)),
inference(symmetry,[status(thm)],[778]) ).
tff(813,plain,
product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a4,a4))),product(product(a9,a4),product(a9,a4))) = product(product(a6,a1),product(product(a8,a1),product(a8,a1))),
inference(symmetry,[status(thm)],[776]) ).
tff(814,plain,
product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a9,a4))),product(product(product(a9,a4),product(a4,a4)),product(product(a9,a4),product(a9,a4)))) = product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a4,a4))),product(product(a9,a4),product(a9,a4))),
inference(symmetry,[status(thm)],[766]) ).
tff(815,plain,
product(product(product(a9,a4),product(a9,a4)),product(product(a10,a5),product(a10,a5))) = product(product(product(product(a9,a4),product(a9,a4)),product(product(a9,a4),product(a9,a4))),product(product(product(a9,a4),product(a4,a4)),product(product(a9,a4),product(a9,a4)))),
inference(symmetry,[status(thm)],[764]) ).
tff(816,plain,
product(product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))),product(product(a10,a5),product(a10,a5))) = product(product(product(a9,a4),product(a9,a4)),product(product(a10,a5),product(a10,a5))),
inference(symmetry,[status(thm)],[759]) ).
tff(817,plain,
product(product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))),product(product(product(a9,a4),product(a9,a4)),product(product(a4,a10),product(a4,a10)))) = product(product(product(product(a10,a5),product(a10,a5)),product(product(a4,a10),product(a4,a10))),product(product(a10,a5),product(a10,a5))),
inference(symmetry,[status(thm)],[746]) ).
tff(818,plain,
product(a9,product(product(a4,a10),product(a4,a10))) = product(product(product(product(a10,a5),product(a10,a5)),product(product(a9,a4),product(a9,a4))),product(product(a4,a10),product(a4,a10))),
inference(symmetry,[status(thm)],[742]) ).
tff(819,plain,
product(product(product(product(a7,a3),product(a3,a3)),a1),product(product(product(a3,a3),product(a7,a3)),a1)) = product(a9,product(product(a4,a10),product(a4,a10))),
inference(symmetry,[status(thm)],[714]) ).
tff(820,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))) = product(product(product(product(a7,a3),product(a3,a3)),product(product(a3,a3),product(a7,a3))),a1),
inference(symmetry,[status(thm)],[703]) ).
tff(821,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a2,a2),product(a2,a2))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[673]) ).
tff(822,plain,
product(product(product(a8,a6),product(a1,a6)),product(product(a1,a6),product(a6,a6))) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(product(a2,a2),product(a2,a2)),product(product(a5,a9),product(a5,a9)))),
inference(symmetry,[status(thm)],[671]) ).
tff(823,plain,
product(product(product(a8,a6),product(a1,a6)),a1) = product(product(product(a8,a6),product(a1,a6)),product(product(a1,a6),product(a6,a6))),
inference(symmetry,[status(thm)],[667]) ).
tff(824,plain,
product(product(product(a8,a1),a6),product(a6,a6)) = product(product(product(a8,a6),product(a1,a6)),a1),
inference(symmetry,[status(thm)],[559]) ).
tff(825,plain,
product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))) = product(product(product(a8,a1),a6),product(a6,a6)),
inference(symmetry,[status(thm)],[558]) ).
tff(826,plain,
product(product(a8,a1),product(a8,a1)) = product(product(product(product(a8,a1),product(a8,a1)),product(product(a5,a9),product(a5,a9))),product(product(a5,a9),product(a5,a9))),
inference(symmetry,[status(thm)],[556]) ).
tff(827,plain,
product(product(a8,a8),a6) = product(product(a8,a8),a1),
inference(symmetry,[status(thm)],[643]) ).
tff(828,plain,
product(product(product(a6,a2),product(a6,a2)),product(product(a5,a9),product(a5,a9))) = product(product(product(a6,a2),product(a6,a2)),a1),
inference(symmetry,[status(thm)],[553]) ).
tff(829,plain,
product(product(a6,a6),product(a6,a6)) = product(a6,a1),
inference(symmetry,[status(thm)],[551]) ).
tff(830,plain,
a6 = a5,
inference(transitivity,[status(thm)],[234,31,804,829,253,251,245,242,828,481,480,479,478,827,156,826,825,824,823,822,821,820,705,819,818,744,817,816,815,814,813,812,811,810,809,787,808,807,390,119,626]) ).
tff(831,plain,
a7 = a6,
inference(transitivity,[status(thm)],[344,186,239,238,511,514,445,450,453,483,805,545,346,341,32,30]) ).
tff(832,plain,
a2 = a1,
inference(transitivity,[status(thm)],[203,802,247,124,396,129,127,110,108,61,55]) ).
tff(833,plain,
tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9) = tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8),
inference(monotonicity,[status(thm)],[832,831,830,806,801,799,794,644,641,554]) ).
tff(834,plain,
tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) = tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(symmetry,[status(thm)],[833]) ).
tff(835,plain,
( ( tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9) )
<=> ( tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(836,axiom,
tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(837,plain,
tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(modus_ponens,[status(thm)],[836,835]) ).
tff(838,plain,
$false,
inference(unit_resolution,[status(thm)],[837,834]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : TOP051-1 : TPTP v9.0.0. Released v8.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 14:06:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% See solution above
% 0.19/0.55 % E exiting
%------------------------------------------------------------------------------