%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP049-1 : 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 0.80s 0.96s
% Output : Proof 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 129
% Syntax : Number of formulae : 806 ( 691 unt; 0 typ; 0 def)
% Number of atoms : 927 ( 923 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 220 ( 102 ~; 98 |; 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 : 12 ( 12 usr; 10 con; 0-9 aty)
% Number of variables : 314 ( 308 !; 0 ?; 314 :)
% Comments :
%------------------------------------------------------------------------------
tff(tuple_type,type,
tuple: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(a6_type,type,
a6: $i ).
tff(a5_type,type,
a5: $i ).
tff(a4_type,type,
a4: $i ).
tff(a3_type,type,
a3: $i ).
tff(a8_type,type,
a8: $i ).
tff(a7_type,type,
a7: $i ).
tff(a9_type,type,
a9: $i ).
tff(a10_type,type,
a10: $i ).
tff(a2_type,type,
a2: $i ).
tff(a1_type,type,
a1: $i ).
tff(product_type,type,
product: ( $i * $i ) > $i ).
tff(1,plain,
( ( a5 = product(a2,a10) )
<=> ( a5 = product(a2,a10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
a5 = product(a2,a10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_05) ).
tff(3,plain,
a5 = product(a2,a10),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
product(a2,a10) = a5,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
^ [Y: $i,X: $i] :
refl(( ( product(product(X,Y),Y) = X )
<=> ( product(product(X,Y),Y) = X ) )),
inference(bind,[status(th)],[]) ).
tff(6,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)],[5]) ).
tff(7,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(8,axiom,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).
tff(9,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(skolemize,[status(sab)],[9]) ).
tff(11,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a2,a10),product(a1,a2)),product(a1,a2)) = product(a2,a10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
product(product(product(a2,a10),product(a1,a2)),product(a1,a2)) = product(a2,a10),
inference(unit_resolution,[status(thm)],[12,11]) ).
tff(14,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a9,a7),product(a3,a4)),product(a3,a4)) = product(a9,a7) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
product(product(product(a9,a7),product(a3,a4)),product(a3,a4)) = product(a9,a7),
inference(unit_resolution,[status(thm)],[14,11]) ).
tff(16,plain,
( ( a2 = product(a3,a4) )
<=> ( a2 = product(a3,a4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
a2 = product(a3,a4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_04) ).
tff(18,plain,
a2 = product(a3,a4),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
product(a3,a4) = a2,
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ( a1 = product(a9,a7) )
<=> ( a1 = product(a9,a7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
a1 = product(a9,a7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot) ).
tff(22,plain,
a1 = product(a9,a7),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
product(a9,a7) = a1,
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
product(product(a9,a7),product(a3,a4)) = product(a1,a2),
inference(monotonicity,[status(thm)],[23,19]) ).
tff(25,plain,
product(a1,a2) = product(product(a9,a7),product(a3,a4)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a1,a2),product(a10,a3)),product(a10,a3)) = product(a1,a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
product(product(product(a1,a2),product(a10,a3)),product(a10,a3)) = product(a1,a2),
inference(unit_resolution,[status(thm)],[26,11]) ).
tff(28,plain,
( ( a4 = product(a10,a3) )
<=> ( a4 = product(a10,a3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
a4 = product(a10,a3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_10) ).
tff(30,plain,
a4 = product(a10,a3),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
product(a10,a3) = a4,
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ( a3 = product(a1,a2) )
<=> ( a3 = product(a1,a2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
a3 = product(a1,a2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_03) ).
tff(34,plain,
a3 = product(a1,a2),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
product(a1,a2) = a3,
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
product(product(a1,a2),product(a10,a3)) = product(a3,a4),
inference(monotonicity,[status(thm)],[35,31]) ).
tff(37,plain,
product(a3,a4) = product(product(a1,a2),product(a10,a3)),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
product(product(a3,a4),product(a10,a3)) = product(product(product(a1,a2),product(a10,a3)),product(a10,a3)),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
product(product(a3,a4),product(a10,a3)) = product(product(a9,a7),product(a3,a4)),
inference(transitivity,[status(thm)],[38,27,25]) ).
tff(40,plain,
product(product(product(a3,a4),product(a10,a3)),product(a3,a4)) = product(product(product(a9,a7),product(a3,a4)),product(a3,a4)),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
product(product(product(a3,a4),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a3,a4),product(a10,a3)),product(a3,a4)),
inference(monotonicity,[status(thm)],[36]) ).
tff(42,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(43,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)],[42]) ).
tff(44,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(45,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(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)],[45,44]) ).
tff(47,plain,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a3,a4),product(a1,a2)),product(a10,a3)) = product(product(product(a3,a4),product(a10,a3)),product(product(a1,a2),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
product(product(product(a3,a4),product(a1,a2)),product(a10,a3)) = product(product(product(a3,a4),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
( ( a10 = product(a8,a9) )
<=> ( a10 = product(a8,a9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
a10 = product(a8,a9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_09) ).
tff(53,plain,
a10 = product(a8,a9),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
product(a8,a9) = a10,
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
product(product(a8,a9),product(a1,a2)) = product(a10,a3),
inference(monotonicity,[status(thm)],[54,35]) ).
tff(56,plain,
product(product(product(a3,a4),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(product(product(a3,a4),product(a1,a2)),product(a10,a3)),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a3,a4),product(a8,a9)),product(a1,a2)) = product(product(product(a3,a4),product(a1,a2)),product(product(a8,a9),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
product(product(product(a3,a4),product(a8,a9)),product(a1,a2)) = product(product(product(a3,a4),product(a1,a2)),product(product(a8,a9),product(a1,a2))),
inference(unit_resolution,[status(thm)],[57,48]) ).
tff(59,plain,
product(product(a3,a4),product(a8,a9)) = product(a2,a10),
inference(monotonicity,[status(thm)],[19,54]) ).
tff(60,plain,
product(a2,a10) = product(product(a3,a4),product(a8,a9)),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
product(product(a2,a10),product(a1,a2)) = product(product(product(a3,a4),product(a8,a9)),product(a1,a2)),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
product(product(a2,a10),product(a1,a2)) = product(a9,a7),
inference(transitivity,[status(thm)],[61,58,56,50,41,40,15]) ).
tff(63,plain,
product(product(product(a2,a10),product(a1,a2)),product(a1,a2)) = product(product(a9,a7),product(a1,a2)),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
product(product(a9,a7),product(a1,a2)) = product(product(product(a2,a10),product(a1,a2)),product(a1,a2)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a7,a4),product(a3,a4)),product(a3,a4)) = product(a7,a4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
product(product(product(a7,a4),product(a3,a4)),product(a3,a4)) = product(a7,a4),
inference(unit_resolution,[status(thm)],[65,11]) ).
tff(67,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(a1,a2)),product(a10,a3)) = product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
product(product(product(a6,a1),product(a1,a2)),product(a10,a3)) = product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(unit_resolution,[status(thm)],[67,48]) ).
tff(69,plain,
product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a6,a1),product(a1,a2)),product(a10,a3)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ( a7 = product(a6,a1) )
<=> ( a7 = product(a6,a1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
a7 = product(a6,a1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_07) ).
tff(72,plain,
a7 = product(a6,a1),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
product(a6,a1) = a7,
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
product(product(a6,a1),product(a10,a3)) = product(a7,a4),
inference(monotonicity,[status(thm)],[73,31]) ).
tff(75,plain,
product(a7,a4) = product(product(a6,a1),product(a10,a3)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
product(product(a7,a4),product(a3,a4)) = product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(monotonicity,[status(thm)],[75,37]) ).
tff(77,plain,
product(product(a7,a4),product(a3,a4)) = product(product(product(a6,a1),product(a1,a2)),product(a10,a3)),
inference(transitivity,[status(thm)],[76,69]) ).
tff(78,plain,
product(product(product(a7,a4),product(a3,a4)),product(a3,a4)) = product(product(product(product(a6,a1),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(monotonicity,[status(thm)],[77,37]) ).
tff(79,plain,
product(product(product(product(a6,a1),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a7,a4),product(a3,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
^ [X: $i] :
refl(( ( product(X,X) = X )
<=> ( product(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [X: $i] : ( product(X,X) = X )
<=> ! [X: $i] : ( product(X,X) = X ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [X: $i] : ( product(X,X) = X )
<=> ! [X: $i] : ( product(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
! [X: $i] : ( product(X,X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle) ).
tff(84,plain,
! [X: $i] : ( product(X,X) = X ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [X: $i] : ( product(X,X) = X ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [X: $i] : ( product(X,X) = X ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(a3,a4),product(a3,a4)) = product(a3,a4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
product(product(a3,a4),product(a3,a4)) = product(a3,a4),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(a3,a4),product(a3,a4)),
inference(monotonicity,[status(thm)],[36,36]) ).
tff(90,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a1,a2),product(a1,a2)),product(a10,a3)) = product(product(product(a1,a2),product(a10,a3)),product(product(a1,a2),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
product(product(product(a1,a2),product(a1,a2)),product(a10,a3)) = product(product(product(a1,a2),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(unit_resolution,[status(thm)],[90,48]) ).
tff(92,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(product(product(a1,a2),product(a1,a2)),product(a10,a3)),
inference(monotonicity,[status(thm)],[55]) ).
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,a2),product(a8,a9)),product(a1,a2)) = product(product(product(a1,a2),product(a1,a2)),product(product(a8,a9),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
product(product(product(a1,a2),product(a8,a9)),product(a1,a2)) = product(product(product(a1,a2),product(a1,a2)),product(product(a8,a9),product(a1,a2))),
inference(unit_resolution,[status(thm)],[93,48]) ).
tff(95,plain,
product(product(product(a1,a2),product(a8,a9)),product(a1,a2)) = product(product(a1,a2),product(a10,a3)),
inference(transitivity,[status(thm)],[94,92,91,89,88,37]) ).
tff(96,plain,
product(product(product(a6,a1),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(product(product(a6,a1),product(a1,a2)),product(a10,a3)),
inference(monotonicity,[status(thm)],[55]) ).
tff(97,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(a8,a9)),product(a1,a2)) = product(product(product(a6,a1),product(a1,a2)),product(product(a8,a9),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
product(product(product(a6,a1),product(a8,a9)),product(a1,a2)) = product(product(product(a6,a1),product(a1,a2)),product(product(a8,a9),product(a1,a2))),
inference(unit_resolution,[status(thm)],[97,48]) ).
tff(99,plain,
product(product(product(a6,a1),product(a8,a9)),product(a1,a2)) = product(product(product(a6,a1),product(a1,a2)),product(a10,a3)),
inference(transitivity,[status(thm)],[98,96]) ).
tff(100,plain,
product(product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))) = product(product(product(product(a6,a1),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(monotonicity,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,a1),product(a8,a9)),product(product(a1,a2),product(a8,a9))),product(a1,a2)) = product(product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
product(product(product(product(a6,a1),product(a8,a9)),product(product(a1,a2),product(a8,a9))),product(a1,a2)) = product(product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))),
inference(unit_resolution,[status(thm)],[101,48]) ).
tff(103,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(a1,a2)),product(a8,a9)) = product(product(product(a6,a1),product(a8,a9)),product(product(a1,a2),product(a8,a9))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
product(product(product(a6,a1),product(a1,a2)),product(a8,a9)) = product(product(product(a6,a1),product(a8,a9)),product(product(a1,a2),product(a8,a9))),
inference(unit_resolution,[status(thm)],[103,48]) ).
tff(105,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(a6,a1)),product(a1,a2)) = product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
product(product(product(a6,a1),product(a6,a1)),product(a1,a2)) = product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))),
inference(unit_resolution,[status(thm)],[105,48]) ).
tff(107,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(a6,a1),product(a6,a1)) = product(a6,a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
product(product(a6,a1),product(a6,a1)) = product(a6,a1),
inference(unit_resolution,[status(thm)],[107,86]) ).
tff(109,plain,
product(a6,a1) = product(product(a6,a1),product(a6,a1)),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
product(product(a6,a1),product(a1,a2)) = product(product(product(a6,a1),product(a6,a1)),product(a1,a2)),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
product(product(a6,a1),product(a1,a2)) = product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))),
inference(transitivity,[status(thm)],[110,106]) ).
tff(112,plain,
product(product(product(a6,a1),product(a1,a2)),product(a8,a9)) = product(product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))),product(a8,a9)),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
product(product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))),product(a8,a9)) = product(product(product(a6,a1),product(a1,a2)),product(a8,a9)),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a8,a9),product(a1,a2)),product(a1,a2)) = product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
product(product(product(a8,a9),product(a1,a2)),product(a1,a2)) = product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),
inference(unit_resolution,[status(thm)],[114,48]) ).
tff(116,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a8,a9),product(a1,a2)),product(a1,a2)) = product(a8,a9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
product(product(product(a8,a9),product(a1,a2)),product(a1,a2)) = product(a8,a9),
inference(unit_resolution,[status(thm)],[116,11]) ).
tff(118,plain,
product(a8,a9) = product(product(product(a8,a9),product(a1,a2)),product(a1,a2)),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
product(a8,a9) = product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[118,115]) ).
tff(120,plain,
product(product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))),product(a8,a9)) = product(product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))),product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2)))),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
product(product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))),product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2)))) = product(product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))),product(a8,a9)),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
product(a10,a3) = product(product(a8,a9),product(a1,a2)),
inference(symmetry,[status(thm)],[55]) ).
tff(123,plain,
product(product(a10,a3),product(a1,a2)) = product(product(product(a8,a9),product(a1,a2)),product(a1,a2)),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
product(product(product(a8,a9),product(a1,a2)),product(a1,a2)) = product(product(a10,a3),product(a1,a2)),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))) = product(product(product(a8,a9),product(a1,a2)),product(a1,a2)),
inference(symmetry,[status(thm)],[115]) ).
tff(126,plain,
product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))) = product(product(a10,a3),product(a1,a2)),
inference(transitivity,[status(thm)],[125,124]) ).
tff(127,plain,
product(product(product(a6,a1),product(a6,a1)),product(a1,a2)) = product(product(a6,a1),product(a1,a2)),
inference(symmetry,[status(thm)],[110]) ).
tff(128,plain,
product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))) = product(product(product(a6,a1),product(a6,a1)),product(a1,a2)),
inference(symmetry,[status(thm)],[106]) ).
tff(129,plain,
product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))) = product(product(a6,a1),product(a1,a2)),
inference(transitivity,[status(thm)],[128,127]) ).
tff(130,plain,
product(product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))),product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2)))) = product(product(product(a6,a1),product(a1,a2)),product(product(a10,a3),product(a1,a2))),
inference(monotonicity,[status(thm)],[129,126]) ).
tff(131,plain,
product(product(product(a6,a1),product(a1,a2)),product(product(a10,a3),product(a1,a2))) = product(product(product(product(a6,a1),product(a1,a2)),product(product(a6,a1),product(a1,a2))),product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2)))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,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(a10,a3)),product(a1,a2)) = product(product(product(a6,a1),product(a1,a2)),product(product(a10,a3),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
product(product(product(a6,a1),product(a10,a3)),product(a1,a2)) = product(product(product(a6,a1),product(a1,a2)),product(product(a10,a3),product(a1,a2))),
inference(unit_resolution,[status(thm)],[132,48]) ).
tff(134,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a1,a2),product(a10,a3)),product(a10,a3)) = product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
product(product(product(a1,a2),product(a10,a3)),product(a10,a3)) = product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),
inference(unit_resolution,[status(thm)],[134,48]) ).
tff(136,plain,
product(a1,a2) = product(product(product(a1,a2),product(a10,a3)),product(a10,a3)),
inference(symmetry,[status(thm)],[27]) ).
tff(137,plain,
product(a1,a2) = product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),
inference(transitivity,[status(thm)],[136,135]) ).
tff(138,plain,
product(product(product(a6,a1),product(a10,a3)),product(a1,a2)) = product(product(a7,a4),product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(monotonicity,[status(thm)],[74,137]) ).
tff(139,plain,
product(product(a7,a4),product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3)))) = product(product(product(a6,a1),product(a10,a3)),product(a1,a2)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
product(product(product(a1,a2),product(a10,a3)),product(a10,a3)) = product(product(a3,a4),product(a10,a3)),
inference(symmetry,[status(thm)],[38]) ).
tff(141,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))) = product(product(product(a1,a2),product(a10,a3)),product(a10,a3)),
inference(symmetry,[status(thm)],[135]) ).
tff(142,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))) = product(product(a3,a4),product(a10,a3)),
inference(transitivity,[status(thm)],[141,140]) ).
tff(143,plain,
product(product(a7,a4),product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3)))) = product(product(product(a6,a1),product(a10,a3)),product(product(a3,a4),product(a10,a3))),
inference(monotonicity,[status(thm)],[75,142]) ).
tff(144,plain,
product(product(product(a6,a1),product(a10,a3)),product(product(a3,a4),product(a10,a3))) = product(product(a7,a4),product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(symmetry,[status(thm)],[143]) ).
tff(145,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(a3,a4)),product(a10,a3)) = product(product(product(a6,a1),product(a10,a3)),product(product(a3,a4),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
product(product(product(a6,a1),product(a3,a4)),product(a10,a3)) = product(product(product(a6,a1),product(a10,a3)),product(product(a3,a4),product(a10,a3))),
inference(unit_resolution,[status(thm)],[145,48]) ).
tff(147,plain,
product(product(a2,a10),product(a10,a3)) = product(a5,a4),
inference(monotonicity,[status(thm)],[4,31]) ).
tff(148,plain,
product(a5,a4) = product(product(a2,a10),product(a10,a3)),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
product(product(a5,a4),product(a3,a4)) = product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(monotonicity,[status(thm)],[148,37]) ).
tff(150,plain,
product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(a5,a4),product(a3,a4)),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)) = product(product(product(a5,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))),
inference(monotonicity,[status(thm)],[150,25]) ).
tff(152,plain,
product(product(product(a5,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))) = product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a5,a4),product(a9,a7)),product(a3,a4)) = product(product(product(a5,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
product(product(product(a5,a4),product(a9,a7)),product(a3,a4)) = product(product(product(a5,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))),
inference(unit_resolution,[status(thm)],[153,48]) ).
tff(155,plain,
( ( a6 = product(a5,a4) )
<=> ( a6 = product(a5,a4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,axiom,
a6 = product(a5,a4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_06) ).
tff(157,plain,
a6 = product(a5,a4),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
product(a5,a4) = a6,
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
product(product(a5,a4),product(a9,a7)) = product(a6,a1),
inference(monotonicity,[status(thm)],[158,23]) ).
tff(160,plain,
product(a6,a1) = product(product(a5,a4),product(a9,a7)),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
product(product(a6,a1),product(a3,a4)) = product(product(product(a5,a4),product(a9,a7)),product(a3,a4)),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
product(product(a6,a1),product(a3,a4)) = product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),
inference(transitivity,[status(thm)],[161,154,152]) ).
tff(163,plain,
product(product(product(a6,a1),product(a3,a4)),product(a10,a3)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(a8,a9),product(a1,a2))),
inference(monotonicity,[status(thm)],[162,122]) ).
tff(164,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(product(product(a6,a1),product(a3,a4)),product(a10,a3)),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(a10,a3)),
inference(monotonicity,[status(thm)],[55]) ).
tff(166,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(a10,a3)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(a8,a9),product(a1,a2))),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(a10,a3)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(product(a1,a2),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(a10,a3)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(unit_resolution,[status(thm)],[167,48]) ).
tff(169,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(a10,a3)),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(a3,a4)),
inference(monotonicity,[status(thm)],[36]) ).
tff(171,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(a3,a4)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a2,a10),product(a1,a2)),product(a10,a3)) = product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
product(product(product(a2,a10),product(a1,a2)),product(a10,a3)) = product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(unit_resolution,[status(thm)],[172,48]) ).
tff(174,plain,
product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)) = product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(a10,a3)),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(a10,a3)) = product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)) = product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(product(product(a2,a10),product(a1,a2)),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(178,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)) = product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(product(product(a2,a10),product(a1,a2)),product(a10,a3))),
inference(unit_resolution,[status(thm)],[177,48]) ).
tff(179,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(product(product(a2,a10),product(a1,a2)),product(a10,a3))) = product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
product(product(product(a2,a10),product(a1,a2)),product(a10,a3)) = product(product(a5,a4),product(a3,a4)),
inference(transitivity,[status(thm)],[173,150]) ).
tff(181,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(product(product(a2,a10),product(a1,a2)),product(a10,a3))) = product(product(product(a5,a4),product(a3,a4)),product(product(a5,a4),product(a3,a4))),
inference(monotonicity,[status(thm)],[180,180]) ).
tff(182,plain,
product(product(product(a5,a4),product(a3,a4)),product(product(a5,a4),product(a3,a4))) = product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(product(product(a2,a10),product(a1,a2)),product(a10,a3))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a5,a4),product(a5,a4)),product(a3,a4)) = product(product(product(a5,a4),product(a3,a4)),product(product(a5,a4),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
product(product(product(a5,a4),product(a5,a4)),product(a3,a4)) = product(product(product(a5,a4),product(a3,a4)),product(product(a5,a4),product(a3,a4))),
inference(unit_resolution,[status(thm)],[183,48]) ).
tff(185,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(a5,a4),product(a5,a4)) = product(a5,a4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
product(product(a5,a4),product(a5,a4)) = product(a5,a4),
inference(unit_resolution,[status(thm)],[185,86]) ).
tff(187,plain,
product(product(a5,a4),product(a5,a4)) = product(product(a2,a10),product(a10,a3)),
inference(transitivity,[status(thm)],[186,148]) ).
tff(188,plain,
product(product(product(a5,a4),product(a5,a4)),product(a3,a4)) = product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(monotonicity,[status(thm)],[187,37]) ).
tff(189,plain,
product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a5,a4),product(a5,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
product(product(product(a2,a10),product(a1,a2)),product(a10,a3)) = product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),
inference(transitivity,[status(thm)],[173,189,184,182,179]) ).
tff(191,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(a10,a3)) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(a10,a3)),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(a10,a3)) = product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(a10,a3)),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(a10,a3)) = product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(a10,a3)) = product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),
inference(unit_resolution,[status(thm)],[193,11]) ).
tff(195,plain,
product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(a10,a3)),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))) = product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),
inference(transitivity,[status(thm)],[195,192,176]) ).
tff(197,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a3,a4)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(a3,a4)),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a3,a4)) = product(product(product(a6,a1),product(a8,a9)),product(product(a1,a2),product(a8,a9))),
inference(transitivity,[status(thm)],[197,171,169,166,164,146,144,139,133,131,121,113,104]) ).
tff(199,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a3,a4)),product(a1,a2)) = product(product(product(product(a6,a1),product(a8,a9)),product(product(a1,a2),product(a8,a9))),product(a1,a2)),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a3,a4)),product(a1,a2)) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),product(product(a3,a4),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a3,a4)),product(a1,a2)) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),product(product(a3,a4),product(a1,a2))),
inference(unit_resolution,[status(thm)],[200,48]) ).
tff(202,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),product(product(a3,a4),product(a1,a2))) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a3,a4)),product(a1,a2)),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
product(a3,a4) = product(product(a3,a4),product(a3,a4)),
inference(symmetry,[status(thm)],[88]) ).
tff(204,plain,
product(product(a3,a4),product(a1,a2)) = product(product(product(a3,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))),
inference(monotonicity,[status(thm)],[203,25]) ).
tff(205,plain,
product(product(product(a3,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))) = product(product(a3,a4),product(a1,a2)),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
product(product(product(a1,a2),product(a8,a9)),product(a1,a2)) = product(product(a3,a4),product(a3,a4)),
inference(transitivity,[status(thm)],[94,92,91,89]) ).
tff(207,plain,
product(product(product(product(a1,a2),product(a8,a9)),product(a1,a2)),product(a1,a2)) = product(product(product(a3,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))),
inference(monotonicity,[status(thm)],[206,25]) ).
tff(208,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a1,a2),product(a8,a9)),product(a1,a2)),product(a1,a2)) = product(product(a1,a2),product(a8,a9)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
product(product(product(product(a1,a2),product(a8,a9)),product(a1,a2)),product(a1,a2)) = product(product(a1,a2),product(a8,a9)),
inference(unit_resolution,[status(thm)],[208,11]) ).
tff(210,plain,
product(product(a1,a2),product(a8,a9)) = product(product(product(product(a1,a2),product(a8,a9)),product(a1,a2)),product(a1,a2)),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
product(product(a1,a2),product(a8,a9)) = product(product(a3,a4),product(a1,a2)),
inference(transitivity,[status(thm)],[210,207,205]) ).
tff(212,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(a2,a10),product(a2,a10)) = product(a2,a10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
product(product(a2,a10),product(a2,a10)) = product(a2,a10),
inference(unit_resolution,[status(thm)],[212,86]) ).
tff(214,plain,
product(product(product(a2,a10),product(a2,a10)),product(a1,a2)) = product(product(a2,a10),product(a1,a2)),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a2,a10),product(a2,a10)),product(a1,a2)) = product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
product(product(product(a2,a10),product(a2,a10)),product(a1,a2)) = product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),
inference(unit_resolution,[status(thm)],[215,48]) ).
tff(217,plain,
product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))) = product(product(product(a2,a10),product(a2,a10)),product(a1,a2)),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))) = product(product(a2,a10),product(a1,a2)),
inference(transitivity,[status(thm)],[217,214]) ).
tff(219,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)) = product(product(product(a2,a10),product(a1,a2)),product(a1,a2)),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
product(product(product(a2,a10),product(a1,a2)),product(a1,a2)) = product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
product(a2,a10) = product(product(product(a2,a10),product(a1,a2)),product(a1,a2)),
inference(symmetry,[status(thm)],[13]) ).
tff(222,plain,
product(a2,a10) = product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),
inference(transitivity,[status(thm)],[221,220]) ).
tff(223,plain,
product(product(a2,a10),product(product(a1,a2),product(a8,a9))) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),product(product(a3,a4),product(a1,a2))),
inference(monotonicity,[status(thm)],[222,211]) ).
tff(224,plain,
product(product(product(a3,a4),product(a8,a9)),product(product(a1,a2),product(a8,a9))) = product(product(a2,a10),product(product(a1,a2),product(a8,a9))),
inference(monotonicity,[status(thm)],[59]) ).
tff(225,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a3,a4),product(a1,a2)),product(a8,a9)) = product(product(product(a3,a4),product(a8,a9)),product(product(a1,a2),product(a8,a9))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(226,plain,
product(product(product(a3,a4),product(a1,a2)),product(a8,a9)) = product(product(product(a3,a4),product(a8,a9)),product(product(a1,a2),product(a8,a9))),
inference(unit_resolution,[status(thm)],[225,48]) ).
tff(227,plain,
product(product(a10,a3),product(a1,a2)) = product(a8,a9),
inference(transitivity,[status(thm)],[123,117]) ).
tff(228,plain,
product(product(product(a3,a4),product(a1,a2)),product(product(a10,a3),product(a1,a2))) = product(product(product(a3,a4),product(a1,a2)),product(a8,a9)),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a3,a4),product(a10,a3)),product(a1,a2)) = product(product(product(a3,a4),product(a1,a2)),product(product(a10,a3),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(230,plain,
product(product(product(a3,a4),product(a10,a3)),product(a1,a2)) = product(product(product(a3,a4),product(a1,a2)),product(product(a10,a3),product(a1,a2))),
inference(unit_resolution,[status(thm)],[229,48]) ).
tff(231,plain,
product(a1,a2) = product(product(a3,a4),product(a10,a3)),
inference(transitivity,[status(thm)],[136,140]) ).
tff(232,plain,
product(product(a1,a2),product(a1,a2)) = product(product(product(a3,a4),product(a10,a3)),product(a1,a2)),
inference(monotonicity,[status(thm)],[231]) ).
tff(233,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(a1,a2),product(a1,a2)) = product(a1,a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,plain,
product(product(a1,a2),product(a1,a2)) = product(a1,a2),
inference(unit_resolution,[status(thm)],[233,86]) ).
tff(235,plain,
product(a1,a2) = product(product(a1,a2),product(a1,a2)),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
product(a1,a2) = product(a7,a4),
inference(transitivity,[status(thm)],[235,232,230,228,226,224,223,202,199,102,100,79,66]) ).
tff(237,plain,
product(product(a9,a7),product(a1,a2)) = product(product(a9,a7),product(a7,a4)),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
product(product(a9,a7),product(a7,a4)) = product(product(a9,a7),product(a1,a2)),
inference(symmetry,[status(thm)],[237]) ).
tff(239,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a6,a1),product(a10,a3)),product(a10,a3)) = product(a6,a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
product(product(product(a6,a1),product(a10,a3)),product(a10,a3)) = product(a6,a1),
inference(unit_resolution,[status(thm)],[239,11]) ).
tff(241,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(a10,a3)),product(a10,a3)) = product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(242,plain,
product(product(product(a6,a1),product(a10,a3)),product(a10,a3)) = product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),
inference(unit_resolution,[status(thm)],[241,48]) ).
tff(243,plain,
product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))) = product(product(product(a6,a1),product(a10,a3)),product(a10,a3)),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))) = a7,
inference(transitivity,[status(thm)],[243,240,73]) ).
tff(245,plain,
( ( a9 = product(a4,a8) )
<=> ( a9 = product(a4,a8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(246,axiom,
a9 = product(a4,a8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_11) ).
tff(247,plain,
a9 = product(a4,a8),
inference(modus_ponens,[status(thm)],[246,245]) ).
tff(248,plain,
product(a4,a8) = a9,
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
product(product(a4,a8),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))) = product(a9,a7),
inference(monotonicity,[status(thm)],[248,244]) ).
tff(250,plain,
product(a9,a7) = product(product(a4,a8),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
product(product(a9,a7),product(a7,a4)) = product(product(product(a4,a8),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
product(product(product(a4,a8),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)) = product(product(a9,a7),product(a7,a4)),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a4,a8),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)) = product(product(product(a4,a8),product(a7,a4)),product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
product(product(product(a4,a8),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)) = product(product(product(a4,a8),product(a7,a4)),product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4))),
inference(unit_resolution,[status(thm)],[253,48]) ).
tff(255,plain,
product(product(product(a4,a8),product(a7,a4)),product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4))) = product(product(product(a4,a8),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(a8,a9),product(a8,a9)) = product(a8,a9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(257,plain,
product(product(a8,a9),product(a8,a9)) = product(a8,a9),
inference(unit_resolution,[status(thm)],[256,86]) ).
tff(258,plain,
( ( a8 = product(a7,a4) )
<=> ( a8 = product(a7,a4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(259,axiom,
a8 = product(a7,a4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_08) ).
tff(260,plain,
a8 = product(a7,a4),
inference(modus_ponens,[status(thm)],[259,258]) ).
tff(261,plain,
product(a7,a4) = a8,
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
product(product(a7,a4),product(a4,a8)) = product(a8,a9),
inference(monotonicity,[status(thm)],[261,248]) ).
tff(263,plain,
product(product(product(a7,a4),product(a4,a8)),product(product(a7,a4),product(a4,a8))) = product(product(a8,a9),product(a8,a9)),
inference(monotonicity,[status(thm)],[262,262]) ).
tff(264,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a7,a4),product(a7,a4)),product(a4,a8)) = product(product(product(a7,a4),product(a4,a8)),product(product(a7,a4),product(a4,a8))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(265,plain,
product(product(product(a7,a4),product(a7,a4)),product(a4,a8)) = product(product(product(a7,a4),product(a4,a8)),product(product(a7,a4),product(a4,a8))),
inference(unit_resolution,[status(thm)],[264,48]) ).
tff(266,plain,
product(product(a10,a3),product(a7,a4)) = product(a4,a8),
inference(monotonicity,[status(thm)],[31,261]) ).
tff(267,plain,
product(product(product(a7,a4),product(a7,a4)),product(product(a10,a3),product(a7,a4))) = product(product(product(a7,a4),product(a7,a4)),product(a4,a8)),
inference(monotonicity,[status(thm)],[266]) ).
tff(268,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a7,a4),product(a10,a3)),product(a7,a4)) = product(product(product(a7,a4),product(a7,a4)),product(product(a10,a3),product(a7,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(269,plain,
product(product(product(a7,a4),product(a10,a3)),product(a7,a4)) = product(product(product(a7,a4),product(a7,a4)),product(product(a10,a3),product(a7,a4))),
inference(unit_resolution,[status(thm)],[268,48]) ).
tff(270,plain,
product(product(a7,a4),product(a10,a3)) = product(product(product(a6,a1),product(a10,a3)),product(a10,a3)),
inference(monotonicity,[status(thm)],[75]) ).
tff(271,plain,
product(product(product(a6,a1),product(a10,a3)),product(a10,a3)) = product(product(a7,a4),product(a10,a3)),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))) = product(product(a7,a4),product(a10,a3)),
inference(transitivity,[status(thm)],[243,271]) ).
tff(273,plain,
product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)) = product(product(product(a7,a4),product(a10,a3)),product(a7,a4)),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)) = product(a8,a9),
inference(transitivity,[status(thm)],[273,269,267,265,263,257]) ).
tff(275,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a10,a3),product(a7,a4)),product(a7,a4)) = product(a10,a3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(276,plain,
product(product(product(a10,a3),product(a7,a4)),product(a7,a4)) = product(a10,a3),
inference(unit_resolution,[status(thm)],[275,11]) ).
tff(277,plain,
product(product(product(a10,a3),product(a7,a4)),product(a7,a4)) = product(product(a4,a8),product(a7,a4)),
inference(monotonicity,[status(thm)],[266]) ).
tff(278,plain,
product(product(a4,a8),product(a7,a4)) = product(product(product(a10,a3),product(a7,a4)),product(a7,a4)),
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
product(product(a4,a8),product(a7,a4)) = product(a10,a3),
inference(transitivity,[status(thm)],[278,276]) ).
tff(280,plain,
product(product(product(a4,a8),product(a7,a4)),product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4))) = product(product(a10,a3),product(a8,a9)),
inference(monotonicity,[status(thm)],[279,274]) ).
tff(281,plain,
product(product(a10,a3),product(a8,a9)) = product(product(product(a4,a8),product(a7,a4)),product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4))),
inference(symmetry,[status(thm)],[280]) ).
tff(282,plain,
product(product(a10,a3),product(a8,a9)) = product(product(product(a8,a9),product(a1,a2)),product(a8,a9)),
inference(monotonicity,[status(thm)],[122]) ).
tff(283,plain,
product(product(product(a8,a9),product(a1,a2)),product(a8,a9)) = product(product(a10,a3),product(a8,a9)),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a8,a9),product(a1,a2)),product(a8,a9)) = product(product(product(a8,a9),product(a8,a9)),product(product(a1,a2),product(a8,a9))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(285,plain,
product(product(product(a8,a9),product(a1,a2)),product(a8,a9)) = product(product(product(a8,a9),product(a8,a9)),product(product(a1,a2),product(a8,a9))),
inference(unit_resolution,[status(thm)],[284,48]) ).
tff(286,plain,
product(product(product(a8,a9),product(a8,a9)),product(product(a1,a2),product(a8,a9))) = product(product(product(a8,a9),product(a1,a2)),product(a8,a9)),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
product(product(product(a8,a9),product(a8,a9)),product(product(a1,a2),product(a8,a9))) = product(product(a8,a9),product(product(a1,a2),product(a8,a9))),
inference(monotonicity,[status(thm)],[257]) ).
tff(288,plain,
product(product(a8,a9),product(product(a1,a2),product(a8,a9))) = product(product(product(a8,a9),product(a8,a9)),product(product(a1,a2),product(a8,a9))),
inference(symmetry,[status(thm)],[287]) ).
tff(289,plain,
product(a8,a9) = product(product(a10,a3),product(a1,a2)),
inference(transitivity,[status(thm)],[118,124]) ).
tff(290,plain,
product(product(a8,a9),product(product(a1,a2),product(a8,a9))) = product(product(product(a10,a3),product(a1,a2)),product(product(a3,a4),product(a1,a2))),
inference(monotonicity,[status(thm)],[289,211]) ).
tff(291,plain,
product(product(product(a10,a3),product(a1,a2)),product(product(a3,a4),product(a1,a2))) = product(product(a8,a9),product(product(a1,a2),product(a8,a9))),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a10,a3),product(a3,a4)),product(a1,a2)) = product(product(product(a10,a3),product(a1,a2)),product(product(a3,a4),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(293,plain,
product(product(product(a10,a3),product(a3,a4)),product(a1,a2)) = product(product(product(a10,a3),product(a1,a2)),product(product(a3,a4),product(a1,a2))),
inference(unit_resolution,[status(thm)],[292,48]) ).
tff(294,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(a10,a3),product(a10,a3)) = product(a10,a3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
product(product(a10,a3),product(a10,a3)) = product(a10,a3),
inference(unit_resolution,[status(thm)],[294,86]) ).
tff(296,plain,
product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(product(a10,a3),product(a10,a3)),
inference(monotonicity,[status(thm)],[55,55]) ).
tff(297,plain,
product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(a10,a3),
inference(transitivity,[status(thm)],[296,295]) ).
tff(298,plain,
product(product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))),product(a3,a4)) = product(product(a10,a3),product(a3,a4)),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
product(product(a10,a3),product(a3,a4)) = product(product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))),product(a3,a4)),
inference(symmetry,[status(thm)],[298]) ).
tff(300,plain,
product(product(product(a10,a3),product(a3,a4)),product(a1,a2)) = product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))),product(a3,a4)),product(a7,a4)),
inference(monotonicity,[status(thm)],[299,236]) ).
tff(301,plain,
product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))),product(a3,a4)),product(a7,a4)) = product(product(product(a10,a3),product(a3,a4)),product(a1,a2)),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
product(product(a7,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))) = product(product(product(a6,a1),product(a10,a3)),product(product(a7,a4),product(a10,a3))),
inference(monotonicity,[status(thm)],[75,272]) ).
tff(303,plain,
product(product(product(a6,a1),product(a10,a3)),product(product(a7,a4),product(a10,a3))) = product(product(a7,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(symmetry,[status(thm)],[302]) ).
tff(304,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(a7,a4)),product(a10,a3)) = product(product(product(a6,a1),product(a10,a3)),product(product(a7,a4),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(305,plain,
product(product(product(a6,a1),product(a7,a4)),product(a10,a3)) = product(product(product(a6,a1),product(a10,a3)),product(product(a7,a4),product(a10,a3))),
inference(unit_resolution,[status(thm)],[304,48]) ).
tff(306,plain,
product(a6,a1) = product(product(product(a6,a1),product(a10,a3)),product(a10,a3)),
inference(symmetry,[status(thm)],[240]) ).
tff(307,plain,
product(a6,a1) = product(product(a7,a4),product(a10,a3)),
inference(transitivity,[status(thm)],[306,271]) ).
tff(308,plain,
product(product(a6,a1),product(a7,a4)) = product(product(product(a7,a4),product(a10,a3)),product(a7,a4)),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
product(product(a6,a1),product(a7,a4)) = product(a8,a9),
inference(transitivity,[status(thm)],[308,269,267,265,263,257]) ).
tff(310,plain,
product(product(product(a6,a1),product(a7,a4)),product(a10,a3)) = product(product(a8,a9),product(a10,a3)),
inference(monotonicity,[status(thm)],[309]) ).
tff(311,plain,
product(product(a8,a9),product(a10,a3)) = product(product(product(a6,a1),product(a7,a4)),product(a10,a3)),
inference(symmetry,[status(thm)],[310]) ).
tff(312,plain,
product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))) = product(product(a1,a2),product(a1,a2)),
inference(monotonicity,[status(thm)],[24,24]) ).
tff(313,plain,
product(product(a10,a3),product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4)))) = product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[122,312]) ).
tff(314,plain,
product(product(a10,a3),product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4)))) = product(a8,a9),
inference(transitivity,[status(thm)],[313,125,117]) ).
tff(315,plain,
product(product(product(a10,a3),product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4)))),product(a10,a3)) = product(product(a8,a9),product(a10,a3)),
inference(monotonicity,[status(thm)],[314]) ).
tff(316,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a10,a3),product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4)))),product(a10,a3)) = product(product(product(a10,a3),product(a10,a3)),product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(317,plain,
product(product(product(a10,a3),product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4)))),product(a10,a3)) = product(product(product(a10,a3),product(a10,a3)),product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a10,a3))),
inference(unit_resolution,[status(thm)],[316,48]) ).
tff(318,plain,
product(product(product(a10,a3),product(a10,a3)),product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a10,a3))) = product(product(product(a10,a3),product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4)))),product(a10,a3)),
inference(symmetry,[status(thm)],[317]) ).
tff(319,plain,
product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a10,a3)) = product(product(product(a1,a2),product(a1,a2)),product(a10,a3)),
inference(monotonicity,[status(thm)],[312]) ).
tff(320,plain,
product(product(product(a1,a2),product(a1,a2)),product(a10,a3)) = product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a10,a3)),
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a1,a2),product(a1,a2)),product(a10,a3)),
inference(symmetry,[status(thm)],[91]) ).
tff(322,plain,
product(product(a3,a4),product(a3,a4)) = product(product(product(a1,a2),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(symmetry,[status(thm)],[89]) ).
tff(323,plain,
product(a3,a4) = product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a10,a3)),
inference(transitivity,[status(thm)],[203,322,321,320]) ).
tff(324,plain,
product(a10,a3) = product(product(a10,a3),product(a10,a3)),
inference(symmetry,[status(thm)],[295]) ).
tff(325,plain,
product(product(a10,a3),product(a3,a4)) = product(product(product(a10,a3),product(a10,a3)),product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a10,a3))),
inference(monotonicity,[status(thm)],[324,323]) ).
tff(326,plain,
product(product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))),product(a3,a4)) = product(product(a7,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(transitivity,[status(thm)],[298,325,318,315,311,305,303]) ).
tff(327,plain,
product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))),product(a3,a4)),product(a7,a4)) = product(product(product(a7,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)),
inference(monotonicity,[status(thm)],[326]) ).
tff(328,plain,
product(product(product(a7,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)) = product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))),product(a3,a4)),product(a7,a4)),
inference(symmetry,[status(thm)],[327]) ).
tff(329,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a7,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)) = product(product(product(a7,a4),product(a7,a4)),product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(330,plain,
product(product(product(a7,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)) = product(product(product(a7,a4),product(a7,a4)),product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4))),
inference(unit_resolution,[status(thm)],[329,48]) ).
tff(331,plain,
product(product(product(a7,a4),product(a7,a4)),product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4))) = product(product(product(a7,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(a7,a4),product(a7,a4)) = product(a7,a4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
product(product(a7,a4),product(a7,a4)) = product(a7,a4),
inference(unit_resolution,[status(thm)],[332,86]) ).
tff(334,plain,
product(product(product(a7,a4),product(a7,a4)),product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4))) = product(product(a7,a4),product(a8,a9)),
inference(monotonicity,[status(thm)],[333,274]) ).
tff(335,plain,
product(product(a7,a4),product(a8,a9)) = product(product(product(a7,a4),product(a7,a4)),product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4))),
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
product(a8,a9) = product(product(a7,a4),product(a4,a8)),
inference(symmetry,[status(thm)],[262]) ).
tff(337,plain,
product(product(a8,a9),product(a4,a8)) = product(product(product(a7,a4),product(a4,a8)),product(a4,a8)),
inference(monotonicity,[status(thm)],[336]) ).
tff(338,plain,
product(product(product(a7,a4),product(a4,a8)),product(a4,a8)) = product(product(a8,a9),product(a4,a8)),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a7,a4),product(a4,a8)),product(a4,a8)) = product(a7,a4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(340,plain,
product(product(product(a7,a4),product(a4,a8)),product(a4,a8)) = product(a7,a4),
inference(unit_resolution,[status(thm)],[339,11]) ).
tff(341,plain,
product(a7,a4) = product(product(product(a7,a4),product(a4,a8)),product(a4,a8)),
inference(symmetry,[status(thm)],[340]) ).
tff(342,plain,
product(a7,a4) = product(product(a8,a9),product(a4,a8)),
inference(transitivity,[status(thm)],[341,338]) ).
tff(343,plain,
product(product(a7,a4),product(a8,a9)) = product(product(product(a8,a9),product(a4,a8)),product(product(a7,a4),product(a4,a8))),
inference(monotonicity,[status(thm)],[342,336]) ).
tff(344,plain,
product(product(product(a8,a9),product(a4,a8)),product(product(a7,a4),product(a4,a8))) = product(product(a7,a4),product(a8,a9)),
inference(symmetry,[status(thm)],[343]) ).
tff(345,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a8,a9),product(a7,a4)),product(a4,a8)) = product(product(product(a8,a9),product(a4,a8)),product(product(a7,a4),product(a4,a8))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(346,plain,
product(product(product(a8,a9),product(a7,a4)),product(a4,a8)) = product(product(product(a8,a9),product(a4,a8)),product(product(a7,a4),product(a4,a8))),
inference(unit_resolution,[status(thm)],[345,48]) ).
tff(347,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a10,a3),product(a7,a4)),product(a7,a4)) = product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(348,plain,
product(product(product(a10,a3),product(a7,a4)),product(a7,a4)) = product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4))),
inference(unit_resolution,[status(thm)],[347,48]) ).
tff(349,plain,
product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4))) = product(product(product(a10,a3),product(a7,a4)),product(a7,a4)),
inference(symmetry,[status(thm)],[348]) ).
tff(350,plain,
product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4))) = product(a10,a3),
inference(transitivity,[status(thm)],[349,276]) ).
tff(351,plain,
product(product(a7,a4),product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4)))) = product(product(a7,a4),product(a10,a3)),
inference(monotonicity,[status(thm)],[350]) ).
tff(352,plain,
product(product(a4,a8),product(a7,a4)) = product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4))),
inference(transitivity,[status(thm)],[278,348]) ).
tff(353,plain,
product(product(product(a7,a4),product(a7,a4)),product(product(a4,a8),product(a7,a4))) = product(product(a7,a4),product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4)))),
inference(monotonicity,[status(thm)],[333,352]) ).
tff(354,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a7,a4),product(a4,a8)),product(a7,a4)) = product(product(product(a7,a4),product(a7,a4)),product(product(a4,a8),product(a7,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(355,plain,
product(product(product(a7,a4),product(a4,a8)),product(a7,a4)) = product(product(product(a7,a4),product(a7,a4)),product(product(a4,a8),product(a7,a4))),
inference(unit_resolution,[status(thm)],[354,48]) ).
tff(356,plain,
product(product(a8,a9),product(a7,a4)) = product(product(product(a7,a4),product(a4,a8)),product(a7,a4)),
inference(monotonicity,[status(thm)],[336]) ).
tff(357,plain,
product(product(a8,a9),product(a7,a4)) = product(a6,a1),
inference(transitivity,[status(thm)],[356,355,353,351,270,240]) ).
tff(358,plain,
product(product(product(a8,a9),product(a7,a4)),product(a4,a8)) = product(product(a6,a1),product(a4,a8)),
inference(monotonicity,[status(thm)],[357]) ).
tff(359,plain,
product(product(a6,a1),product(a4,a8)) = product(product(product(a8,a9),product(a7,a4)),product(a4,a8)),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
product(product(a4,a8),product(a6,a1)) = product(a9,a7),
inference(monotonicity,[status(thm)],[248,73]) ).
tff(361,plain,
product(a9,a7) = product(product(a4,a8),product(a6,a1)),
inference(symmetry,[status(thm)],[360]) ).
tff(362,plain,
product(product(a9,a7),product(a6,a1)) = product(product(product(a4,a8),product(a6,a1)),product(a6,a1)),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
product(product(product(a4,a8),product(a6,a1)),product(a6,a1)) = product(product(a9,a7),product(a6,a1)),
inference(symmetry,[status(thm)],[362]) ).
tff(364,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a4,a8),product(a6,a1)),product(a6,a1)) = product(a4,a8) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(365,plain,
product(product(product(a4,a8),product(a6,a1)),product(a6,a1)) = product(a4,a8),
inference(unit_resolution,[status(thm)],[364,11]) ).
tff(366,plain,
product(a4,a8) = product(product(product(a4,a8),product(a6,a1)),product(a6,a1)),
inference(symmetry,[status(thm)],[365]) ).
tff(367,plain,
product(a4,a8) = product(product(a9,a7),product(a6,a1)),
inference(transitivity,[status(thm)],[366,363]) ).
tff(368,plain,
product(product(a6,a1),product(a4,a8)) = product(product(product(a6,a1),product(a6,a1)),product(product(a9,a7),product(a6,a1))),
inference(monotonicity,[status(thm)],[109,367]) ).
tff(369,plain,
product(product(product(a6,a1),product(a6,a1)),product(product(a9,a7),product(a6,a1))) = product(product(a6,a1),product(a4,a8)),
inference(symmetry,[status(thm)],[368]) ).
tff(370,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(a9,a7)),product(a6,a1)) = product(product(product(a6,a1),product(a6,a1)),product(product(a9,a7),product(a6,a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(371,plain,
product(product(product(a6,a1),product(a9,a7)),product(a6,a1)) = product(product(product(a6,a1),product(a6,a1)),product(product(a9,a7),product(a6,a1))),
inference(unit_resolution,[status(thm)],[370,48]) ).
tff(372,plain,
product(product(product(a6,a1),product(a9,a7)),product(a6,a1)) = product(product(product(a6,a1),product(a9,a7)),product(product(a5,a4),product(a9,a7))),
inference(monotonicity,[status(thm)],[160]) ).
tff(373,plain,
product(product(product(a6,a1),product(a9,a7)),product(product(a5,a4),product(a9,a7))) = product(product(product(a6,a1),product(a9,a7)),product(a6,a1)),
inference(symmetry,[status(thm)],[372]) ).
tff(374,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a5,a4),product(a9,a7)),product(a9,a7)) = product(a5,a4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(375,plain,
product(product(product(a5,a4),product(a9,a7)),product(a9,a7)) = product(a5,a4),
inference(unit_resolution,[status(thm)],[374,11]) ).
tff(376,plain,
product(product(a6,a1),product(a9,a7)) = product(product(product(a5,a4),product(a9,a7)),product(a9,a7)),
inference(monotonicity,[status(thm)],[160]) ).
tff(377,plain,
product(product(a6,a1),product(a9,a7)) = product(a5,a4),
inference(transitivity,[status(thm)],[376,375]) ).
tff(378,plain,
product(product(product(a6,a1),product(a9,a7)),product(product(a5,a4),product(a9,a7))) = product(product(a5,a4),product(a6,a1)),
inference(monotonicity,[status(thm)],[377,159]) ).
tff(379,plain,
product(product(a5,a4),product(a6,a1)) = product(product(product(a6,a1),product(a9,a7)),product(product(a5,a4),product(a9,a7))),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a3,a4),product(a8,a9)),product(a8,a9)) = product(a3,a4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(381,plain,
product(product(product(a3,a4),product(a8,a9)),product(a8,a9)) = product(a3,a4),
inference(unit_resolution,[status(thm)],[380,11]) ).
tff(382,plain,
product(product(product(a3,a4),product(a8,a9)),product(a8,a9)) = product(product(a2,a10),product(a8,a9)),
inference(monotonicity,[status(thm)],[59]) ).
tff(383,plain,
product(product(a2,a10),product(a8,a9)) = product(product(product(a3,a4),product(a8,a9)),product(a8,a9)),
inference(symmetry,[status(thm)],[382]) ).
tff(384,plain,
product(product(a2,a10),product(a8,a9)) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),product(product(a10,a3),product(a1,a2))),
inference(monotonicity,[status(thm)],[222,289]) ).
tff(385,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),product(product(a10,a3),product(a1,a2))) = product(product(a2,a10),product(a8,a9)),
inference(symmetry,[status(thm)],[384]) ).
tff(386,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(a1,a2)) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),product(product(a10,a3),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(387,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(a1,a2)) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),product(product(a10,a3),product(a1,a2))),
inference(unit_resolution,[status(thm)],[386,48]) ).
tff(388,plain,
product(product(product(a5,a4),product(a3,a4)),product(product(a5,a4),product(a3,a4))) = product(product(product(a5,a4),product(a5,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[184]) ).
tff(389,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)) = product(product(a5,a4),product(a3,a4)),
inference(transitivity,[status(thm)],[178,181,388,188,150]) ).
tff(390,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(a1,a2)) = product(product(product(a5,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))),
inference(monotonicity,[status(thm)],[389,25]) ).
tff(391,plain,
product(product(product(a5,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(a1,a2)),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
product(product(a6,a1),product(a3,a4)) = product(a3,a4),
inference(transitivity,[status(thm)],[161,154,391,387,385,383,381]) ).
tff(393,plain,
product(product(product(a6,a1),product(a3,a4)),product(a3,a4)) = product(product(a3,a4),product(a3,a4)),
inference(monotonicity,[status(thm)],[392]) ).
tff(394,plain,
product(product(product(a1,a2),product(a8,a9)),product(a1,a2)) = product(a3,a4),
inference(transitivity,[status(thm)],[94,92,91,89,88]) ).
tff(395,plain,
product(product(product(a5,a4),product(a9,a7)),product(a3,a4)) = product(product(a6,a1),product(a3,a4)),
inference(symmetry,[status(thm)],[161]) ).
tff(396,plain,
product(product(product(a5,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))) = product(product(product(a5,a4),product(a9,a7)),product(a3,a4)),
inference(symmetry,[status(thm)],[154]) ).
tff(397,plain,
product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)) = product(product(a6,a1),product(a3,a4)),
inference(transitivity,[status(thm)],[151,396,395]) ).
tff(398,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))) = product(product(product(a6,a1),product(a3,a4)),product(a3,a4)),
inference(monotonicity,[status(thm)],[397,394]) ).
tff(399,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(product(product(a1,a2),product(a8,a9)),product(a1,a2)),
inference(symmetry,[status(thm)],[94]) ).
tff(400,plain,
product(product(product(a1,a2),product(a1,a2)),product(a10,a3)) = product(product(product(a1,a2),product(a1,a2)),product(product(a8,a9),product(a1,a2))),
inference(symmetry,[status(thm)],[92]) ).
tff(401,plain,
product(a3,a4) = product(product(product(a1,a2),product(a8,a9)),product(a1,a2)),
inference(transitivity,[status(thm)],[203,322,321,400,399]) ).
tff(402,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(a3,a4)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))),
inference(monotonicity,[status(thm)],[401]) ).
tff(403,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(a3,a4)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)),product(product(a1,a2),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(404,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(a3,a4)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)),product(product(a1,a2),product(a3,a4))),
inference(unit_resolution,[status(thm)],[403,48]) ).
tff(405,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)),product(product(a1,a2),product(a3,a4))) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(a3,a4)),
inference(symmetry,[status(thm)],[404]) ).
tff(406,plain,
product(product(a1,a2),product(a3,a4)) = product(product(product(a9,a7),product(a3,a4)),product(a3,a4)),
inference(monotonicity,[status(thm)],[25]) ).
tff(407,plain,
product(product(product(a9,a7),product(a3,a4)),product(a3,a4)) = product(product(a1,a2),product(a3,a4)),
inference(symmetry,[status(thm)],[406]) ).
tff(408,plain,
product(a9,a7) = product(product(product(a9,a7),product(a3,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[15]) ).
tff(409,plain,
a1 = product(product(a1,a2),product(a3,a4)),
inference(transitivity,[status(thm)],[22,408,407]) ).
tff(410,plain,
product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)) = product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(monotonicity,[status(thm)],[174,37]) ).
tff(411,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)),
inference(symmetry,[status(thm)],[410]) ).
tff(412,plain,
product(product(a5,a4),product(a3,a4)) = product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),
inference(transitivity,[status(thm)],[149,174]) ).
tff(413,plain,
product(product(product(a5,a4),product(a3,a4)),product(a3,a4)) = product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(monotonicity,[status(thm)],[412,37]) ).
tff(414,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a5,a4),product(a3,a4)),product(a3,a4)) = product(a5,a4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(415,plain,
product(product(product(a5,a4),product(a3,a4)),product(a3,a4)) = product(a5,a4),
inference(unit_resolution,[status(thm)],[414,11]) ).
tff(416,plain,
product(a5,a4) = product(product(product(a5,a4),product(a3,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[415]) ).
tff(417,plain,
a6 = product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)),
inference(transitivity,[status(thm)],[157,416,413,411]) ).
tff(418,plain,
product(a6,a1) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)),product(product(a1,a2),product(a3,a4))),
inference(monotonicity,[status(thm)],[417,409]) ).
tff(419,plain,
product(a6,a1) = product(product(a1,a2),product(a10,a3)),
inference(transitivity,[status(thm)],[418,405,402,398,393,88,37]) ).
tff(420,plain,
product(product(a5,a4),product(a6,a1)) = product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(monotonicity,[status(thm)],[148,419]) ).
tff(421,plain,
product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(a5,a4),product(a6,a1)),
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
product(product(product(a2,a10),product(a1,a2)),product(a10,a3)) = product(product(product(a2,a10),product(a1,a2)),product(product(a8,a9),product(a1,a2))),
inference(monotonicity,[status(thm)],[122]) ).
tff(423,plain,
product(product(product(a2,a10),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),
inference(symmetry,[status(thm)],[422]) ).
tff(424,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a2,a10),product(a8,a9)),product(a1,a2)) = product(product(product(a2,a10),product(a1,a2)),product(product(a8,a9),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(425,plain,
product(product(product(a2,a10),product(a8,a9)),product(a1,a2)) = product(product(product(a2,a10),product(a1,a2)),product(product(a8,a9),product(a1,a2))),
inference(unit_resolution,[status(thm)],[424,48]) ).
tff(426,plain,
product(product(a2,a10),product(a8,a9)) = product(product(a3,a4),product(a3,a4)),
inference(transitivity,[status(thm)],[383,381,203]) ).
tff(427,plain,
product(product(product(a2,a10),product(a8,a9)),product(a1,a2)) = product(product(product(a3,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))),
inference(monotonicity,[status(thm)],[426,25]) ).
tff(428,plain,
product(product(product(a3,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))) = product(product(product(a2,a10),product(a8,a9)),product(a1,a2)),
inference(symmetry,[status(thm)],[427]) ).
tff(429,plain,
product(product(a9,a7),product(a3,a4)) = product(product(a6,a1),product(a10,a3)),
inference(transitivity,[status(thm)],[24,235,232,230,228,226,224,223,202,199,102,100,79,66,75]) ).
tff(430,plain,
product(product(a3,a4),product(a3,a4)) = product(product(a1,a2),product(a10,a3)),
inference(transitivity,[status(thm)],[88,37]) ).
tff(431,plain,
product(product(product(a3,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))) = product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))),
inference(monotonicity,[status(thm)],[430,429]) ).
tff(432,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))) = product(product(product(a3,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))),
inference(symmetry,[status(thm)],[431]) ).
tff(433,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)),product(product(a1,a2),product(a3,a4))) = product(a6,a1),
inference(symmetry,[status(thm)],[418]) ).
tff(434,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(a3,a4)),
inference(symmetry,[status(thm)],[402]) ).
tff(435,plain,
product(product(product(a6,a1),product(a3,a4)),product(a3,a4)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))),
inference(symmetry,[status(thm)],[398]) ).
tff(436,plain,
product(product(a3,a4),product(a3,a4)) = product(product(product(a6,a1),product(a3,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[393]) ).
tff(437,plain,
product(product(a1,a2),product(a10,a3)) = product(a6,a1),
inference(transitivity,[status(thm)],[36,203,436,435,434,404,433]) ).
tff(438,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))) = product(product(a6,a1),product(a7,a4)),
inference(monotonicity,[status(thm)],[437,74]) ).
tff(439,plain,
product(product(a6,a1),product(a7,a4)) = product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))),
inference(symmetry,[status(thm)],[438]) ).
tff(440,plain,
product(product(product(a7,a4),product(a10,a3)),product(a7,a4)) = product(product(a6,a1),product(a7,a4)),
inference(symmetry,[status(thm)],[308]) ).
tff(441,plain,
product(product(product(a7,a4),product(a7,a4)),product(product(a10,a3),product(a7,a4))) = product(product(product(a7,a4),product(a10,a3)),product(a7,a4)),
inference(symmetry,[status(thm)],[269]) ).
tff(442,plain,
product(product(product(a7,a4),product(a7,a4)),product(a4,a8)) = product(product(product(a7,a4),product(a7,a4)),product(product(a10,a3),product(a7,a4))),
inference(symmetry,[status(thm)],[267]) ).
tff(443,plain,
product(product(product(a7,a4),product(a4,a8)),product(product(a7,a4),product(a4,a8))) = product(product(product(a7,a4),product(a7,a4)),product(a4,a8)),
inference(symmetry,[status(thm)],[265]) ).
tff(444,plain,
product(product(a8,a9),product(a8,a9)) = product(product(product(a7,a4),product(a4,a8)),product(product(a7,a4),product(a4,a8))),
inference(symmetry,[status(thm)],[263]) ).
tff(445,plain,
product(a8,a9) = product(product(a8,a9),product(a8,a9)),
inference(symmetry,[status(thm)],[257]) ).
tff(446,plain,
product(a1,a2) = a8,
inference(transitivity,[status(thm)],[235,232,230,228,226,224,223,202,199,102,100,79,66,261]) ).
tff(447,plain,
product(product(a8,a9),product(a1,a2)) = a4,
inference(transitivity,[status(thm)],[55,31]) ).
tff(448,plain,
product(product(product(a8,a9),product(a1,a2)),product(a1,a2)) = product(a4,a8),
inference(monotonicity,[status(thm)],[447,446]) ).
tff(449,plain,
product(a4,a8) = product(product(product(a8,a9),product(a1,a2)),product(a1,a2)),
inference(symmetry,[status(thm)],[448]) ).
tff(450,plain,
product(a6,a1) = a2,
inference(transitivity,[status(thm)],[418,405,402,398,393,88,19]) ).
tff(451,plain,
product(product(a4,a8),product(a6,a1)) = a1,
inference(transitivity,[status(thm)],[360,23]) ).
tff(452,plain,
product(product(product(a4,a8),product(a6,a1)),product(a6,a1)) = product(a1,a2),
inference(monotonicity,[status(thm)],[451,450]) ).
tff(453,plain,
product(a1,a2) = product(product(product(a4,a8),product(a6,a1)),product(a6,a1)),
inference(symmetry,[status(thm)],[452]) ).
tff(454,plain,
product(product(product(a3,a4),product(a10,a3)),product(a1,a2)) = product(product(a1,a2),product(a1,a2)),
inference(symmetry,[status(thm)],[232]) ).
tff(455,plain,
product(product(product(a3,a4),product(a1,a2)),product(product(a10,a3),product(a1,a2))) = product(product(product(a3,a4),product(a10,a3)),product(a1,a2)),
inference(symmetry,[status(thm)],[230]) ).
tff(456,plain,
product(product(product(a3,a4),product(a1,a2)),product(a8,a9)) = product(product(product(a3,a4),product(a1,a2)),product(product(a10,a3),product(a1,a2))),
inference(symmetry,[status(thm)],[228]) ).
tff(457,plain,
product(product(product(a3,a4),product(a8,a9)),product(product(a1,a2),product(a8,a9))) = product(product(product(a3,a4),product(a1,a2)),product(a8,a9)),
inference(symmetry,[status(thm)],[226]) ).
tff(458,plain,
product(product(a2,a10),product(product(a1,a2),product(a8,a9))) = product(product(product(a3,a4),product(a8,a9)),product(product(a1,a2),product(a8,a9))),
inference(symmetry,[status(thm)],[224]) ).
tff(459,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),product(product(a3,a4),product(a1,a2))) = product(product(a2,a10),product(product(a1,a2),product(a8,a9))),
inference(symmetry,[status(thm)],[223]) ).
tff(460,plain,
product(product(product(product(a6,a1),product(a8,a9)),product(product(a1,a2),product(a8,a9))),product(a1,a2)) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a3,a4)),product(a1,a2)),
inference(symmetry,[status(thm)],[199]) ).
tff(461,plain,
product(product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))) = product(product(product(product(a6,a1),product(a8,a9)),product(product(a1,a2),product(a8,a9))),product(a1,a2)),
inference(symmetry,[status(thm)],[102]) ).
tff(462,plain,
product(product(product(product(a6,a1),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))),
inference(symmetry,[status(thm)],[100]) ).
tff(463,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a1,a2)),product(product(a10,a3),product(a1,a2))) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(a1,a2)),
inference(symmetry,[status(thm)],[387]) ).
tff(464,plain,
product(a3,a4) = product(product(product(a3,a4),product(a8,a9)),product(a8,a9)),
inference(symmetry,[status(thm)],[381]) ).
tff(465,plain,
product(product(a1,a2),product(a10,a3)) = product(product(a6,a1),product(a3,a4)),
inference(transitivity,[status(thm)],[36,464,382,384,463,390,396,395]) ).
tff(466,plain,
product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(a7,a4),product(a3,a4)),
inference(symmetry,[status(thm)],[76]) ).
tff(467,plain,
product(product(product(a6,a1),product(a1,a2)),product(a10,a3)) = product(product(a7,a4),product(a3,a4)),
inference(transitivity,[status(thm)],[68,466]) ).
tff(468,plain,
product(product(product(product(a6,a1),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a7,a4),product(a3,a4)),product(product(a6,a1),product(a3,a4))),
inference(monotonicity,[status(thm)],[467,465]) ).
tff(469,plain,
product(product(product(a7,a4),product(a3,a4)),product(product(a6,a1),product(a3,a4))) = product(product(product(product(a6,a1),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(symmetry,[status(thm)],[468]) ).
tff(470,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a7,a4),product(a6,a1)),product(a3,a4)) = product(product(product(a7,a4),product(a3,a4)),product(product(a6,a1),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(471,plain,
product(product(product(a7,a4),product(a6,a1)),product(a3,a4)) = product(product(product(a7,a4),product(a3,a4)),product(product(a6,a1),product(a3,a4))),
inference(unit_resolution,[status(thm)],[470,48]) ).
tff(472,plain,
product(product(product(a10,a3),product(a10,a3)),product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a10,a3))) = product(product(a10,a3),product(a3,a4)),
inference(symmetry,[status(thm)],[325]) ).
tff(473,plain,
product(product(a8,a9),product(a10,a3)) = product(product(product(a10,a3),product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4)))),product(a10,a3)),
inference(symmetry,[status(thm)],[315]) ).
tff(474,plain,
product(product(product(a6,a1),product(a10,a3)),product(product(a7,a4),product(a10,a3))) = product(product(product(a6,a1),product(a7,a4)),product(a10,a3)),
inference(symmetry,[status(thm)],[305]) ).
tff(475,plain,
product(a6,a1) = product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),
inference(transitivity,[status(thm)],[306,242]) ).
tff(476,plain,
product(product(a7,a4),product(a6,a1)) = product(product(a7,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(monotonicity,[status(thm)],[475]) ).
tff(477,plain,
product(product(a7,a4),product(a6,a1)) = product(product(a10,a3),product(a3,a4)),
inference(transitivity,[status(thm)],[476,302,474,310,473,317,472]) ).
tff(478,plain,
product(product(product(a7,a4),product(a6,a1)),product(a3,a4)) = product(product(product(a10,a3),product(a3,a4)),product(a3,a4)),
inference(monotonicity,[status(thm)],[477]) ).
tff(479,plain,
product(product(product(a10,a3),product(a3,a4)),product(a3,a4)) = product(product(product(a7,a4),product(a6,a1)),product(a3,a4)),
inference(symmetry,[status(thm)],[478]) ).
tff(480,plain,
product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))) = product(product(a10,a3),product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4)))),
inference(symmetry,[status(thm)],[313]) ).
tff(481,plain,
product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a10,a3)) = product(product(product(a10,a3),product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4)))),product(a10,a3)),
inference(monotonicity,[status(thm)],[480]) ).
tff(482,plain,
product(product(product(a10,a3),product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4)))),product(a10,a3)) = product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a10,a3)),
inference(symmetry,[status(thm)],[481]) ).
tff(483,plain,
product(product(a10,a3),product(a3,a4)) = product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a10,a3)),
inference(transitivity,[status(thm)],[325,318,482]) ).
tff(484,plain,
product(product(product(a10,a3),product(a3,a4)),product(a3,a4)) = product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(monotonicity,[status(thm)],[483,37]) ).
tff(485,plain,
product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a10,a3),product(a3,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[484]) ).
tff(486,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a1,a2)),product(a10,a3)) = product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a10,a3)),product(product(a1,a2),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(487,plain,
product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a1,a2)),product(a10,a3)) = product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(unit_resolution,[status(thm)],[486,48]) ).
tff(488,plain,
product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))) = a10,
inference(transitivity,[status(thm)],[125,117,54]) ).
tff(489,plain,
product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a1,a2)) = product(a10,a3),
inference(monotonicity,[status(thm)],[488,35]) ).
tff(490,plain,
product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a1,a2)),product(a10,a3)) = product(product(a10,a3),product(a10,a3)),
inference(monotonicity,[status(thm)],[489]) ).
tff(491,plain,
product(product(a10,a3),product(a10,a3)) = product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a1,a2)),product(a10,a3)),
inference(symmetry,[status(thm)],[490]) ).
tff(492,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a10,a3),product(a6,a1)),product(a10,a3)) = product(product(product(a10,a3),product(a10,a3)),product(product(a6,a1),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(493,plain,
product(product(product(a10,a3),product(a6,a1)),product(a10,a3)) = product(product(product(a10,a3),product(a10,a3)),product(product(a6,a1),product(a10,a3))),
inference(unit_resolution,[status(thm)],[492,48]) ).
tff(494,plain,
product(product(product(a10,a3),product(a10,a3)),product(product(a6,a1),product(a10,a3))) = product(product(product(a10,a3),product(a6,a1)),product(a10,a3)),
inference(symmetry,[status(thm)],[493]) ).
tff(495,plain,
product(product(product(a10,a3),product(a10,a3)),product(product(a6,a1),product(a10,a3))) = product(product(product(a10,a3),product(a10,a3)),product(a7,a4)),
inference(monotonicity,[status(thm)],[74]) ).
tff(496,plain,
product(product(product(a10,a3),product(a10,a3)),product(a7,a4)) = product(product(product(a10,a3),product(a10,a3)),product(product(a6,a1),product(a10,a3))),
inference(symmetry,[status(thm)],[495]) ).
tff(497,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a10,a3),product(a10,a3)),product(a7,a4)) = product(product(product(a10,a3),product(a7,a4)),product(product(a10,a3),product(a7,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(498,plain,
product(product(product(a10,a3),product(a10,a3)),product(a7,a4)) = product(product(product(a10,a3),product(a7,a4)),product(product(a10,a3),product(a7,a4))),
inference(unit_resolution,[status(thm)],[497,48]) ).
tff(499,plain,
product(product(product(a10,a3),product(a7,a4)),product(product(a10,a3),product(a7,a4))) = product(product(product(a10,a3),product(a10,a3)),product(a7,a4)),
inference(symmetry,[status(thm)],[498]) ).
tff(500,plain,
product(product(product(a10,a3),product(a7,a4)),product(product(a10,a3),product(a7,a4))) = product(product(a4,a8),product(a4,a8)),
inference(monotonicity,[status(thm)],[266,266]) ).
tff(501,plain,
product(product(a4,a8),product(a4,a8)) = product(product(product(a10,a3),product(a7,a4)),product(product(a10,a3),product(a7,a4))),
inference(symmetry,[status(thm)],[500]) ).
tff(502,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(product(a4,a8),product(a4,a8)) = product(a4,a8) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(503,plain,
product(product(a4,a8),product(a4,a8)) = product(a4,a8),
inference(unit_resolution,[status(thm)],[502,86]) ).
tff(504,plain,
product(a4,a8) = product(product(a4,a8),product(a4,a8)),
inference(symmetry,[status(thm)],[503]) ).
tff(505,plain,
product(a4,a8) = product(product(product(a10,a3),product(a6,a1)),product(a10,a3)),
inference(transitivity,[status(thm)],[504,501,499,496,494]) ).
tff(506,plain,
product(product(a4,a8),product(a7,a4)) = product(product(product(product(a10,a3),product(a6,a1)),product(a10,a3)),product(product(a6,a1),product(a10,a3))),
inference(monotonicity,[status(thm)],[505,75]) ).
tff(507,plain,
product(product(product(product(a10,a3),product(a6,a1)),product(a10,a3)),product(product(a6,a1),product(a10,a3))) = product(product(a4,a8),product(a7,a4)),
inference(symmetry,[status(thm)],[506]) ).
tff(508,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a10,a3),product(a6,a1)),product(a6,a1)),product(a10,a3)) = product(product(product(product(a10,a3),product(a6,a1)),product(a10,a3)),product(product(a6,a1),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(509,plain,
product(product(product(product(a10,a3),product(a6,a1)),product(a6,a1)),product(a10,a3)) = product(product(product(product(a10,a3),product(a6,a1)),product(a10,a3)),product(product(a6,a1),product(a10,a3))),
inference(unit_resolution,[status(thm)],[508,48]) ).
tff(510,plain,
product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))) = product(product(a4,a8),product(a6,a1)),
inference(transitivity,[status(thm)],[217,214,61,58,56,50,41,40,15,361]) ).
tff(511,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(product(a10,a3),product(a6,a1))) = product(product(product(a4,a8),product(a6,a1)),product(product(a10,a3),product(a6,a1))),
inference(monotonicity,[status(thm)],[510]) ).
tff(512,plain,
product(product(product(a4,a8),product(a6,a1)),product(product(a10,a3),product(a6,a1))) = product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(product(a10,a3),product(a6,a1))),
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(a4,a8),product(a10,a3)),product(a6,a1)) = product(product(product(a4,a8),product(a6,a1)),product(product(a10,a3),product(a6,a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(514,plain,
product(product(product(a4,a8),product(a10,a3)),product(a6,a1)) = product(product(product(a4,a8),product(a6,a1)),product(product(a10,a3),product(a6,a1))),
inference(unit_resolution,[status(thm)],[513,48]) ).
tff(515,plain,
product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))) = product(a6,a1),
inference(transitivity,[status(thm)],[243,240]) ).
tff(516,plain,
product(product(a10,a3),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))) = product(product(a10,a3),product(a6,a1)),
inference(monotonicity,[status(thm)],[515]) ).
tff(517,plain,
product(product(a7,a4),product(a10,a3)) = product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),
inference(transitivity,[status(thm)],[270,242]) ).
tff(518,plain,
product(product(product(a10,a3),product(a10,a3)),product(product(a7,a4),product(a10,a3))) = product(product(a10,a3),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(monotonicity,[status(thm)],[295,517]) ).
tff(519,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a10,a3),product(a7,a4)),product(a10,a3)) = product(product(product(a10,a3),product(a10,a3)),product(product(a7,a4),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(520,plain,
product(product(product(a10,a3),product(a7,a4)),product(a10,a3)) = product(product(product(a10,a3),product(a10,a3)),product(product(a7,a4),product(a10,a3))),
inference(unit_resolution,[status(thm)],[519,48]) ).
tff(521,plain,
product(a4,a8) = product(product(a10,a3),product(a7,a4)),
inference(symmetry,[status(thm)],[266]) ).
tff(522,plain,
product(product(a4,a8),product(a10,a3)) = product(product(product(a10,a3),product(a7,a4)),product(a10,a3)),
inference(monotonicity,[status(thm)],[521]) ).
tff(523,plain,
product(product(a4,a8),product(a10,a3)) = product(product(a10,a3),product(a6,a1)),
inference(transitivity,[status(thm)],[522,520,518,516]) ).
tff(524,plain,
product(product(product(a4,a8),product(a10,a3)),product(a6,a1)) = product(product(product(a10,a3),product(a6,a1)),product(a6,a1)),
inference(monotonicity,[status(thm)],[523]) ).
tff(525,plain,
product(product(product(a10,a3),product(a6,a1)),product(a6,a1)) = product(product(product(a4,a8),product(a10,a3)),product(a6,a1)),
inference(symmetry,[status(thm)],[524]) ).
tff(526,plain,
product(product(product(a10,a3),product(a6,a1)),product(a6,a1)) = product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(product(a10,a3),product(a6,a1))),
inference(transitivity,[status(thm)],[525,514,512]) ).
tff(527,plain,
product(product(product(product(a10,a3),product(a6,a1)),product(a6,a1)),product(a10,a3)) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(product(a10,a3),product(a6,a1))),product(a10,a3)),
inference(monotonicity,[status(thm)],[526]) ).
tff(528,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(product(a10,a3),product(a6,a1))),product(a10,a3)) = product(product(product(product(a10,a3),product(a6,a1)),product(a6,a1)),product(a10,a3)),
inference(symmetry,[status(thm)],[527]) ).
tff(529,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(product(a10,a3),product(a6,a1))),product(a10,a3)) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(product(product(a10,a3),product(a6,a1)),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(530,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(product(a10,a3),product(a6,a1))),product(a10,a3)) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(product(product(a10,a3),product(a6,a1)),product(a10,a3))),
inference(unit_resolution,[status(thm)],[529,48]) ).
tff(531,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(product(product(a10,a3),product(a6,a1)),product(a10,a3))) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(product(a10,a3),product(a6,a1))),product(a10,a3)),
inference(symmetry,[status(thm)],[530]) ).
tff(532,plain,
product(product(product(a10,a3),product(a6,a1)),product(a10,a3)) = product(a4,a8),
inference(transitivity,[status(thm)],[493,495,498,500,503]) ).
tff(533,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)) = product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(transitivity,[status(thm)],[178,181,388,188]) ).
tff(534,plain,
product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(product(product(a10,a3),product(a6,a1)),product(a10,a3))) = product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a4,a8)),
inference(monotonicity,[status(thm)],[533,532]) ).
tff(535,plain,
product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a4,a8)) = product(product(product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),product(a10,a3)),product(product(product(a10,a3),product(a6,a1)),product(a10,a3))),
inference(symmetry,[status(thm)],[534]) ).
tff(536,plain,
product(product(product(a3,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))) = product(product(product(product(a1,a2),product(a8,a9)),product(a1,a2)),product(a1,a2)),
inference(symmetry,[status(thm)],[207]) ).
tff(537,plain,
product(product(product(a2,a10),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(product(product(a2,a10),product(a8,a9)),product(a1,a2)),
inference(symmetry,[status(thm)],[425]) ).
tff(538,plain,
product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(a1,a2),product(a8,a9)),
inference(transitivity,[status(thm)],[174,422,537,427,536,209]) ).
tff(539,plain,
product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a4,a8)) = product(product(product(a1,a2),product(a8,a9)),product(a4,a8)),
inference(monotonicity,[status(thm)],[538]) ).
tff(540,plain,
product(product(product(a1,a2),product(a8,a9)),product(a4,a8)) = product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a4,a8)),
inference(symmetry,[status(thm)],[539]) ).
tff(541,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a1,a2),product(a8,a9)),product(a4,a8)) = product(product(product(a1,a2),product(a4,a8)),product(product(a8,a9),product(a4,a8))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(542,plain,
product(product(product(a1,a2),product(a8,a9)),product(a4,a8)) = product(product(product(a1,a2),product(a4,a8)),product(product(a8,a9),product(a4,a8))),
inference(unit_resolution,[status(thm)],[541,48]) ).
tff(543,plain,
product(product(product(a1,a2),product(a4,a8)),product(product(a8,a9),product(a4,a8))) = product(product(product(a1,a2),product(a8,a9)),product(a4,a8)),
inference(symmetry,[status(thm)],[542]) ).
tff(544,plain,
product(product(a8,a9),product(a4,a8)) = product(a7,a4),
inference(transitivity,[status(thm)],[337,340]) ).
tff(545,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))) = product(a1,a2),
inference(transitivity,[status(thm)],[141,27]) ).
tff(546,plain,
product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)) = product(product(a1,a2),product(a4,a8)),
inference(monotonicity,[status(thm)],[545]) ).
tff(547,plain,
product(product(a1,a2),product(a4,a8)) = product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),
inference(symmetry,[status(thm)],[546]) ).
tff(548,plain,
product(product(product(a1,a2),product(a4,a8)),product(product(a8,a9),product(a4,a8))) = product(product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)),
inference(monotonicity,[status(thm)],[547,544]) ).
tff(549,plain,
product(product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)) = product(product(product(a1,a2),product(a4,a8)),product(product(a8,a9),product(a4,a8))),
inference(symmetry,[status(thm)],[548]) ).
tff(550,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,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)) = product(product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(551,plain,
product(product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)) = product(product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))),
inference(unit_resolution,[status(thm)],[550,48]) ).
tff(552,plain,
product(product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))) = product(product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)),
inference(symmetry,[status(thm)],[551]) ).
tff(553,plain,
product(product(a3,a4),product(a10,a3)) = product(a1,a2),
inference(transitivity,[status(thm)],[38,27]) ).
tff(554,plain,
product(product(product(a3,a4),product(a10,a3)),product(a7,a4)) = product(product(a1,a2),product(a7,a4)),
inference(monotonicity,[status(thm)],[553]) ).
tff(555,plain,
product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)) = product(product(product(a3,a4),product(a10,a3)),product(a7,a4)),
inference(monotonicity,[status(thm)],[142]) ).
tff(556,plain,
product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)) = product(product(a1,a2),product(a7,a4)),
inference(transitivity,[status(thm)],[555,554]) ).
tff(557,plain,
product(product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))) = product(product(product(a1,a2),product(a7,a4)),product(a10,a3)),
inference(monotonicity,[status(thm)],[556,279]) ).
tff(558,plain,
product(product(product(a1,a2),product(a7,a4)),product(a10,a3)) = product(product(product(product(product(a1,a2),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))),
inference(symmetry,[status(thm)],[557]) ).
tff(559,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a1,a2),product(a7,a4)),product(a10,a3)) = product(product(product(a1,a2),product(a10,a3)),product(product(a7,a4),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(560,plain,
product(product(product(a1,a2),product(a7,a4)),product(a10,a3)) = product(product(product(a1,a2),product(a10,a3)),product(product(a7,a4),product(a10,a3))),
inference(unit_resolution,[status(thm)],[559,48]) ).
tff(561,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a7,a4),product(a10,a3))) = product(product(product(a1,a2),product(a7,a4)),product(a10,a3)),
inference(symmetry,[status(thm)],[560]) ).
tff(562,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a7,a4),product(a10,a3))) = product(product(a3,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(monotonicity,[status(thm)],[36,517]) ).
tff(563,plain,
product(product(a3,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))) = product(product(product(a1,a2),product(a10,a3)),product(product(a7,a4),product(a10,a3))),
inference(symmetry,[status(thm)],[562]) ).
tff(564,plain,
product(product(a3,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))) = product(product(a3,a4),product(a6,a1)),
inference(monotonicity,[status(thm)],[515]) ).
tff(565,plain,
product(product(a3,a4),product(a6,a1)) = product(product(a3,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(symmetry,[status(thm)],[564]) ).
tff(566,plain,
product(a6,a1) = product(a3,a4),
inference(transitivity,[status(thm)],[418,405,402,398,393,88]) ).
tff(567,plain,
product(product(a3,a4),product(a6,a1)) = product(product(a3,a4),product(a3,a4)),
inference(monotonicity,[status(thm)],[566]) ).
tff(568,plain,
product(product(a3,a4),product(a3,a4)) = product(product(a3,a4),product(a6,a1)),
inference(symmetry,[status(thm)],[567]) ).
tff(569,plain,
product(product(product(a7,a4),product(a4,a8)),product(a7,a4)) = product(product(a8,a9),product(a7,a4)),
inference(symmetry,[status(thm)],[356]) ).
tff(570,plain,
product(product(product(a7,a4),product(a7,a4)),product(product(a4,a8),product(a7,a4))) = product(product(product(a7,a4),product(a4,a8)),product(a7,a4)),
inference(symmetry,[status(thm)],[355]) ).
tff(571,plain,
product(product(a7,a4),product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4)))) = product(product(product(a7,a4),product(a7,a4)),product(product(a4,a8),product(a7,a4))),
inference(symmetry,[status(thm)],[353]) ).
tff(572,plain,
product(product(a7,a4),product(a10,a3)) = product(product(a7,a4),product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4)))),
inference(symmetry,[status(thm)],[351]) ).
tff(573,plain,
product(product(a5,a4),product(a9,a7)) = product(product(a8,a9),product(a7,a4)),
inference(transitivity,[status(thm)],[159,306,271,572,571,570,569]) ).
tff(574,plain,
product(product(product(a5,a4),product(a9,a7)),product(a3,a4)) = product(product(product(a8,a9),product(a7,a4)),product(a3,a4)),
inference(monotonicity,[status(thm)],[573]) ).
tff(575,plain,
product(product(product(a8,a9),product(a7,a4)),product(a3,a4)) = product(product(product(a5,a4),product(a9,a7)),product(a3,a4)),
inference(symmetry,[status(thm)],[574]) ).
tff(576,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a8,a9),product(a7,a4)),product(a3,a4)) = product(product(product(a8,a9),product(a3,a4)),product(product(a7,a4),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(577,plain,
product(product(product(a8,a9),product(a7,a4)),product(a3,a4)) = product(product(product(a8,a9),product(a3,a4)),product(product(a7,a4),product(a3,a4))),
inference(unit_resolution,[status(thm)],[576,48]) ).
tff(578,plain,
product(product(product(a8,a9),product(a3,a4)),product(product(a7,a4),product(a3,a4))) = product(product(product(a8,a9),product(a7,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[577]) ).
tff(579,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a3,a4),product(a10,a3)),product(a3,a4)) = product(product(product(a3,a4),product(a3,a4)),product(product(a10,a3),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(580,plain,
product(product(product(a3,a4),product(a10,a3)),product(a3,a4)) = product(product(product(a3,a4),product(a3,a4)),product(product(a10,a3),product(a3,a4))),
inference(unit_resolution,[status(thm)],[579,48]) ).
tff(581,plain,
product(product(product(a3,a4),product(a3,a4)),product(product(a10,a3),product(a3,a4))) = product(product(product(a3,a4),product(a10,a3)),product(a3,a4)),
inference(symmetry,[status(thm)],[580]) ).
tff(582,plain,
product(product(a6,a1),product(a3,a4)) = product(product(a3,a4),product(a3,a4)),
inference(transitivity,[status(thm)],[161,154,391,387,385,383,381,203]) ).
tff(583,plain,
product(product(product(a6,a1),product(a3,a4)),product(product(a10,a3),product(a3,a4))) = product(product(product(a3,a4),product(a3,a4)),product(product(a10,a3),product(a3,a4))),
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(a6,a1),product(a10,a3)),product(a3,a4)) = product(product(product(a6,a1),product(a3,a4)),product(product(a10,a3),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(585,plain,
product(product(product(a6,a1),product(a10,a3)),product(a3,a4)) = product(product(product(a6,a1),product(a3,a4)),product(product(a10,a3),product(a3,a4))),
inference(unit_resolution,[status(thm)],[584,48]) ).
tff(586,plain,
product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a6,a1),product(a10,a3)),product(a3,a4)),
inference(monotonicity,[status(thm)],[36]) ).
tff(587,plain,
product(product(a7,a4),product(a3,a4)) = product(product(a1,a2),product(a3,a4)),
inference(transitivity,[status(thm)],[76,586,585,583,581,40,407]) ).
tff(588,plain,
product(product(product(a8,a9),product(a3,a4)),product(product(a7,a4),product(a3,a4))) = product(product(product(a8,a9),product(a3,a4)),product(product(a1,a2),product(a3,a4))),
inference(monotonicity,[status(thm)],[587]) ).
tff(589,plain,
product(product(product(a8,a9),product(a3,a4)),product(product(a1,a2),product(a3,a4))) = product(product(product(a8,a9),product(a3,a4)),product(product(a7,a4),product(a3,a4))),
inference(symmetry,[status(thm)],[588]) ).
tff(590,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a8,a9),product(a1,a2)),product(a3,a4)) = product(product(product(a8,a9),product(a3,a4)),product(product(a1,a2),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(591,plain,
product(product(product(a8,a9),product(a1,a2)),product(a3,a4)) = product(product(product(a8,a9),product(a3,a4)),product(product(a1,a2),product(a3,a4))),
inference(unit_resolution,[status(thm)],[590,48]) ).
tff(592,plain,
product(product(product(a8,a9),product(a1,a2)),product(a3,a4)) = product(product(a10,a3),product(a3,a4)),
inference(monotonicity,[status(thm)],[55]) ).
tff(593,plain,
product(product(a10,a3),product(a3,a4)) = product(product(product(a8,a9),product(a1,a2)),product(a3,a4)),
inference(symmetry,[status(thm)],[592]) ).
tff(594,plain,
product(a10,a3) = product(product(product(a10,a3),product(a7,a4)),product(a7,a4)),
inference(symmetry,[status(thm)],[276]) ).
tff(595,plain,
product(a10,a3) = product(product(a4,a8),product(a7,a4)),
inference(transitivity,[status(thm)],[594,277]) ).
tff(596,plain,
product(product(product(a7,a4),product(a10,a3)),product(a7,a4)) = product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),
inference(symmetry,[status(thm)],[273]) ).
tff(597,plain,
product(a8,a9) = product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),
inference(transitivity,[status(thm)],[445,444,443,442,441,596]) ).
tff(598,plain,
product(product(a8,a9),product(a10,a3)) = product(product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))),
inference(monotonicity,[status(thm)],[597,595]) ).
tff(599,plain,
product(product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))) = product(product(a8,a9),product(a10,a3)),
inference(symmetry,[status(thm)],[598]) ).
tff(600,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)) = product(product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(601,plain,
product(product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)) = product(product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))),
inference(unit_resolution,[status(thm)],[600,48]) ).
tff(602,plain,
product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)) = product(product(a6,a1),product(a4,a8)),
inference(monotonicity,[status(thm)],[515]) ).
tff(603,plain,
product(product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)) = product(product(product(a6,a1),product(a4,a8)),product(product(a8,a9),product(a4,a8))),
inference(monotonicity,[status(thm)],[602,342]) ).
tff(604,plain,
product(product(product(a6,a1),product(a4,a8)),product(product(a8,a9),product(a4,a8))) = product(product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)),
inference(symmetry,[status(thm)],[603]) ).
tff(605,plain,
product(product(a5,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))) = product(product(a5,a4),product(a6,a1)),
inference(monotonicity,[status(thm)],[515]) ).
tff(606,plain,
product(product(a5,a4),product(a6,a1)) = product(product(a5,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(symmetry,[status(thm)],[605]) ).
tff(607,plain,
product(product(product(a6,a1),product(a6,a1)),product(product(a9,a7),product(a6,a1))) = product(product(product(a6,a1),product(a9,a7)),product(a6,a1)),
inference(symmetry,[status(thm)],[371]) ).
tff(608,plain,
product(product(a6,a1),product(a4,a8)) = product(product(a5,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(transitivity,[status(thm)],[368,607,372,378,606]) ).
tff(609,plain,
product(product(product(a6,a1),product(a4,a8)),product(product(a8,a9),product(a4,a8))) = product(product(product(a5,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)),
inference(monotonicity,[status(thm)],[608,544]) ).
tff(610,plain,
product(product(product(a5,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)) = product(product(product(a6,a1),product(a4,a8)),product(product(a8,a9),product(a4,a8))),
inference(symmetry,[status(thm)],[609]) ).
tff(611,plain,
product(a3,a4) = product(product(a2,a10),product(a8,a9)),
inference(transitivity,[status(thm)],[464,382]) ).
tff(612,plain,
product(product(a3,a4),product(a4,a8)) = product(product(product(a2,a10),product(a8,a9)),product(a4,a8)),
inference(monotonicity,[status(thm)],[611]) ).
tff(613,plain,
product(product(product(a2,a10),product(a8,a9)),product(a4,a8)) = product(product(a3,a4),product(a4,a8)),
inference(symmetry,[status(thm)],[612]) ).
tff(614,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a2,a10),product(a8,a9)),product(a4,a8)) = product(product(product(a2,a10),product(a4,a8)),product(product(a8,a9),product(a4,a8))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(615,plain,
product(product(product(a2,a10),product(a8,a9)),product(a4,a8)) = product(product(product(a2,a10),product(a4,a8)),product(product(a8,a9),product(a4,a8))),
inference(unit_resolution,[status(thm)],[614,48]) ).
tff(616,plain,
product(product(product(a2,a10),product(a4,a8)),product(product(a8,a9),product(a4,a8))) = product(product(product(a2,a10),product(a8,a9)),product(a4,a8)),
inference(symmetry,[status(thm)],[615]) ).
tff(617,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(a2,a10),product(a10,a3)),product(a10,a3)) = product(a2,a10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(618,plain,
product(product(product(a2,a10),product(a10,a3)),product(a10,a3)) = product(a2,a10),
inference(unit_resolution,[status(thm)],[617,11]) ).
tff(619,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a2,a10),product(a10,a3)),product(a10,a3)) = product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(620,plain,
product(product(product(a2,a10),product(a10,a3)),product(a10,a3)) = product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),
inference(unit_resolution,[status(thm)],[619,48]) ).
tff(621,plain,
product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))) = product(product(product(a2,a10),product(a10,a3)),product(a10,a3)),
inference(symmetry,[status(thm)],[620]) ).
tff(622,plain,
product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))) = product(a2,a10),
inference(transitivity,[status(thm)],[621,618]) ).
tff(623,plain,
product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)) = product(product(a2,a10),product(a4,a8)),
inference(monotonicity,[status(thm)],[622]) ).
tff(624,plain,
product(product(a2,a10),product(a4,a8)) = product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),
inference(symmetry,[status(thm)],[623]) ).
tff(625,plain,
product(product(product(a2,a10),product(a4,a8)),product(product(a8,a9),product(a4,a8))) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)),
inference(monotonicity,[status(thm)],[624,544]) ).
tff(626,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)) = product(product(product(a2,a10),product(a4,a8)),product(product(a8,a9),product(a4,a8))),
inference(symmetry,[status(thm)],[625]) ).
tff(627,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(628,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))),
inference(unit_resolution,[status(thm)],[627,48]) ).
tff(629,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)),
inference(symmetry,[status(thm)],[628]) ).
tff(630,plain,
product(product(a5,a4),product(a10,a3)) = product(product(product(a2,a10),product(a10,a3)),product(a10,a3)),
inference(monotonicity,[status(thm)],[148]) ).
tff(631,plain,
product(product(product(a2,a10),product(a10,a3)),product(a10,a3)) = product(product(a5,a4),product(a10,a3)),
inference(symmetry,[status(thm)],[630]) ).
tff(632,plain,
product(a2,a10) = product(product(product(a2,a10),product(a10,a3)),product(a10,a3)),
inference(symmetry,[status(thm)],[618]) ).
tff(633,plain,
product(a2,a10) = product(product(a5,a4),product(a10,a3)),
inference(transitivity,[status(thm)],[632,631]) ).
tff(634,plain,
product(product(a2,a10),product(a7,a4)) = product(product(product(a5,a4),product(a10,a3)),product(a7,a4)),
inference(monotonicity,[status(thm)],[633]) ).
tff(635,plain,
product(product(product(a5,a4),product(a10,a3)),product(a7,a4)) = product(product(a2,a10),product(a7,a4)),
inference(symmetry,[status(thm)],[634]) ).
tff(636,plain,
product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))) = product(product(a5,a4),product(a10,a3)),
inference(transitivity,[status(thm)],[621,631]) ).
tff(637,plain,
product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)) = product(product(product(a5,a4),product(a10,a3)),product(a7,a4)),
inference(monotonicity,[status(thm)],[636]) ).
tff(638,plain,
product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)) = product(product(a2,a10),product(a7,a4)),
inference(transitivity,[status(thm)],[637,635]) ).
tff(639,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))) = product(product(product(a2,a10),product(a7,a4)),product(a10,a3)),
inference(monotonicity,[status(thm)],[638,279]) ).
tff(640,plain,
product(product(product(a2,a10),product(a7,a4)),product(a10,a3)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))),
inference(symmetry,[status(thm)],[639]) ).
tff(641,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a2,a10),product(a7,a4)),product(a10,a3)) = product(product(product(a2,a10),product(a10,a3)),product(product(a7,a4),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(642,plain,
product(product(product(a2,a10),product(a7,a4)),product(a10,a3)) = product(product(product(a2,a10),product(a10,a3)),product(product(a7,a4),product(a10,a3))),
inference(unit_resolution,[status(thm)],[641,48]) ).
tff(643,plain,
product(product(product(a2,a10),product(a10,a3)),product(product(a7,a4),product(a10,a3))) = product(product(product(a2,a10),product(a7,a4)),product(a10,a3)),
inference(symmetry,[status(thm)],[642]) ).
tff(644,plain,
product(product(product(a2,a10),product(a10,a3)),product(product(a7,a4),product(a10,a3))) = product(product(a5,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),
inference(monotonicity,[status(thm)],[147,517]) ).
tff(645,plain,
product(product(a5,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))) = product(product(product(a2,a10),product(a10,a3)),product(product(a7,a4),product(a10,a3))),
inference(symmetry,[status(thm)],[644]) ).
tff(646,plain,
product(product(a5,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))) = product(product(a3,a4),product(a4,a8)),
inference(transitivity,[status(thm)],[645,643,640,629,626,616,613]) ).
tff(647,plain,
product(product(product(a5,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)) = product(product(product(a3,a4),product(a4,a8)),product(a7,a4)),
inference(monotonicity,[status(thm)],[646]) ).
tff(648,plain,
product(product(product(a3,a4),product(a4,a8)),product(a7,a4)) = product(product(product(a5,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))),product(a7,a4)),
inference(symmetry,[status(thm)],[647]) ).
tff(649,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a3,a4),product(a4,a8)),product(a7,a4)) = product(product(product(a3,a4),product(a7,a4)),product(product(a4,a8),product(a7,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(650,plain,
product(product(product(a3,a4),product(a4,a8)),product(a7,a4)) = product(product(product(a3,a4),product(a7,a4)),product(product(a4,a8),product(a7,a4))),
inference(unit_resolution,[status(thm)],[649,48]) ).
tff(651,plain,
product(product(product(a3,a4),product(a7,a4)),product(product(a4,a8),product(a7,a4))) = product(product(product(a3,a4),product(a4,a8)),product(a7,a4)),
inference(symmetry,[status(thm)],[650]) ).
tff(652,plain,
product(product(a3,a4),product(a7,a4)) = product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))),
inference(monotonicity,[status(thm)],[37,75]) ).
tff(653,plain,
product(product(product(a3,a4),product(a7,a4)),product(product(a4,a8),product(a7,a4))) = product(product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))),product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4)))),
inference(monotonicity,[status(thm)],[652,352]) ).
tff(654,plain,
product(product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))),product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4)))) = product(product(product(a3,a4),product(a7,a4)),product(product(a4,a8),product(a7,a4))),
inference(symmetry,[status(thm)],[653]) ).
tff(655,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a1,a2),product(a6,a1)),product(a10,a3)) = product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(656,plain,
product(product(product(a1,a2),product(a6,a1)),product(a10,a3)) = product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))),
inference(unit_resolution,[status(thm)],[655,48]) ).
tff(657,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))) = product(product(product(a1,a2),product(a6,a1)),product(a10,a3)),
inference(symmetry,[status(thm)],[656]) ).
tff(658,plain,
product(product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))),product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4)))) = product(product(product(product(a1,a2),product(a6,a1)),product(a10,a3)),product(a10,a3)),
inference(monotonicity,[status(thm)],[657,350]) ).
tff(659,plain,
product(product(product(product(a1,a2),product(a6,a1)),product(a10,a3)),product(a10,a3)) = product(product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))),product(product(product(a10,a3),product(a7,a4)),product(product(a7,a4),product(a7,a4)))),
inference(symmetry,[status(thm)],[658]) ).
tff(660,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))),product(a10,a3)) = product(product(product(product(a1,a2),product(a6,a1)),product(a10,a3)),product(product(product(a1,a2),product(a6,a1)),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(661,plain,
product(product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))),product(a10,a3)) = product(product(product(product(a1,a2),product(a6,a1)),product(a10,a3)),product(product(product(a1,a2),product(a6,a1)),product(a10,a3))),
inference(unit_resolution,[status(thm)],[660,48]) ).
tff(662,plain,
product(product(product(product(a1,a2),product(a6,a1)),product(a10,a3)),product(product(product(a1,a2),product(a6,a1)),product(a10,a3))) = product(product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))),product(a10,a3)),
inference(symmetry,[status(thm)],[661]) ).
tff(663,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))) = product(product(a3,a4),product(a7,a4)),
inference(symmetry,[status(thm)],[652]) ).
tff(664,plain,
product(product(product(a1,a2),product(a6,a1)),product(a10,a3)) = product(product(a3,a4),product(a7,a4)),
inference(transitivity,[status(thm)],[656,663]) ).
tff(665,plain,
product(product(product(product(a1,a2),product(a6,a1)),product(a10,a3)),product(product(product(a1,a2),product(a6,a1)),product(a10,a3))) = product(product(product(a3,a4),product(a7,a4)),product(product(a3,a4),product(a7,a4))),
inference(monotonicity,[status(thm)],[664,664]) ).
tff(666,plain,
product(product(product(a3,a4),product(a7,a4)),product(product(a3,a4),product(a7,a4))) = product(product(product(product(a1,a2),product(a6,a1)),product(a10,a3)),product(product(product(a1,a2),product(a6,a1)),product(a10,a3))),
inference(symmetry,[status(thm)],[665]) ).
tff(667,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a3,a4),product(a3,a4)),product(a7,a4)) = product(product(product(a3,a4),product(a7,a4)),product(product(a3,a4),product(a7,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(668,plain,
product(product(product(a3,a4),product(a3,a4)),product(a7,a4)) = product(product(product(a3,a4),product(a7,a4)),product(product(a3,a4),product(a7,a4))),
inference(unit_resolution,[status(thm)],[667,48]) ).
tff(669,plain,
product(product(product(a3,a4),product(a3,a4)),product(a7,a4)) = product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))),
inference(monotonicity,[status(thm)],[430,75]) ).
tff(670,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(a6,a1),product(a10,a3))) = product(product(product(a3,a4),product(a3,a4)),product(a7,a4)),
inference(symmetry,[status(thm)],[669]) ).
tff(671,plain,
product(product(product(a1,a2),product(a6,a1)),product(a10,a3)) = product(product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))),product(a10,a3)),
inference(transitivity,[status(thm)],[656,670,668,666,662]) ).
tff(672,plain,
product(product(product(product(a1,a2),product(a6,a1)),product(a10,a3)),product(a10,a3)) = product(product(product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))),product(a10,a3)),product(a10,a3)),
inference(monotonicity,[status(thm)],[671]) ).
tff(673,plain,
product(product(product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))),product(a10,a3)),product(a10,a3)) = product(product(product(product(a1,a2),product(a6,a1)),product(a10,a3)),product(a10,a3)),
inference(symmetry,[status(thm)],[672]) ).
tff(674,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))),product(a10,a3)),product(a10,a3)) = product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(675,plain,
product(product(product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))),product(a10,a3)),product(a10,a3)) = product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))),
inference(unit_resolution,[status(thm)],[674,11]) ).
tff(676,plain,
product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))) = product(product(product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))),product(a10,a3)),product(a10,a3)),
inference(symmetry,[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(a1,a2),product(a1,a2)),product(a6,a1)) = product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(678,plain,
product(product(product(a1,a2),product(a1,a2)),product(a6,a1)) = product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))),
inference(unit_resolution,[status(thm)],[677,48]) ).
tff(679,plain,
product(product(a1,a2),product(a1,a2)) = product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),
inference(symmetry,[status(thm)],[312]) ).
tff(680,plain,
product(product(product(a1,a2),product(a1,a2)),product(a6,a1)) = product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a6,a1)),
inference(monotonicity,[status(thm)],[679]) ).
tff(681,plain,
product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a6,a1)) = product(product(product(a1,a2),product(a1,a2)),product(a6,a1)),
inference(symmetry,[status(thm)],[680]) ).
tff(682,plain,
product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))) = product(a1,a2),
inference(transitivity,[status(thm)],[312,234]) ).
tff(683,plain,
product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a6,a1)) = product(product(a1,a2),product(a6,a1)),
inference(monotonicity,[status(thm)],[682]) ).
tff(684,plain,
product(product(a1,a2),product(a6,a1)) = product(product(product(product(a9,a7),product(a3,a4)),product(product(a9,a7),product(a3,a4))),product(a6,a1)),
inference(symmetry,[status(thm)],[683]) ).
tff(685,plain,
product(product(a1,a2),product(a6,a1)) = product(product(product(a9,a7),product(a3,a4)),product(a3,a4)),
inference(monotonicity,[status(thm)],[25,566]) ).
tff(686,plain,
product(product(product(a9,a7),product(a3,a4)),product(a3,a4)) = product(product(a1,a2),product(a6,a1)),
inference(symmetry,[status(thm)],[685]) ).
tff(687,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a5,a4),product(a3,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[413]) ).
tff(688,plain,
product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)) = product(a5,a4),
inference(transitivity,[status(thm)],[410,687,415]) ).
tff(689,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)),product(a10,a3)) = product(product(a5,a4),product(a10,a3)),
inference(monotonicity,[status(thm)],[688]) ).
tff(690,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)),product(a10,a3)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(product(a3,a4),product(a10,a3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(691,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)),product(a10,a3)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(product(a3,a4),product(a10,a3))),
inference(unit_resolution,[status(thm)],[690,48]) ).
tff(692,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(product(a3,a4),product(a10,a3))) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a3,a4)),product(a10,a3)),
inference(symmetry,[status(thm)],[691]) ).
tff(693,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(a1,a2)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(product(a3,a4),product(a10,a3))),
inference(monotonicity,[status(thm)],[231]) ).
tff(694,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(a1,a2)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(a10,a3),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(695,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(a1,a2)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(a10,a3),product(a1,a2))),
inference(unit_resolution,[status(thm)],[694,48]) ).
tff(696,plain,
product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(a10,a3),product(a1,a2))) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a10,a3)),product(a1,a2)),
inference(symmetry,[status(thm)],[695]) ).
tff(697,plain,
product(product(product(a6,a1),product(a3,a4)),product(a8,a9)) = product(product(product(product(product(a2,a10),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a1,a2)),product(product(a10,a3),product(a1,a2))),
inference(monotonicity,[status(thm)],[162,289]) ).
tff(698,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(a3,a4)),product(a8,a9)) = product(product(product(a6,a1),product(a8,a9)),product(product(a3,a4),product(a8,a9))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(699,plain,
product(product(product(a6,a1),product(a3,a4)),product(a8,a9)) = product(product(product(a6,a1),product(a8,a9)),product(product(a3,a4),product(a8,a9))),
inference(unit_resolution,[status(thm)],[698,48]) ).
tff(700,plain,
product(product(product(a6,a1),product(a8,a9)),product(product(a3,a4),product(a8,a9))) = product(product(product(a6,a1),product(a3,a4)),product(a8,a9)),
inference(symmetry,[status(thm)],[699]) ).
tff(701,plain,
product(product(product(a6,a1),product(a8,a9)),product(a2,a10)) = product(product(product(a6,a1),product(a8,a9)),product(product(a3,a4),product(a8,a9))),
inference(monotonicity,[status(thm)],[60]) ).
tff(702,plain,
product(product(product(a6,a1),product(a8,a9)),product(a2,a10)) = product(a2,a10),
inference(transitivity,[status(thm)],[701,700,697,696,693,692,689,630,618]) ).
tff(703,plain,
product(product(product(product(a6,a1),product(a8,a9)),product(a2,a10)),product(a1,a2)) = product(product(a2,a10),product(a1,a2)),
inference(monotonicity,[status(thm)],[702]) ).
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(a6,a1),product(a8,a9)),product(a2,a10)),product(a1,a2)) = product(product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),product(product(a2,a10),product(a1,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(705,plain,
product(product(product(product(a6,a1),product(a8,a9)),product(a2,a10)),product(a1,a2)) = product(product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),product(product(a2,a10),product(a1,a2))),
inference(unit_resolution,[status(thm)],[704,48]) ).
tff(706,plain,
product(product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),product(product(a2,a10),product(a1,a2))) = product(product(product(product(a6,a1),product(a8,a9)),product(a2,a10)),product(a1,a2)),
inference(symmetry,[status(thm)],[705]) ).
tff(707,plain,
product(product(product(a6,a1),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),
inference(symmetry,[status(thm)],[98]) ).
tff(708,plain,
product(product(product(a6,a1),product(a1,a2)),product(a10,a3)) = product(product(product(a6,a1),product(a1,a2)),product(product(a8,a9),product(a1,a2))),
inference(symmetry,[status(thm)],[96]) ).
tff(709,plain,
product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),
inference(transitivity,[status(thm)],[69,708,707]) ).
tff(710,plain,
product(product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2)))) = product(product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),product(product(a2,a10),product(a1,a2))),
inference(monotonicity,[status(thm)],[709,218]) ).
tff(711,plain,
product(product(a2,a10),product(a1,a2)) = product(product(product(a2,a10),product(a2,a10)),product(a1,a2)),
inference(symmetry,[status(thm)],[214]) ).
tff(712,plain,
product(product(product(a3,a4),product(a8,a9)),product(a1,a2)) = product(product(a2,a10),product(a1,a2)),
inference(symmetry,[status(thm)],[61]) ).
tff(713,plain,
product(product(product(a3,a4),product(a1,a2)),product(product(a8,a9),product(a1,a2))) = product(product(product(a3,a4),product(a8,a9)),product(a1,a2)),
inference(symmetry,[status(thm)],[58]) ).
tff(714,plain,
product(product(product(a3,a4),product(a1,a2)),product(a10,a3)) = product(product(product(a3,a4),product(a1,a2)),product(product(a8,a9),product(a1,a2))),
inference(symmetry,[status(thm)],[56]) ).
tff(715,plain,
product(product(product(a3,a4),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(a3,a4),product(a1,a2)),product(a10,a3)),
inference(symmetry,[status(thm)],[50]) ).
tff(716,plain,
product(product(product(a3,a4),product(a10,a3)),product(a3,a4)) = product(product(product(a3,a4),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(symmetry,[status(thm)],[41]) ).
tff(717,plain,
product(product(product(a9,a7),product(a3,a4)),product(a3,a4)) = product(product(product(a3,a4),product(a10,a3)),product(a3,a4)),
inference(symmetry,[status(thm)],[40]) ).
tff(718,plain,
product(a9,a7) = product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2))),
inference(transitivity,[status(thm)],[408,717,716,715,714,713,712,711,216]) ).
tff(719,plain,
product(product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a9,a7)) = product(product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2)))),
inference(monotonicity,[status(thm)],[718]) ).
tff(720,plain,
product(product(product(a7,a4),product(a3,a4)),product(a9,a7)) = product(product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a9,a7)),
inference(monotonicity,[status(thm)],[76]) ).
tff(721,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a7,a4),product(a3,a4)),product(a9,a7)) = product(product(product(a7,a4),product(a9,a7)),product(product(a3,a4),product(a9,a7))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(722,plain,
product(product(product(a7,a4),product(a3,a4)),product(a9,a7)) = product(product(product(a7,a4),product(a9,a7)),product(product(a3,a4),product(a9,a7))),
inference(unit_resolution,[status(thm)],[721,48]) ).
tff(723,plain,
product(product(product(a7,a4),product(a9,a7)),product(product(a3,a4),product(a9,a7))) = product(product(product(a7,a4),product(a3,a4)),product(a9,a7)),
inference(symmetry,[status(thm)],[722]) ).
tff(724,plain,
product(product(a1,a2),product(a3,a4)) = product(a9,a7),
inference(transitivity,[status(thm)],[406,15]) ).
tff(725,plain,
product(product(product(a3,a4),product(a3,a4)),product(product(a1,a2),product(a3,a4))) = product(product(a3,a4),product(a9,a7)),
inference(monotonicity,[status(thm)],[88,724]) ).
tff(726,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a3,a4),product(a1,a2)),product(a3,a4)) = product(product(product(a3,a4),product(a3,a4)),product(product(a1,a2),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(727,plain,
product(product(product(a3,a4),product(a1,a2)),product(a3,a4)) = product(product(product(a3,a4),product(a3,a4)),product(product(a1,a2),product(a3,a4))),
inference(unit_resolution,[status(thm)],[726,48]) ).
tff(728,plain,
product(product(product(a3,a4),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))) = product(product(product(a3,a4),product(a1,a2)),product(a3,a4)),
inference(monotonicity,[status(thm)],[394]) ).
tff(729,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a3,a4),product(a9,a7)),product(a3,a4)) = product(product(product(a3,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(730,plain,
product(product(product(a3,a4),product(a9,a7)),product(a3,a4)) = product(product(product(a3,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))),
inference(unit_resolution,[status(thm)],[729,48]) ).
tff(731,plain,
product(product(product(a3,a4),product(a9,a7)),product(a3,a4)) = product(product(a3,a4),product(a1,a2)),
inference(transitivity,[status(thm)],[730,205]) ).
tff(732,plain,
product(product(product(product(a3,a4),product(a9,a7)),product(a3,a4)),product(a3,a4)) = product(product(product(a3,a4),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))),
inference(monotonicity,[status(thm)],[731,401]) ).
tff(733,plain,
product(product(product(a3,a4),product(a3,a4)),product(product(a9,a7),product(a3,a4))) = product(product(product(a3,a4),product(a9,a7)),product(a3,a4)),
inference(symmetry,[status(thm)],[730]) ).
tff(734,plain,
product(product(product(a2,a10),product(a1,a2)),product(a10,a3)) = product(product(product(a3,a4),product(a9,a7)),product(a3,a4)),
inference(transitivity,[status(thm)],[422,537,427,733]) ).
tff(735,plain,
product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(product(a3,a4),product(a9,a7)),product(a3,a4)),product(a3,a4)),
inference(monotonicity,[status(thm)],[734,36]) ).
tff(736,plain,
product(a5,a4) = product(product(a3,a4),product(a9,a7)),
inference(transitivity,[status(thm)],[416,413,735,732,728,727,725]) ).
tff(737,plain,
product(product(product(a7,a4),product(a9,a7)),product(a5,a4)) = product(product(product(a7,a4),product(a9,a7)),product(product(a3,a4),product(a9,a7))),
inference(monotonicity,[status(thm)],[736]) ).
tff(738,plain,
product(product(product(a7,a4),product(a9,a7)),product(product(a6,a1),product(a9,a7))) = product(product(product(a7,a4),product(a9,a7)),product(a5,a4)),
inference(monotonicity,[status(thm)],[377]) ).
tff(739,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a7,a4),product(a6,a1)),product(a9,a7)) = product(product(product(a7,a4),product(a9,a7)),product(product(a6,a1),product(a9,a7))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(740,plain,
product(product(product(a7,a4),product(a6,a1)),product(a9,a7)) = product(product(product(a7,a4),product(a9,a7)),product(product(a6,a1),product(a9,a7))),
inference(unit_resolution,[status(thm)],[739,48]) ).
tff(741,plain,
product(product(a7,a4),product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3)))) = product(product(a7,a4),product(a6,a1)),
inference(symmetry,[status(thm)],[476]) ).
tff(742,plain,
product(product(a10,a3),product(a10,a3)) = product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))),
inference(symmetry,[status(thm)],[296]) ).
tff(743,plain,
product(product(product(a10,a3),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))),product(a3,a4)),
inference(monotonicity,[status(thm)],[742,36]) ).
tff(744,plain,
product(product(product(a10,a3),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(a7,a4),product(a6,a1)),
inference(transitivity,[status(thm)],[743,298,325,318,315,311,305,303,741]) ).
tff(745,plain,
product(product(product(product(a10,a3),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a9,a7)) = product(product(product(a7,a4),product(a6,a1)),product(a9,a7)),
inference(monotonicity,[status(thm)],[744]) ).
tff(746,plain,
product(product(product(product(a8,a9),product(a1,a2)),product(product(a8,a9),product(a1,a2))),product(a3,a4)) = product(product(product(a10,a3),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(symmetry,[status(thm)],[743]) ).
tff(747,plain,
product(product(a10,a3),product(a3,a4)) = product(product(product(a10,a3),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(transitivity,[status(thm)],[299,746]) ).
tff(748,plain,
product(product(product(a10,a3),product(a3,a4)),product(product(a1,a2),product(a3,a4))) = product(product(product(product(a10,a3),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a9,a7)),
inference(monotonicity,[status(thm)],[747,724]) ).
tff(749,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a10,a3),product(a1,a2)),product(a3,a4)) = product(product(product(a10,a3),product(a3,a4)),product(product(a1,a2),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(750,plain,
product(product(product(a10,a3),product(a1,a2)),product(a3,a4)) = product(product(product(a10,a3),product(a3,a4)),product(product(a1,a2),product(a3,a4))),
inference(unit_resolution,[status(thm)],[749,48]) ).
tff(751,plain,
product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a3,a4)) = product(product(product(a10,a3),product(a1,a2)),product(a3,a4)),
inference(monotonicity,[status(thm)],[126]) ).
tff(752,plain,
product(product(a8,a9),product(a3,a4)) = product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a3,a4)),
inference(monotonicity,[status(thm)],[119]) ).
tff(753,plain,
product(product(product(a6,a1),product(a7,a4)),product(a3,a4)) = product(product(a8,a9),product(a3,a4)),
inference(monotonicity,[status(thm)],[309]) ).
tff(754,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(a7,a4)),product(a3,a4)) = product(product(product(a6,a1),product(a3,a4)),product(product(a7,a4),product(a3,a4))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(755,plain,
product(product(product(a6,a1),product(a7,a4)),product(a3,a4)) = product(product(product(a6,a1),product(a3,a4)),product(product(a7,a4),product(a3,a4))),
inference(unit_resolution,[status(thm)],[754,48]) ).
tff(756,plain,
product(product(product(a6,a1),product(a3,a4)),product(product(a7,a4),product(a3,a4))) = product(product(product(a6,a1),product(a7,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[755]) ).
tff(757,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(product(a6,a1),product(a1,a2)),product(a10,a3))) = product(product(product(a6,a1),product(a3,a4)),product(product(a7,a4),product(a3,a4))),
inference(monotonicity,[status(thm)],[465,467]) ).
tff(758,plain,
product(product(product(a6,a1),product(a10,a3)),product(a3,a4)) = product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(symmetry,[status(thm)],[586]) ).
tff(759,plain,
product(product(product(a6,a1),product(a3,a4)),product(product(a10,a3),product(a3,a4))) = product(product(product(a6,a1),product(a10,a3)),product(a3,a4)),
inference(symmetry,[status(thm)],[585]) ).
tff(760,plain,
product(product(product(a3,a4),product(a3,a4)),product(product(a10,a3),product(a3,a4))) = product(product(product(a6,a1),product(a3,a4)),product(product(a10,a3),product(a3,a4))),
inference(symmetry,[status(thm)],[583]) ).
tff(761,plain,
product(a9,a7) = product(product(product(a6,a1),product(a1,a2)),product(a10,a3)),
inference(transitivity,[status(thm)],[408,717,580,760,759,758,69]) ).
tff(762,plain,
product(product(a3,a4),product(a9,a7)) = product(product(product(a1,a2),product(a10,a3)),product(product(product(a6,a1),product(a1,a2)),product(a10,a3))),
inference(monotonicity,[status(thm)],[37,761]) ).
tff(763,plain,
a6 = a5,
inference(transitivity,[status(thm)],[157,416,413,735,732,728,727,725,762,757,756,753,752,751,750,748,745,740,738,737,723,720,719,710,706,703,61,58,56,50,41,40,686,684,681,678,676,673,659,654,651,648,610,604,601,599,473,317,472,593,591,589,578,575,154,391,387,385,383,381,203,568,565,563,561,558,552,549,543,540,535,531,528,509,507,278,276,324,491,487,485,479,471,469,462,461,460,201,459,458,457,456,455,454,234,453,365,449,117,445,444,443,442,441,440,439,432,428,425,423,173,421,379,373,371,369,359,346,344,335,331,328,301,293,291,288,286,283,281,255,252,238,64,13,4]) ).
tff(764,plain,
product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a10,a3)),product(product(a1,a2),product(a10,a3))) = product(product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a1,a2)),product(a10,a3)),
inference(symmetry,[status(thm)],[487]) ).
tff(765,plain,
product(product(product(a7,a4),product(a3,a4)),product(product(a6,a1),product(a3,a4))) = product(product(product(a7,a4),product(a6,a1)),product(a3,a4)),
inference(symmetry,[status(thm)],[471]) ).
tff(766,plain,
product(product(product(a8,a9),product(a4,a8)),product(product(a7,a4),product(a4,a8))) = product(product(product(a8,a9),product(a7,a4)),product(a4,a8)),
inference(symmetry,[status(thm)],[346]) ).
tff(767,plain,
product(product(product(a10,a3),product(a1,a2)),product(product(a3,a4),product(a1,a2))) = product(product(product(a10,a3),product(a3,a4)),product(a1,a2)),
inference(symmetry,[status(thm)],[293]) ).
tff(768,plain,
a5 = a4,
inference(transitivity,[status(thm)],[3,221,63,237,251,254,280,282,285,287,290,767,300,327,330,334,343,766,358,368,607,372,378,420,174,422,537,427,431,438,308,269,267,265,263,257,118,448,366,452,235,232,230,228,226,224,223,202,199,102,100,468,765,478,484,764,490,295,31]) ).
tff(769,plain,
a4 = a3,
inference(transitivity,[status(thm)],[30,324,491,487,485,479,471,469,462,461,460,201,459,458,457,456,455,454,234,35]) ).
tff(770,plain,
product(product(product(product(a10,a3),product(a6,a1)),product(a10,a3)),product(product(a6,a1),product(a10,a3))) = product(product(product(product(a10,a3),product(a6,a1)),product(a6,a1)),product(a10,a3)),
inference(symmetry,[status(thm)],[509]) ).
tff(771,plain,
a3 = a2,
inference(transitivity,[status(thm)],[34,235,232,230,228,226,224,223,202,199,102,100,468,765,478,484,764,490,295,594,277,506,770,527,530,534,539,542,548,551,557,560,562,564,567,88,19]) ).
tff(772,plain,
product(a7,a4) = product(product(product(a7,a4),product(a3,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[66]) ).
tff(773,plain,
a8 = a7,
inference(transitivity,[status(thm)],[260,772,78,468,765,478,484,764,490,295,594,277,506,770,527,530,534,539,542,548,551,557,560,562,564,567,436,435,434,404,433,73]) ).
tff(774,plain,
product(product(product(product(a3,a4),product(a9,a7)),product(a3,a4)),product(a3,a4)) = product(product(product(product(a2,a10),product(a1,a2)),product(a10,a3)),product(product(a1,a2),product(a10,a3))),
inference(symmetry,[status(thm)],[735]) ).
tff(775,plain,
product(product(product(a3,a4),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))) = product(product(product(product(a3,a4),product(a9,a7)),product(a3,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[732]) ).
tff(776,plain,
product(product(product(a3,a4),product(a1,a2)),product(a3,a4)) = product(product(product(a3,a4),product(a1,a2)),product(product(product(a1,a2),product(a8,a9)),product(a1,a2))),
inference(symmetry,[status(thm)],[728]) ).
tff(777,plain,
product(product(product(a3,a4),product(a3,a4)),product(product(a1,a2),product(a3,a4))) = product(product(product(a3,a4),product(a1,a2)),product(a3,a4)),
inference(symmetry,[status(thm)],[727]) ).
tff(778,plain,
product(product(a3,a4),product(a9,a7)) = product(product(product(a3,a4),product(a3,a4)),product(product(a1,a2),product(a3,a4))),
inference(symmetry,[status(thm)],[725]) ).
tff(779,plain,
product(product(product(a1,a2),product(a10,a3)),product(product(product(a6,a1),product(a1,a2)),product(a10,a3))) = product(product(a3,a4),product(a9,a7)),
inference(symmetry,[status(thm)],[762]) ).
tff(780,plain,
product(product(product(a6,a1),product(a3,a4)),product(product(a7,a4),product(a3,a4))) = product(product(product(a1,a2),product(a10,a3)),product(product(product(a6,a1),product(a1,a2)),product(a10,a3))),
inference(symmetry,[status(thm)],[757]) ).
tff(781,plain,
product(product(a8,a9),product(a3,a4)) = product(product(product(a6,a1),product(a7,a4)),product(a3,a4)),
inference(symmetry,[status(thm)],[753]) ).
tff(782,plain,
product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a3,a4)) = product(product(a8,a9),product(a3,a4)),
inference(symmetry,[status(thm)],[752]) ).
tff(783,plain,
product(product(product(a10,a3),product(a1,a2)),product(a3,a4)) = product(product(product(product(a8,a9),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a3,a4)),
inference(symmetry,[status(thm)],[751]) ).
tff(784,plain,
product(product(product(a10,a3),product(a3,a4)),product(product(a1,a2),product(a3,a4))) = product(product(product(a10,a3),product(a1,a2)),product(a3,a4)),
inference(symmetry,[status(thm)],[750]) ).
tff(785,plain,
product(product(product(product(a10,a3),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a9,a7)) = product(product(product(a10,a3),product(a3,a4)),product(product(a1,a2),product(a3,a4))),
inference(symmetry,[status(thm)],[748]) ).
tff(786,plain,
product(product(product(a7,a4),product(a6,a1)),product(a9,a7)) = product(product(product(product(a10,a3),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a9,a7)),
inference(symmetry,[status(thm)],[745]) ).
tff(787,plain,
product(product(product(a7,a4),product(a9,a7)),product(product(a6,a1),product(a9,a7))) = product(product(product(a7,a4),product(a6,a1)),product(a9,a7)),
inference(symmetry,[status(thm)],[740]) ).
tff(788,plain,
product(product(product(a7,a4),product(a9,a7)),product(a5,a4)) = product(product(product(a7,a4),product(a9,a7)),product(product(a6,a1),product(a9,a7))),
inference(symmetry,[status(thm)],[738]) ).
tff(789,plain,
product(product(product(a7,a4),product(a9,a7)),product(product(a3,a4),product(a9,a7))) = product(product(product(a7,a4),product(a9,a7)),product(a5,a4)),
inference(symmetry,[status(thm)],[737]) ).
tff(790,plain,
product(product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a9,a7)) = product(product(product(a7,a4),product(a3,a4)),product(a9,a7)),
inference(symmetry,[status(thm)],[720]) ).
tff(791,plain,
product(product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2)))) = product(product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(a9,a7)),
inference(symmetry,[status(thm)],[719]) ).
tff(792,plain,
product(product(product(product(a6,a1),product(a8,a9)),product(a1,a2)),product(product(a2,a10),product(a1,a2))) = product(product(product(product(a6,a1),product(a10,a3)),product(product(a1,a2),product(a10,a3))),product(product(product(a2,a10),product(a1,a2)),product(product(a2,a10),product(a1,a2)))),
inference(symmetry,[status(thm)],[710]) ).
tff(793,plain,
product(product(a2,a10),product(a1,a2)) = product(product(product(product(a6,a1),product(a8,a9)),product(a2,a10)),product(a1,a2)),
inference(symmetry,[status(thm)],[703]) ).
tff(794,plain,
product(product(product(a1,a2),product(a6,a1)),product(product(a1,a2),product(a6,a1))) = product(product(product(a1,a2),product(a1,a2)),product(a6,a1)),
inference(symmetry,[status(thm)],[678]) ).
tff(795,plain,
product(product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a7,a4)),product(product(a4,a8),product(a7,a4))) = product(product(product(product(product(a6,a1),product(a10,a3)),product(product(a10,a3),product(a10,a3))),product(a4,a8)),product(a7,a4)),
inference(symmetry,[status(thm)],[601]) ).
tff(796,plain,
product(product(product(a8,a9),product(a3,a4)),product(product(a1,a2),product(a3,a4))) = product(product(product(a8,a9),product(a1,a2)),product(a3,a4)),
inference(symmetry,[status(thm)],[591]) ).
tff(797,plain,
a7 = a6,
inference(transitivity,[status(thm)],[72,418,405,402,398,393,88,464,382,384,463,390,396,574,577,588,796,592,325,318,315,598,795,603,609,647,650,653,658,672,675,794,680,683,685,717,716,715,714,713,712,793,705,792,791,790,722,789,788,787,786,785,784,783,782,781,755,780,779,778,777,776,775,774,687,415,158]) ).
tff(798,plain,
a9 = a8,
inference(transitivity,[status(thm)],[247,366,452,235,232,230,228,226,224,223,202,199,102,100,79,66,261]) ).
tff(799,plain,
a10 = a9,
inference(transitivity,[status(thm)],[53,118,448,248]) ).
tff(800,plain,
a2 = a1,
inference(transitivity,[status(thm)],[18,464,382,384,463,390,396,574,577,588,796,592,325,318,315,598,795,603,609,647,650,653,658,672,675,794,680,683,685,15,23]) ).
tff(801,plain,
tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5),
inference(monotonicity,[status(thm)],[800,799,798,797,773,771,769,768,763]) ).
tff(802,plain,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(symmetry,[status(thm)],[801]) ).
tff(803,plain,
( ( tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) )
<=> ( tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(804,axiom,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(805,plain,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(modus_ponens,[status(thm)],[804,803]) ).
tff(806,plain,
$false,
inference(unit_resolution,[status(thm)],[805,802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP049-1 : TPTP v9.0.0. Released v8.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 14:06:24 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.80/0.96 % SZS status Unsatisfiable
% 0.80/0.96 % SZS output start Proof
% See solution above
% 0.86/1.06 % E exiting
%------------------------------------------------------------------------------