%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP053-1 : 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 3.55s 3.73s
% Output : Proof 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 198
% Syntax : Number of formulae : 1509 (1330 unt; 0 typ; 0 def)
% Number of atoms : 1694 (1690 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 343 ( 161 ~; 157 |; 0 &)
% ( 25 <=>; 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 : 17 ( 17 usr; 15 con; 0-14 aty)
% Number of variables : 474 ( 468 !; 0 ?; 474 :)
% Comments :
%------------------------------------------------------------------------------
tff(tuple_type,type,
tuple: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(a15_type,type,
a15: $i ).
tff(a14_type,type,
a14: $i ).
tff(a13_type,type,
a13: $i ).
tff(a12_type,type,
a12: $i ).
tff(a11_type,type,
a11: $i ).
tff(a10_type,type,
a10: $i ).
tff(a9_type,type,
a9: $i ).
tff(a8_type,type,
a8: $i ).
tff(a7_type,type,
a7: $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(a2_type,type,
a2: $i ).
tff(a1_type,type,
a1: $i ).
tff(product_type,type,
product: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( product(X,X) = X )
<=> ( product(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( product(X,X) = X )
<=> ! [X: $i] : ( product(X,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( product(X,X) = X )
<=> ! [X: $i] : ( product(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( product(X,X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle) ).
tff(5,plain,
! [X: $i] : ( product(X,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( product(X,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( product(X,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a14,a14) = a14 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
product(a14,a14) = a14,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( product(a2,a12) = a14 )
<=> ( product(a2,a12) = a14 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
product(a2,a12) = a14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_12) ).
tff(12,plain,
product(a2,a12) = a14,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
a14 = product(a2,a12),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
product(a14,a14) = product(product(a2,a12),product(a2,a12)),
inference(monotonicity,[status(thm)],[13,13]) ).
tff(15,plain,
product(product(a2,a12),product(a2,a12)) = product(a14,a14),
inference(symmetry,[status(thm)],[14]) ).
tff(16,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(17,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)],[16]) ).
tff(18,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(19,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(20,plain,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a2,a2),a12) = product(product(a2,a12),product(a2,a12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
product(product(a2,a2),a12) = product(product(a2,a12),product(a2,a12)),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ( product(a6,a7) = a2 )
<=> ( product(a6,a7) = a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
product(a6,a7) = a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_11) ).
tff(27,plain,
product(a6,a7) = a2,
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
a2 = product(a6,a7),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ( product(a4,a7) = a11 )
<=> ( product(a4,a7) = a11 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
product(a4,a7) = a11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_15) ).
tff(31,plain,
product(a4,a7) = a11,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
a11 = product(a4,a7),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
product(a11,a2) = product(product(a4,a7),product(a6,a7)),
inference(monotonicity,[status(thm)],[32,28]) ).
tff(34,plain,
product(product(a4,a7),product(a6,a7)) = product(a11,a2),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a4,a6),a7) = product(product(a4,a7),product(a6,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
product(product(a4,a6),a7) = product(product(a4,a7),product(a6,a7)),
inference(unit_resolution,[status(thm)],[35,22]) ).
tff(37,plain,
( ( product(a5,a6) = a7 )
<=> ( product(a5,a6) = a7 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
product(a5,a6) = a7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_04) ).
tff(39,plain,
product(a5,a6) = a7,
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
a7 = product(a5,a6),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
product(a7,a7) = product(product(a5,a6),product(a5,a6)),
inference(monotonicity,[status(thm)],[40,40]) ).
tff(42,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a7,a7) = a7 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
product(a7,a7) = a7,
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
a7 = product(a7,a7),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
a7 = product(product(a5,a6),product(a5,a6)),
inference(transitivity,[status(thm)],[44,41]) ).
tff(46,plain,
( ( product(a1,a2) = a3 )
<=> ( product(a1,a2) = a3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
product(a1,a2) = a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot) ).
tff(48,plain,
product(a1,a2) = a3,
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
a3 = product(a1,a2),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
product(a3,a3) = product(product(a1,a2),product(a1,a2)),
inference(monotonicity,[status(thm)],[49,49]) ).
tff(51,plain,
product(product(a1,a2),product(a1,a2)) = product(a3,a3),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a12,a7),a3) = product(product(a12,a3),product(a7,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
product(product(a12,a7),a3) = product(product(a12,a3),product(a7,a3)),
inference(unit_resolution,[status(thm)],[52,22]) ).
tff(54,plain,
product(product(a12,a3),product(a7,a3)) = product(product(a12,a7),a3),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ( product(a7,a3) = a8 )
<=> ( product(a7,a3) = a8 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
product(a7,a3) = a8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_05) ).
tff(57,plain,
product(a7,a3) = a8,
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( ( product(a12,a3) = a13 )
<=> ( product(a12,a3) = a13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
product(a12,a3) = a13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_09) ).
tff(60,plain,
product(a12,a3) = a13,
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
product(product(a12,a3),product(a7,a3)) = product(a13,a8),
inference(monotonicity,[status(thm)],[60,57]) ).
tff(62,plain,
product(a13,a8) = product(product(a12,a3),product(a7,a3)),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ( product(a13,a8) = a6 )
<=> ( product(a13,a8) = a6 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
product(a13,a8) = a6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_10) ).
tff(65,plain,
product(a13,a8) = a6,
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
a6 = product(a13,a8),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
a6 = product(product(a12,a7),a3),
inference(transitivity,[status(thm)],[66,62,54]) ).
tff(68,plain,
product(a6,product(product(a1,a2),product(a1,a2))) = product(product(product(a12,a7),a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[67,51]) ).
tff(69,plain,
product(product(product(a12,a7),a3),product(a3,a3)) = product(a6,product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a3,a3) = a3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
product(a3,a3) = a3,
inference(unit_resolution,[status(thm)],[70,7]) ).
tff(72,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a14,a12),a7) = product(product(a14,a7),product(a12,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
product(product(a14,a12),a7) = product(product(a14,a7),product(a12,a7)),
inference(unit_resolution,[status(thm)],[72,22]) ).
tff(74,plain,
product(product(a14,a12),a7) = product(product(a14,a12),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[45]) ).
tff(75,plain,
product(product(a14,a12),product(product(a5,a6),product(a5,a6))) = product(product(a14,a12),a7),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
product(product(a5,a6),product(a5,a6)) = product(a7,a7),
inference(symmetry,[status(thm)],[41]) ).
tff(77,plain,
product(product(a5,a6),product(a5,a6)) = a7,
inference(transitivity,[status(thm)],[76,43]) ).
tff(78,plain,
product(product(a6,a7),product(a6,a7)) = product(a2,a2),
inference(monotonicity,[status(thm)],[27,27]) ).
tff(79,plain,
product(a2,a2) = product(product(a6,a7),product(a6,a7)),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a2,a2) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
product(a2,a2) = a2,
inference(unit_resolution,[status(thm)],[80,7]) ).
tff(82,plain,
a2 = product(a2,a2),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
^ [Y: $i,X: $i] :
refl(( ( product(product(X,Y),Y) = X )
<=> ( product(product(X,Y),Y) = X ) )),
inference(bind,[status(th)],[]) ).
tff(84,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)],[83]) ).
tff(85,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(86,axiom,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).
tff(87,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(a2,a12),a12) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
product(product(a2,a12),a12) = a2,
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
product(a14,a12) = product(product(a2,a12),a12),
inference(monotonicity,[status(thm)],[13]) ).
tff(93,plain,
product(a14,a12) = product(product(a6,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[92,91,82,79]) ).
tff(94,plain,
product(product(a14,a12),product(product(a5,a6),product(a5,a6))) = product(product(product(a6,a7),product(a6,a7)),a7),
inference(monotonicity,[status(thm)],[93,77]) ).
tff(95,plain,
product(product(product(a6,a7),product(a6,a7)),a7) = product(product(a14,a12),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
product(a6,product(product(a5,a6),product(a5,a6))) = product(a6,a7),
inference(monotonicity,[status(thm)],[77]) ).
tff(97,plain,
product(a6,product(product(a5,a6),product(a5,a6))) = product(product(a6,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[96,27,82,79]) ).
tff(98,plain,
product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = product(product(product(a6,a7),product(a6,a7)),a7),
inference(monotonicity,[status(thm)],[97,77]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = a6 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = a6,
inference(unit_resolution,[status(thm)],[99,89]) ).
tff(101,plain,
a6 = product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
product(product(a12,a7),a3) = product(product(a14,a7),product(a12,a7)),
inference(transitivity,[status(thm)],[53,61,65,101,98,95,75,73]) ).
tff(103,plain,
product(product(product(a12,a7),a3),product(a3,a3)) = product(product(product(a14,a7),product(a12,a7)),a3),
inference(monotonicity,[status(thm)],[102,71]) ).
tff(104,plain,
product(product(product(a14,a7),product(a12,a7)),a3) = product(product(product(a12,a7),a3),product(a3,a3)),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a14,a7),product(a12,a7)),a3) = product(product(product(a14,a7),a3),product(product(a12,a7),a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
product(product(product(a14,a7),product(a12,a7)),a3) = product(product(product(a14,a7),a3),product(product(a12,a7),a3)),
inference(unit_resolution,[status(thm)],[105,22]) ).
tff(107,plain,
product(product(product(a14,a7),a3),product(product(a12,a7),a3)) = product(product(product(a14,a7),product(a12,a7)),a3),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
product(product(a12,a7),a3) = product(a13,a8),
inference(transitivity,[status(thm)],[53,61]) ).
tff(109,plain,
( ( product(a14,a3) = a15 )
<=> ( product(a14,a3) = a15 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,axiom,
product(a14,a3) = a15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_13) ).
tff(111,plain,
product(a14,a3) = a15,
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
product(product(a14,a3),product(a7,a3)) = product(a15,a8),
inference(monotonicity,[status(thm)],[111,57]) ).
tff(113,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a14,a7),a3) = product(product(a14,a3),product(a7,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
product(product(a14,a7),a3) = product(product(a14,a3),product(a7,a3)),
inference(unit_resolution,[status(thm)],[113,22]) ).
tff(115,plain,
product(product(a14,a7),a3) = product(a15,a8),
inference(transitivity,[status(thm)],[114,112]) ).
tff(116,plain,
product(product(product(a14,a7),a3),product(product(a12,a7),a3)) = product(product(a15,a8),product(a13,a8)),
inference(monotonicity,[status(thm)],[115,108]) ).
tff(117,plain,
product(product(a15,a8),product(a13,a8)) = product(product(product(a14,a7),a3),product(product(a12,a7),a3)),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
( ( product(a15,a8) = a4 )
<=> ( product(a15,a8) = a4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,axiom,
product(a15,a8) = a4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_14) ).
tff(120,plain,
product(a15,a8) = a4,
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
a4 = product(a15,a8),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
product(a4,a6) = product(product(a15,a8),product(a13,a8)),
inference(monotonicity,[status(thm)],[121,66]) ).
tff(123,plain,
product(a4,a6) = product(a6,product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[122,117,107,104,69]) ).
tff(124,plain,
product(product(a4,a6),a7) = product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[123,45]) ).
tff(125,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(product(a4,a6),a7),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
a8 = product(a7,a3),
inference(symmetry,[status(thm)],[57]) ).
tff(127,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a8,a8) = a8 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
product(a8,a8) = a8,
inference(unit_resolution,[status(thm)],[127,7]) ).
tff(129,plain,
product(a8,a8) = product(product(a7,a3),product(a7,a3)),
inference(monotonicity,[status(thm)],[126,126]) ).
tff(130,plain,
product(product(a7,a3),product(a7,a3)) = product(a8,a8),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
product(product(a7,a3),product(a7,a3)) = product(a7,a3),
inference(transitivity,[status(thm)],[130,128,126]) ).
tff(132,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2))) = product(product(a7,a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[131,51]) ).
tff(133,plain,
product(product(a7,a3),product(a3,a3)) = product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
product(product(a1,a2),product(a1,a2)) = a3,
inference(transitivity,[status(thm)],[51,71]) ).
tff(135,plain,
product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2))) = product(product(a7,a7),a3),
inference(monotonicity,[status(thm)],[76,134]) ).
tff(136,plain,
product(product(a7,a7),a3) = product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a7,a7),a3) = product(product(a7,a3),product(a7,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
product(product(a7,a7),a3) = product(product(a7,a3),product(a7,a3)),
inference(unit_resolution,[status(thm)],[137,22]) ).
tff(139,plain,
product(product(a7,a3),product(a7,a3)) = product(product(a7,a7),a3),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
a8 = product(a8,a8),
inference(symmetry,[status(thm)],[128]) ).
tff(141,plain,
product(a7,a3) = product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[57,140,129,139,136]) ).
tff(142,plain,
product(product(a7,a3),product(a3,a3)) = product(product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[141,50]) ).
tff(143,plain,
product(product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a7,a3),product(a3,a3)),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a5,a6),product(a5,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
product(product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a5,a6),product(a5,a6)),
inference(unit_resolution,[status(thm)],[144,89]) ).
tff(146,plain,
product(product(a5,a6),product(a5,a6)) = product(product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
product(product(a5,a6),product(a5,a6)) = product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[146,143,133]) ).
tff(148,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2)))),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2)))) = product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,product(product(a7,a3),product(a7,a3))),product(product(a1,a2),product(a1,a2))) = product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
product(product(a6,product(product(a7,a3),product(a7,a3))),product(product(a1,a2),product(a1,a2))) = product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2)))),
inference(unit_resolution,[status(thm)],[150,22]) ).
tff(152,plain,
a13 = product(a12,a3),
inference(symmetry,[status(thm)],[60]) ).
tff(153,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a13,a13) = a13 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
product(a13,a13) = a13,
inference(unit_resolution,[status(thm)],[153,7]) ).
tff(155,plain,
product(a13,a13) = product(product(a12,a3),product(a12,a3)),
inference(monotonicity,[status(thm)],[152,152]) ).
tff(156,plain,
product(product(a12,a3),product(a12,a3)) = product(a13,a13),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))) = product(product(a12,a3),product(a12,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
product(product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))) = product(product(a12,a3),product(a12,a3)),
inference(unit_resolution,[status(thm)],[157,89]) ).
tff(159,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a6,a6) = a6 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
product(a6,a6) = a6,
inference(unit_resolution,[status(thm)],[159,7]) ).
tff(161,plain,
product(product(a13,a8),product(a13,a8)) = product(a6,a6),
inference(monotonicity,[status(thm)],[65,65]) ).
tff(162,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a13,a13),a8) = product(product(a13,a8),product(a13,a8)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
product(product(a13,a13),a8) = product(product(a13,a8),product(a13,a8)),
inference(unit_resolution,[status(thm)],[162,22]) ).
tff(164,plain,
product(product(a7,a3),product(a7,a3)) = a8,
inference(transitivity,[status(thm)],[130,128]) ).
tff(165,plain,
product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a7,a3))) = product(product(a13,a13),a8),
inference(monotonicity,[status(thm)],[156,164]) ).
tff(166,plain,
product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a7,a3))) = product(a13,a8),
inference(transitivity,[status(thm)],[165,163,161,160,66]) ).
tff(167,plain,
product(product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))) = product(product(a13,a8),product(a8,a8)),
inference(monotonicity,[status(thm)],[166,130]) ).
tff(168,plain,
product(product(a13,a8),product(a8,a8)) = product(product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
product(a6,product(product(a7,a3),product(a7,a3))) = product(product(a13,a8),product(a8,a8)),
inference(monotonicity,[status(thm)],[66,130]) ).
tff(170,plain,
product(a6,product(product(a7,a3),product(a7,a3))) = product(a12,a3),
inference(transitivity,[status(thm)],[169,168,158,156,154,152]) ).
tff(171,plain,
product(product(a6,product(product(a7,a3),product(a7,a3))),product(product(a1,a2),product(a1,a2))) = product(product(a12,a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[170,51]) ).
tff(172,plain,
product(product(a12,a3),product(a3,a3)) = product(product(a6,product(product(a7,a3),product(a7,a3))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ( product(a10,a11) = a12 )
<=> ( product(a10,a11) = a12 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,axiom,
product(a10,a11) = a12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_08) ).
tff(175,plain,
product(a10,a11) = a12,
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
a12 = product(a10,a11),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
product(a12,a12) = product(product(a10,a11),product(a10,a11)),
inference(monotonicity,[status(thm)],[176,176]) ).
tff(178,plain,
product(product(a10,a11),product(a10,a11)) = product(a12,a12),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a1,a2),product(a1,a2))) = product(product(a12,a12),a3),
inference(monotonicity,[status(thm)],[178,134]) ).
tff(180,plain,
product(product(a12,a12),a3) = product(product(product(a10,a11),product(a10,a11)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a12,a12),a3) = product(product(a12,a3),product(a12,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(182,plain,
product(product(a12,a12),a3) = product(product(a12,a3),product(a12,a3)),
inference(unit_resolution,[status(thm)],[181,22]) ).
tff(183,plain,
product(product(a12,a3),product(a12,a3)) = product(product(a12,a12),a3),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
a13 = product(a13,a13),
inference(symmetry,[status(thm)],[154]) ).
tff(185,plain,
product(a12,a3) = product(product(product(a10,a11),product(a10,a11)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[60,184,155,183,180]) ).
tff(186,plain,
product(product(a12,a3),product(a3,a3)) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[185,50]) ).
tff(187,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a12,a3),product(a3,a3)),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a10,a11),product(a10,a11)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a10,a11),product(a10,a11)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a10,a11),product(a10,a11)),
inference(unit_resolution,[status(thm)],[188,89]) ).
tff(190,plain,
product(product(a10,a11),product(a10,a11)) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a12,a12) = a12 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
product(a12,a12) = a12,
inference(unit_resolution,[status(thm)],[191,7]) ).
tff(193,plain,
a12 = product(a12,a12),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
a12 = product(a11,a2),
inference(transitivity,[status(thm)],[193,177,190,187,172,151,149,125,36,34]) ).
tff(195,plain,
product(product(a2,a2),a12) = product(product(a2,a2),product(a11,a2)),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
product(product(a2,a2),product(a11,a2)) = product(product(a2,a2),a12),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
product(product(a6,a7),product(a6,a7)) = a2,
inference(transitivity,[status(thm)],[78,81]) ).
tff(198,plain,
product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7))) = product(product(product(a9,a1),product(a9,a1)),a2),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
product(product(product(a9,a1),product(a9,a1)),a2) = product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
a2 = product(product(a6,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[82,79]) ).
tff(201,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a1,a1) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
product(a1,a1) = a1,
inference(unit_resolution,[status(thm)],[201,7]) ).
tff(203,plain,
( ( product(a11,a10) = a1 )
<=> ( product(a11,a10) = a1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(204,axiom,
product(a11,a10) = a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_16) ).
tff(205,plain,
product(a11,a10) = a1,
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
a1 = product(a11,a10),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
product(a1,a1) = product(product(a11,a10),product(a11,a10)),
inference(monotonicity,[status(thm)],[206,206]) ).
tff(208,plain,
product(product(a11,a10),product(a11,a10)) = product(a1,a1),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
product(product(a11,a10),product(a11,a10)) = a1,
inference(transitivity,[status(thm)],[208,202]) ).
tff(210,plain,
( ( product(a8,a2) = a9 )
<=> ( product(a8,a2) = a9 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(211,axiom,
product(a8,a2) = a9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_06) ).
tff(212,plain,
product(a8,a2) = a9,
inference(modus_ponens,[status(thm)],[211,210]) ).
tff(213,plain,
a9 = product(a8,a2),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
product(a9,a9) = product(product(a8,a2),product(a8,a2)),
inference(monotonicity,[status(thm)],[213,213]) ).
tff(215,plain,
product(product(a8,a2),product(a8,a2)) = product(a9,a9),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))) = product(product(a9,a9),a1),
inference(monotonicity,[status(thm)],[215,209]) ).
tff(217,plain,
product(product(a9,a9),a1) = product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a9,a9),a1) = product(product(a9,a1),product(a9,a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(219,plain,
product(product(a9,a9),a1) = product(product(a9,a1),product(a9,a1)),
inference(unit_resolution,[status(thm)],[218,22]) ).
tff(220,plain,
product(product(a9,a1),product(a9,a1)) = product(product(a9,a9),a1),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
product(product(a9,a1),product(a9,a1)) = product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),
inference(transitivity,[status(thm)],[220,217]) ).
tff(222,plain,
product(product(product(a9,a1),product(a9,a1)),a2) = product(product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[221,200]) ).
tff(223,plain,
product(product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))) = product(product(product(a9,a1),product(a9,a1)),a2),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7))),product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(225,plain,
product(product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7))),product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[224,22]) ).
tff(226,plain,
product(product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7))),product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,a1),a2) = product(product(a1,a2),product(a1,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(228,plain,
product(product(a1,a1),a2) = product(product(a1,a2),product(a1,a2)),
inference(unit_resolution,[status(thm)],[227,22]) ).
tff(229,plain,
product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))) = product(product(a1,a1),a2),
inference(monotonicity,[status(thm)],[208,197]) ).
tff(230,plain,
product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))) = a3,
inference(transitivity,[status(thm)],[229,228,51,71]) ).
tff(231,plain,
product(a14,a12) = product(a2,a2),
inference(transitivity,[status(thm)],[92,91,82]) ).
tff(232,plain,
product(a9,product(a14,a12)) = product(product(a8,a2),product(a2,a2)),
inference(monotonicity,[status(thm)],[213,231]) ).
tff(233,plain,
product(product(a8,a2),product(a2,a2)) = product(a9,product(a14,a12)),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a9,a9) = a9 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(235,plain,
product(a9,a9) = a9,
inference(unit_resolution,[status(thm)],[234,7]) ).
tff(236,plain,
product(product(a8,a2),product(a8,a2)) = product(a8,a2),
inference(transitivity,[status(thm)],[215,235,213]) ).
tff(237,plain,
product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7))) = product(product(a8,a2),product(a2,a2)),
inference(monotonicity,[status(thm)],[236,78]) ).
tff(238,plain,
product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7))) = product(a9,product(a14,a12)),
inference(transitivity,[status(thm)],[237,233]) ).
tff(239,plain,
product(product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7))),product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7)))) = product(product(a9,product(a14,a12)),a3),
inference(monotonicity,[status(thm)],[238,230]) ).
tff(240,plain,
product(product(a9,product(a14,a12)),a3) = product(product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7))),product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7)))),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
a3 = product(a3,a3),
inference(symmetry,[status(thm)],[71]) ).
tff(242,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))),product(product(a6,a7),product(a6,a7))) = product(product(a7,a3),product(a7,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(243,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))),product(product(a6,a7),product(a6,a7))) = product(product(a7,a3),product(a7,a3)),
inference(unit_resolution,[status(thm)],[242,89]) ).
tff(244,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a8,a8),a2) = product(product(a8,a2),product(a8,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(245,plain,
product(product(a8,a8),a2) = product(product(a8,a2),product(a8,a2)),
inference(unit_resolution,[status(thm)],[244,22]) ).
tff(246,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))) = product(product(a8,a8),a2),
inference(monotonicity,[status(thm)],[130,197]) ).
tff(247,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))) = product(a8,a2),
inference(transitivity,[status(thm)],[246,245,215,235,213]) ).
tff(248,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))),product(product(a6,a7),product(a6,a7))) = product(product(a8,a2),product(a2,a2)),
inference(monotonicity,[status(thm)],[247,78]) ).
tff(249,plain,
product(product(a8,a2),product(a2,a2)) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
product(a9,product(a14,a12)) = product(a7,a3),
inference(transitivity,[status(thm)],[232,249,243,130,128,126]) ).
tff(251,plain,
product(product(a9,product(a14,a12)),a3) = product(product(a7,a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[250,241]) ).
tff(252,plain,
product(product(a7,a3),product(a3,a3)) = product(product(a9,product(a14,a12)),a3),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
product(product(a5,a6),product(a5,a6)) = product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7))),
inference(transitivity,[status(thm)],[146,143,252,240,226,223,199]) ).
tff(254,plain,
product(product(a1,a1),a2) = product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[229]) ).
tff(255,plain,
product(product(a1,a2),product(a1,a2)) = product(product(a1,a1),a2),
inference(symmetry,[status(thm)],[228]) ).
tff(256,plain,
a3 = product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),
inference(transitivity,[status(thm)],[241,50,255,254]) ).
tff(257,plain,
product(a3,product(product(a5,a6),product(a5,a6))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))),
inference(monotonicity,[status(thm)],[256,253]) ).
tff(258,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))) = product(a3,product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(260,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[259,22]) ).
tff(261,plain,
product(product(a4,a7),product(a4,a7)) = product(a11,a11),
inference(monotonicity,[status(thm)],[31,31]) ).
tff(262,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a9,a1),product(a9,a1))) = product(product(a4,a7),product(a4,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(263,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a9,a1),product(a9,a1))) = product(product(a4,a7),product(a4,a7)),
inference(unit_resolution,[status(thm)],[262,89]) ).
tff(264,plain,
( ( product(a9,a1) = a10 )
<=> ( product(a9,a1) = a10 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(265,axiom,
product(a9,a1) = a10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_07) ).
tff(266,plain,
product(a9,a1) = a10,
inference(modus_ponens,[status(thm)],[265,264]) ).
tff(267,plain,
a10 = product(a9,a1),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
product(a10,a10) = product(product(a9,a1),product(a9,a1)),
inference(monotonicity,[status(thm)],[267,267]) ).
tff(269,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a10,a10) = a10 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(270,plain,
product(a10,a10) = a10,
inference(unit_resolution,[status(thm)],[269,7]) ).
tff(271,plain,
product(product(a9,a1),product(a9,a1)) = product(a10,a10),
inference(symmetry,[status(thm)],[268]) ).
tff(272,plain,
product(product(a9,a1),product(a9,a1)) = a10,
inference(transitivity,[status(thm)],[271,270]) ).
tff(273,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))) = product(product(a11,a11),a10),
inference(monotonicity,[status(thm)],[261,272]) ).
tff(274,plain,
product(product(a11,a11),a10) = product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a11,a11),a10) = product(product(a11,a10),product(a11,a10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(276,plain,
product(product(a11,a11),a10) = product(product(a11,a10),product(a11,a10)),
inference(unit_resolution,[status(thm)],[275,22]) ).
tff(277,plain,
product(product(a11,a10),product(a11,a10)) = product(product(a11,a11),a10),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
a1 = product(a1,a1),
inference(symmetry,[status(thm)],[202]) ).
tff(279,plain,
product(a11,a10) = product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),
inference(transitivity,[status(thm)],[205,278,207,277,274]) ).
tff(280,plain,
product(product(a11,a10),product(a10,a10)) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a9,a1),product(a9,a1))),
inference(monotonicity,[status(thm)],[279,268]) ).
tff(281,plain,
product(product(a11,a10),product(a11,a10)) = product(a11,a10),
inference(transitivity,[status(thm)],[208,202,206]) ).
tff(282,plain,
product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))) = product(product(a11,a10),product(a10,a10)),
inference(monotonicity,[status(thm)],[281,271]) ).
tff(283,plain,
product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))) = product(a11,a11),
inference(transitivity,[status(thm)],[282,280,263,261]) ).
tff(284,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))) = product(product(a11,a11),a2),
inference(monotonicity,[status(thm)],[283,197]) ).
tff(285,plain,
product(product(a11,a11),a2) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a11,a11) = a11 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(287,plain,
product(a11,a11) = a11,
inference(unit_resolution,[status(thm)],[286,7]) ).
tff(288,plain,
product(a11,a11) = product(a4,a7),
inference(transitivity,[status(thm)],[287,32]) ).
tff(289,plain,
product(product(a11,a11),a2) = product(product(a4,a7),product(a6,a7)),
inference(monotonicity,[status(thm)],[288,28]) ).
tff(290,plain,
product(product(a4,a7),product(a6,a7)) = product(product(a11,a11),a2),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
product(a11,a2) = product(a3,product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[33,290,285,260,258]) ).
tff(292,plain,
product(product(a2,a2),product(a11,a2)) = product(product(product(a6,a7),product(a6,a7)),product(a3,product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[79,291]) ).
tff(293,plain,
product(product(product(a6,a7),product(a6,a7)),product(a3,product(product(a5,a6),product(a5,a6)))) = product(product(a2,a2),product(a11,a2)),
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))) = product(a3,product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[134]) ).
tff(295,plain,
product(a3,product(product(a5,a6),product(a5,a6))) = product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
product(a6,a7) = product(a6,product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[96]) ).
tff(297,plain,
product(product(a6,a7),product(a6,a7)) = product(a6,product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[78,81,28,296]) ).
tff(298,plain,
product(product(product(a6,a7),product(a6,a7)),product(a3,product(product(a5,a6),product(a5,a6)))) = product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[297,295]) ).
tff(299,plain,
product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a6,a7),product(a6,a7)),product(a3,product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[298]) ).
tff(300,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(301,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[300,22]) ).
tff(302,plain,
product(a10,a11) = product(a12,a12),
inference(transitivity,[status(thm)],[175,193]) ).
tff(303,plain,
product(product(a10,a11),product(a10,a11)) = product(product(a12,a12),product(a12,a12)),
inference(monotonicity,[status(thm)],[302,302]) ).
tff(304,plain,
product(product(a12,a12),product(a12,a12)) = product(product(a10,a11),product(a10,a11)),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
a12 = product(product(a10,a11),product(a10,a11)),
inference(transitivity,[status(thm)],[193,177]) ).
tff(306,plain,
product(a12,product(product(a5,a6),product(a5,a6))) = product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[305]) ).
tff(307,plain,
product(a12,a7) = product(a12,product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[45]) ).
tff(308,plain,
product(a12,a7) = product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[307,306]) ).
tff(309,plain,
product(product(a12,a7),product(a7,a7)) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[308,41]) ).
tff(310,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a12,a7),product(a7,a7)),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a10,a11),product(a10,a11)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(312,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a10,a11),product(a10,a11)),
inference(unit_resolution,[status(thm)],[311,89]) ).
tff(313,plain,
product(product(a10,a11),product(a10,a11)) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[312]) ).
tff(314,plain,
product(a12,a12) = product(product(a12,a7),product(a7,a7)),
inference(transitivity,[status(thm)],[177,313,310]) ).
tff(315,plain,
product(product(a12,a12),product(a12,a12)) = product(product(product(a12,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))),
inference(monotonicity,[status(thm)],[314,177]) ).
tff(316,plain,
product(product(product(a12,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))) = product(product(a12,a12),product(a12,a12)),
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
product(a12,product(product(a5,a6),product(a5,a6))) = product(a12,a7),
inference(symmetry,[status(thm)],[307]) ).
tff(318,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))) = product(a12,product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[306]) ).
tff(319,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))) = product(product(a12,a12),a7),
inference(monotonicity,[status(thm)],[178,77]) ).
tff(320,plain,
product(product(a12,a12),a7) = product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a12,a12),a7) = product(product(a12,a7),product(a12,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
product(product(a12,a12),a7) = product(product(a12,a7),product(a12,a7)),
inference(unit_resolution,[status(thm)],[321,22]) ).
tff(323,plain,
product(product(a12,a7),product(a12,a7)) = product(product(a12,a12),a7),
inference(symmetry,[status(thm)],[322]) ).
tff(324,plain,
product(product(a12,a7),product(a12,a7)) = product(a12,a7),
inference(transitivity,[status(thm)],[323,320,318,317]) ).
tff(325,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))) = product(product(a12,a7),product(a7,a7)),
inference(monotonicity,[status(thm)],[324,76]) ).
tff(326,plain,
product(product(a12,a7),product(a7,a7)) = product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
product(product(product(a12,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))),
inference(monotonicity,[status(thm)],[326]) ).
tff(328,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))) = product(product(product(a12,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))),
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(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a10,a11),product(a10,a11))),product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(330,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a10,a11),product(a10,a11))),product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11)))),
inference(unit_resolution,[status(thm)],[329,22]) ).
tff(331,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a10,a11),product(a10,a11))),product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11)))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a7,a7),a12) = product(product(a7,a12),product(a7,a12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
product(product(a7,a7),a12) = product(product(a7,a12),product(a7,a12)),
inference(unit_resolution,[status(thm)],[332,22]) ).
tff(334,plain,
product(product(a7,a7),a12) = product(product(product(a5,a6),product(a5,a6)),a12),
inference(monotonicity,[status(thm)],[41]) ).
tff(335,plain,
product(product(product(a5,a6),product(a5,a6)),a12) = product(product(a7,a7),a12),
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
product(product(product(a5,a6),product(a5,a6)),a12) = product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11))),
inference(monotonicity,[status(thm)],[305]) ).
tff(337,plain,
product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11))) = product(product(product(a5,a6),product(a5,a6)),a12),
inference(symmetry,[status(thm)],[336]) ).
tff(338,plain,
product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11))) = product(product(a7,a12),product(a7,a12)),
inference(transitivity,[status(thm)],[337,335,333]) ).
tff(339,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a12,a7),a12) = product(product(a12,a12),product(a7,a12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(340,plain,
product(product(a12,a7),a12) = product(product(a12,a12),product(a7,a12)),
inference(unit_resolution,[status(thm)],[339,22]) ).
tff(341,plain,
product(product(a10,a11),product(a10,a11)) = a12,
inference(transitivity,[status(thm)],[178,192]) ).
tff(342,plain,
product(product(a12,a7),product(product(a10,a11),product(a10,a11))) = product(product(a12,a7),a12),
inference(monotonicity,[status(thm)],[341]) ).
tff(343,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a10,a11),product(a10,a11))) = product(product(a12,a7),product(product(a10,a11),product(a10,a11))),
inference(monotonicity,[status(thm)],[324]) ).
tff(344,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a10,a11),product(a10,a11))) = product(product(a12,a12),product(a7,a12)),
inference(transitivity,[status(thm)],[343,342,340]) ).
tff(345,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a10,a11),product(a10,a11))),product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11)))) = product(product(product(a12,a12),product(a7,a12)),product(product(a7,a12),product(a7,a12))),
inference(monotonicity,[status(thm)],[344,338]) ).
tff(346,plain,
product(product(product(a12,a12),product(a7,a12)),product(product(a7,a12),product(a7,a12))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a10,a11),product(a10,a11))),product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11)))),
inference(symmetry,[status(thm)],[345]) ).
tff(347,plain,
product(a6,a7) = product(product(a6,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[27,82,79]) ).
tff(348,plain,
product(product(a6,a7),product(a7,a7)) = product(product(product(a6,a7),product(a6,a7)),a7),
inference(monotonicity,[status(thm)],[347,43]) ).
tff(349,plain,
product(product(a6,a7),product(a7,a7)) = product(product(a14,a7),product(a12,a7)),
inference(transitivity,[status(thm)],[348,95,75,73]) ).
tff(350,plain,
product(product(product(a6,a7),product(a7,a7)),product(product(a1,a2),product(a1,a2))) = product(product(product(a14,a7),product(a12,a7)),a3),
inference(monotonicity,[status(thm)],[349,134]) ).
tff(351,plain,
product(product(product(a6,a7),product(a7,a7)),product(product(a1,a2),product(a1,a2))) = product(product(a15,a8),product(a13,a8)),
inference(transitivity,[status(thm)],[350,106,116]) ).
tff(352,plain,
product(product(product(product(a6,a7),product(a7,a7)),product(product(a1,a2),product(a1,a2))),product(product(a10,a11),product(a10,a11))) = product(product(product(a15,a8),product(a13,a8)),a12),
inference(monotonicity,[status(thm)],[351,341]) ).
tff(353,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,a7),product(a7,a7)),product(product(a1,a2),product(a1,a2))),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a6,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))),product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(354,plain,
product(product(product(product(a6,a7),product(a7,a7)),product(product(a1,a2),product(a1,a2))),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a6,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))),product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11)))),
inference(unit_resolution,[status(thm)],[353,22]) ).
tff(355,plain,
product(product(product(product(a6,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))),product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11)))) = product(product(product(product(a6,a7),product(a7,a7)),product(product(a1,a2),product(a1,a2))),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[354]) ).
tff(356,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11))) = product(a3,product(product(a10,a11),product(a10,a11))),
inference(monotonicity,[status(thm)],[134]) ).
tff(357,plain,
product(a3,product(product(a10,a11),product(a10,a11))) = product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
product(a2,a7) = product(product(a6,a7),a7),
inference(monotonicity,[status(thm)],[28]) ).
tff(359,plain,
product(product(a6,a7),a7) = product(a2,a7),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,a7),a7) = product(product(a6,a7),product(a7,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(361,plain,
product(product(a6,a7),a7) = product(product(a6,a7),product(a7,a7)),
inference(unit_resolution,[status(thm)],[360,22]) ).
tff(362,plain,
product(product(a6,a7),product(a7,a7)) = product(product(a6,a7),a7),
inference(symmetry,[status(thm)],[361]) ).
tff(363,plain,
product(product(a6,a7),product(a7,a7)) = product(a2,a7),
inference(transitivity,[status(thm)],[362,359]) ).
tff(364,plain,
product(product(product(a6,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))) = product(product(a2,a7),a12),
inference(monotonicity,[status(thm)],[363,341]) ).
tff(365,plain,
product(product(a2,a7),a12) = product(product(product(a6,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a2,a7),a12) = product(product(a2,a12),product(a7,a12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(367,plain,
product(product(a2,a7),a12) = product(product(a2,a12),product(a7,a12)),
inference(unit_resolution,[status(thm)],[366,22]) ).
tff(368,plain,
product(product(a2,a12),product(a7,a12)) = product(product(a2,a7),a12),
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
product(product(a2,a12),product(a7,a12)) = product(product(product(a6,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))),
inference(transitivity,[status(thm)],[368,365]) ).
tff(370,plain,
product(product(product(a2,a12),product(a7,a12)),product(a3,product(product(a10,a11),product(a10,a11)))) = product(product(product(product(a6,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))),product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11)))),
inference(monotonicity,[status(thm)],[369,357]) ).
tff(371,plain,
product(product(product(a6,a7),product(a6,a7)),a7) = product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[98]) ).
tff(372,plain,
product(a2,a7) = a6,
inference(transitivity,[status(thm)],[358,361,348,371,100]) ).
tff(373,plain,
product(product(a2,a7),a12) = product(a6,a12),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
product(a6,a12) = product(product(a2,a7),a12),
inference(symmetry,[status(thm)],[373]) ).
tff(375,plain,
product(a6,product(product(a10,a11),product(a10,a11))) = product(a6,a12),
inference(monotonicity,[status(thm)],[341]) ).
tff(376,plain,
product(a6,product(product(a10,a11),product(a10,a11))) = product(product(a2,a12),product(a7,a12)),
inference(transitivity,[status(thm)],[375,374,367]) ).
tff(377,plain,
product(product(a6,product(product(a10,a11),product(a10,a11))),product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11)))) = product(product(product(a2,a12),product(a7,a12)),product(a3,product(product(a10,a11),product(a10,a11)))),
inference(monotonicity,[status(thm)],[376,356]) ).
tff(378,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a10,a11),product(a10,a11))) = product(product(a6,product(product(a10,a11),product(a10,a11))),product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(379,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a10,a11),product(a10,a11))) = product(product(a6,product(product(a10,a11),product(a10,a11))),product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11)))),
inference(unit_resolution,[status(thm)],[378,22]) ).
tff(380,plain,
product(product(a12,a3),product(a12,a3)) = product(a12,a3),
inference(transitivity,[status(thm)],[156,154,152]) ).
tff(381,plain,
product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))) = product(product(a12,a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[380,51]) ).
tff(382,plain,
product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))) = product(product(a10,a11),product(a10,a11)),
inference(transitivity,[status(thm)],[381,186,189]) ).
tff(383,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2)))) = product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a10,a11),product(a10,a11))),
inference(monotonicity,[status(thm)],[382]) ).
tff(384,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,product(product(a12,a3),product(a12,a3))),product(product(a1,a2),product(a1,a2))) = product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(385,plain,
product(product(a6,product(product(a12,a3),product(a12,a3))),product(product(a1,a2),product(a1,a2))) = product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2)))),
inference(unit_resolution,[status(thm)],[384,22]) ).
tff(386,plain,
product(product(a12,a3),product(a12,a3)) = a13,
inference(transitivity,[status(thm)],[156,154]) ).
tff(387,plain,
product(a6,product(product(a12,a3),product(a12,a3))) = product(product(a13,a8),a13),
inference(monotonicity,[status(thm)],[66,386]) ).
tff(388,plain,
product(product(a13,a8),a13) = product(a6,product(product(a12,a3),product(a12,a3))),
inference(symmetry,[status(thm)],[387]) ).
tff(389,plain,
product(a13,a8) = product(product(a12,a7),a3),
inference(transitivity,[status(thm)],[62,54]) ).
tff(390,plain,
product(product(a13,a8),a13) = product(product(product(a12,a7),a3),product(a12,a3)),
inference(monotonicity,[status(thm)],[389,152]) ).
tff(391,plain,
product(product(product(a12,a7),a3),product(a12,a3)) = product(product(a13,a8),a13),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a12,a7),a12),a3) = product(product(product(a12,a7),a3),product(a12,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(393,plain,
product(product(product(a12,a7),a12),a3) = product(product(product(a12,a7),a3),product(a12,a3)),
inference(unit_resolution,[status(thm)],[392,22]) ).
tff(394,plain,
product(product(a12,a12),product(a7,a12)) = product(product(a12,a7),a12),
inference(symmetry,[status(thm)],[340]) ).
tff(395,plain,
product(product(product(a12,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))) = product(product(product(a12,a7),a12),a3),
inference(monotonicity,[status(thm)],[394,134]) ).
tff(396,plain,
product(product(product(a12,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))) = product(a6,product(product(a12,a3),product(a12,a3))),
inference(transitivity,[status(thm)],[395,393,391,388]) ).
tff(397,plain,
product(product(product(product(a12,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a6,product(product(a12,a3),product(a12,a3))),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[396]) ).
tff(398,plain,
product(product(product(a12,a7),a12),a3) = product(product(product(a12,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[395]) ).
tff(399,plain,
product(product(product(a12,a7),a3),product(a12,a3)) = product(product(product(a12,a7),a12),a3),
inference(symmetry,[status(thm)],[393]) ).
tff(400,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a13,a8),a13) = product(product(a13,a13),product(a8,a13)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(401,plain,
product(product(a13,a8),a13) = product(product(a13,a13),product(a8,a13)),
inference(unit_resolution,[status(thm)],[400,22]) ).
tff(402,plain,
product(product(a13,a13),product(a8,a13)) = product(product(a13,a8),a13),
inference(symmetry,[status(thm)],[401]) ).
tff(403,plain,
product(a8,a13) = product(product(a7,a3),product(a12,a3)),
inference(monotonicity,[status(thm)],[126,152]) ).
tff(404,plain,
product(product(a7,a3),product(a12,a3)) = product(a8,a13),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a7,a12),a3) = product(product(a7,a3),product(a12,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(406,plain,
product(product(a7,a12),a3) = product(product(a7,a3),product(a12,a3)),
inference(unit_resolution,[status(thm)],[405,22]) ).
tff(407,plain,
product(product(a7,a12),a3) = product(a8,a13),
inference(transitivity,[status(thm)],[406,404]) ).
tff(408,plain,
product(a12,a3) = product(a13,a13),
inference(transitivity,[status(thm)],[60,184]) ).
tff(409,plain,
product(product(a12,a3),product(product(a7,a12),a3)) = product(product(a13,a13),product(a8,a13)),
inference(monotonicity,[status(thm)],[408,407]) ).
tff(410,plain,
product(product(a7,a3),product(a12,a3)) = product(product(a7,a12),a3),
inference(symmetry,[status(thm)],[406]) ).
tff(411,plain,
product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a12,a3))) = product(product(a12,a3),product(product(a7,a12),a3)),
inference(monotonicity,[status(thm)],[380,410]) ).
tff(412,plain,
product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a12,a3))) = product(product(product(a12,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[411,409,402,390,399,398]) ).
tff(413,plain,
product(product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a12,a3))),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a12,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[412]) ).
tff(414,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a12,a3))),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(415,plain,
product(product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a12,a3))),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2)))),
inference(unit_resolution,[status(thm)],[414,22]) ).
tff(416,plain,
product(product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2)))) = product(product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a12,a3))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[415]) ).
tff(417,plain,
product(product(product(a7,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))) = product(product(product(a7,a12),a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[410,51]) ).
tff(418,plain,
product(product(product(a7,a12),a3),product(a3,a3)) = product(product(product(a7,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[417]) ).
tff(419,plain,
product(product(product(a7,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))) = product(product(product(a7,a12),product(a7,a12)),a3),
inference(monotonicity,[status(thm)],[134]) ).
tff(420,plain,
product(product(product(a7,a12),product(a7,a12)),a3) = product(product(product(a7,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[419]) ).
tff(421,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a7,a12),product(a7,a12)),a3) = product(product(product(a7,a12),a3),product(product(a7,a12),a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(422,plain,
product(product(product(a7,a12),product(a7,a12)),a3) = product(product(product(a7,a12),a3),product(product(a7,a12),a3)),
inference(unit_resolution,[status(thm)],[421,22]) ).
tff(423,plain,
product(product(product(a7,a12),a3),product(product(a7,a12),a3)) = product(product(product(a7,a12),product(a7,a12)),a3),
inference(symmetry,[status(thm)],[422]) ).
tff(424,plain,
product(product(product(a7,a12),a3),product(product(a7,a12),a3)) = product(product(a8,a13),product(a8,a13)),
inference(monotonicity,[status(thm)],[407,407]) ).
tff(425,plain,
product(product(a8,a13),product(a8,a13)) = product(product(product(a7,a12),a3),product(product(a7,a12),a3)),
inference(symmetry,[status(thm)],[424]) ).
tff(426,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a8,a8),a13) = product(product(a8,a13),product(a8,a13)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(427,plain,
product(product(a8,a8),a13) = product(product(a8,a13),product(a8,a13)),
inference(unit_resolution,[status(thm)],[426,22]) ).
tff(428,plain,
product(a7,a3) = product(a8,a8),
inference(transitivity,[status(thm)],[57,140]) ).
tff(429,plain,
product(product(a7,a3),product(a12,a3)) = product(product(a8,a8),a13),
inference(monotonicity,[status(thm)],[428,60]) ).
tff(430,plain,
product(product(a7,a12),a3) = product(product(product(a7,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[406,429,427,425,423,420]) ).
tff(431,plain,
product(product(product(a7,a12),a3),product(a3,a3)) = product(product(product(product(a7,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[430,50]) ).
tff(432,plain,
product(product(product(product(a7,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(product(a7,a12),a3),product(a3,a3)),
inference(symmetry,[status(thm)],[431]) ).
tff(433,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a7,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a7,a12),product(a7,a12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(434,plain,
product(product(product(product(a7,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a7,a12),product(a7,a12)),
inference(unit_resolution,[status(thm)],[433,89]) ).
tff(435,plain,
product(product(a7,a12),product(a7,a12)) = product(product(product(product(a7,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[434]) ).
tff(436,plain,
product(a7,a12) = product(product(product(a5,a6),product(a5,a6)),a12),
inference(monotonicity,[status(thm)],[45]) ).
tff(437,plain,
product(a7,a12) = product(product(product(a7,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[436,335,333,435,432,418]) ).
tff(438,plain,
product(product(a12,a3),product(a3,a3)) = product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[381]) ).
tff(439,plain,
product(product(a10,a11),product(a10,a11)) = product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[190,187,438]) ).
tff(440,plain,
product(product(product(a10,a11),product(a10,a11)),product(a7,a12)) = product(product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2)))),
inference(monotonicity,[status(thm)],[439,437]) ).
tff(441,plain,
product(product(a12,a12),product(a7,a12)) = product(product(product(a10,a11),product(a10,a11)),product(a7,a12)),
inference(monotonicity,[status(thm)],[177]) ).
tff(442,plain,
product(product(a12,a12),product(a7,a12)) = product(product(product(a15,a8),product(a13,a8)),a12),
inference(transitivity,[status(thm)],[441,440,416,413,397,385,383,379,377,370,355,352]) ).
tff(443,plain,
product(product(product(a12,a12),product(a7,a12)),product(product(a7,a12),product(a7,a12))) = product(product(product(product(a15,a8),product(a13,a8)),a12),product(product(a7,a12),product(a7,a12))),
inference(monotonicity,[status(thm)],[442]) ).
tff(444,plain,
product(product(product(product(a15,a8),product(a13,a8)),a12),product(product(a7,a12),product(a7,a12))) = product(product(product(a12,a12),product(a7,a12)),product(product(a7,a12),product(a7,a12))),
inference(symmetry,[status(thm)],[443]) ).
tff(445,plain,
product(product(a7,a12),product(a7,a12)) = product(product(a7,a7),a12),
inference(symmetry,[status(thm)],[333]) ).
tff(446,plain,
product(product(a7,a12),product(a7,a12)) = product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11))),
inference(transitivity,[status(thm)],[445,334,336]) ).
tff(447,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a10,a11),product(a10,a11))) = product(product(product(a15,a8),product(a13,a8)),a12),
inference(monotonicity,[status(thm)],[341]) ).
tff(448,plain,
product(product(product(a15,a8),product(a13,a8)),a12) = product(product(product(a15,a8),product(a13,a8)),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[447]) ).
tff(449,plain,
product(product(product(product(a15,a8),product(a13,a8)),a12),product(product(a7,a12),product(a7,a12))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a10,a11),product(a10,a11))),product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11)))),
inference(monotonicity,[status(thm)],[448,446]) ).
tff(450,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a10,a11),product(a10,a11))),product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11)))) = product(product(product(product(a15,a8),product(a13,a8)),a12),product(product(a7,a12),product(a7,a12))),
inference(symmetry,[status(thm)],[449]) ).
tff(451,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a10,a11),product(a10,a11))),product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(452,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a10,a11),product(a10,a11))),product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11)))),
inference(unit_resolution,[status(thm)],[451,22]) ).
tff(453,plain,
product(product(a15,a8),product(a13,a8)) = product(a4,a6),
inference(symmetry,[status(thm)],[122]) ).
tff(454,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))) = product(product(a4,a6),a7),
inference(monotonicity,[status(thm)],[453,77]) ).
tff(455,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))) = product(product(a4,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[454,36]) ).
tff(456,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))) = product(product(product(a4,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))),
inference(monotonicity,[status(thm)],[455]) ).
tff(457,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[456]) ).
tff(458,plain,
product(a4,product(product(a5,a6),product(a5,a6))) = product(a4,a7),
inference(monotonicity,[status(thm)],[77]) ).
tff(459,plain,
product(a4,a7) = product(a4,product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[458]) ).
tff(460,plain,
product(product(a4,a7),product(a4,a7)) = product(a4,product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[261,287,32,459]) ).
tff(461,plain,
product(product(a5,a6),a6) = product(a7,a6),
inference(monotonicity,[status(thm)],[39]) ).
tff(462,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a5,a6),a6) = product(product(a5,a6),product(a6,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(463,plain,
product(product(a5,a6),a6) = product(product(a5,a6),product(a6,a6)),
inference(unit_resolution,[status(thm)],[462,22]) ).
tff(464,plain,
product(product(a5,a6),product(a6,a6)) = product(product(a5,a6),a6),
inference(symmetry,[status(thm)],[463]) ).
tff(465,plain,
product(product(a5,a6),product(a6,a6)) = product(a7,a6),
inference(transitivity,[status(thm)],[464,461]) ).
tff(466,plain,
product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6))) = product(product(a7,a6),a7),
inference(monotonicity,[status(thm)],[465,77]) ).
tff(467,plain,
product(product(a7,a6),a7) = product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[466]) ).
tff(468,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a7,a6),a7) = product(product(a7,a7),product(a6,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(469,plain,
product(product(a7,a6),a7) = product(product(a7,a7),product(a6,a7)),
inference(unit_resolution,[status(thm)],[468,22]) ).
tff(470,plain,
product(product(a7,a7),product(a6,a7)) = product(product(a7,a6),a7),
inference(symmetry,[status(thm)],[469]) ).
tff(471,plain,
product(product(a7,a7),product(a6,a7)) = product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[470,467]) ).
tff(472,plain,
product(product(product(a7,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))) = product(product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[471,460]) ).
tff(473,plain,
product(product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))) = product(product(product(a7,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))),
inference(symmetry,[status(thm)],[472]) ).
tff(474,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a5,a6),product(a6,a6)),a4),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(475,plain,
product(product(product(product(a5,a6),product(a6,a6)),a4),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[474,22]) ).
tff(476,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a1,a2),product(a1,a2)),a4),a4) = product(product(a1,a2),product(a1,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(477,plain,
product(product(product(product(a1,a2),product(a1,a2)),a4),a4) = product(product(a1,a2),product(a1,a2)),
inference(unit_resolution,[status(thm)],[476,89]) ).
tff(478,plain,
product(product(product(a1,a2),product(a1,a2)),a4) = product(product(a3,a3),a4),
inference(monotonicity,[status(thm)],[51]) ).
tff(479,plain,
product(product(a3,a3),a4) = product(product(product(a1,a2),product(a1,a2)),a4),
inference(symmetry,[status(thm)],[478]) ).
tff(480,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a3,a3),a4) = product(product(a3,a4),product(a3,a4)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(481,plain,
product(product(a3,a3),a4) = product(product(a3,a4),product(a3,a4)),
inference(unit_resolution,[status(thm)],[480,22]) ).
tff(482,plain,
product(product(a3,a4),product(a3,a4)) = product(product(a3,a3),a4),
inference(symmetry,[status(thm)],[481]) ).
tff(483,plain,
product(product(a3,a4),product(a3,a4)) = product(product(product(a1,a2),product(a1,a2)),a4),
inference(transitivity,[status(thm)],[482,479]) ).
tff(484,plain,
product(product(product(a3,a4),product(a3,a4)),a4) = product(product(product(product(a1,a2),product(a1,a2)),a4),a4),
inference(monotonicity,[status(thm)],[483]) ).
tff(485,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a3,a4),product(a3,a4)),a6),a6) = product(product(a3,a4),product(a3,a4)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(486,plain,
product(product(product(product(a3,a4),product(a3,a4)),a6),a6) = product(product(a3,a4),product(a3,a4)),
inference(unit_resolution,[status(thm)],[485,89]) ).
tff(487,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a5,a5),a6) = product(product(a5,a6),product(a5,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(488,plain,
product(product(a5,a5),a6) = product(product(a5,a6),product(a5,a6)),
inference(unit_resolution,[status(thm)],[487,22]) ).
tff(489,plain,
( ( product(a3,a4) = a5 )
<=> ( product(a3,a4) = a5 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(490,axiom,
product(a3,a4) = a5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_03) ).
tff(491,plain,
product(a3,a4) = a5,
inference(modus_ponens,[status(thm)],[490,489]) ).
tff(492,plain,
a5 = product(a3,a4),
inference(symmetry,[status(thm)],[491]) ).
tff(493,plain,
product(a5,a5) = product(product(a3,a4),product(a3,a4)),
inference(monotonicity,[status(thm)],[492,492]) ).
tff(494,plain,
product(product(a3,a4),product(a3,a4)) = product(a5,a5),
inference(symmetry,[status(thm)],[493]) ).
tff(495,plain,
product(product(product(a3,a4),product(a3,a4)),a6) = product(product(a5,a5),a6),
inference(monotonicity,[status(thm)],[494]) ).
tff(496,plain,
product(product(product(a3,a4),product(a3,a4)),a6) = a7,
inference(transitivity,[status(thm)],[495,488,76,43]) ).
tff(497,plain,
product(product(product(product(a3,a4),product(a3,a4)),a6),a6) = product(a7,a6),
inference(monotonicity,[status(thm)],[496]) ).
tff(498,plain,
product(a7,a6) = product(product(product(product(a3,a4),product(a3,a4)),a6),a6),
inference(symmetry,[status(thm)],[497]) ).
tff(499,plain,
product(product(a5,a6),product(a6,a6)) = product(product(a3,a4),product(a3,a4)),
inference(transitivity,[status(thm)],[464,461,498,486]) ).
tff(500,plain,
product(product(product(a5,a6),product(a6,a6)),a4) = product(product(product(a3,a4),product(a3,a4)),a4),
inference(monotonicity,[status(thm)],[499]) ).
tff(501,plain,
product(product(product(a5,a6),product(a6,a6)),a4) = a3,
inference(transitivity,[status(thm)],[500,484,477,51,71]) ).
tff(502,plain,
product(product(product(product(a5,a6),product(a6,a6)),a4),product(product(a5,a6),product(a5,a6))) = product(a3,product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[501]) ).
tff(503,plain,
product(a3,product(product(a5,a6),product(a5,a6))) = product(product(product(product(a5,a6),product(a6,a6)),a4),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[502]) ).
tff(504,plain,
product(product(a4,a7),product(a6,a7)) = product(product(product(a7,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))),
inference(transitivity,[status(thm)],[290,285,260,258,503,475,473]) ).
tff(505,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a7,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))),product(product(a10,a11),product(a10,a11))),
inference(monotonicity,[status(thm)],[504]) ).
tff(506,plain,
product(product(product(product(a7,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))),product(product(a10,a11),product(a10,a11))) = product(product(product(a4,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[505]) ).
tff(507,plain,
product(product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a5,a6),product(a6,a6)),a4),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[475]) ).
tff(508,plain,
product(product(product(a7,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))) = product(a3,product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[472,507,502]) ).
tff(509,plain,
product(product(product(product(a7,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))),product(product(a10,a11),product(a10,a11))) = product(product(a3,product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))),
inference(monotonicity,[status(thm)],[508]) ).
tff(510,plain,
product(product(a3,product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a7,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[509]) ).
tff(511,plain,
product(product(a10,a11),product(a10,a11)) = product(product(a12,a7),product(a7,a7)),
inference(transitivity,[status(thm)],[313,310]) ).
tff(512,plain,
product(product(a3,product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))) = product(product(a3,product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a7,a7))),
inference(monotonicity,[status(thm)],[511]) ).
tff(513,plain,
product(product(a3,product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a7,a7))) = product(product(a3,product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[512]) ).
tff(514,plain,
product(product(a3,product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a7,a7))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[295,326]) ).
tff(515,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6)))) = product(product(a3,product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a7,a7))),
inference(symmetry,[status(thm)],[514]) ).
tff(516,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(a1,a2)),product(product(a12,a7),product(a12,a7))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(517,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a12,a7),product(a12,a7))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[516,22]) ).
tff(518,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a12,a7),product(a12,a7))) = product(a3,product(a12,a7)),
inference(monotonicity,[status(thm)],[134,324]) ).
tff(519,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a12,a7),product(a12,a7))),product(product(a5,a6),product(a5,a6))) = product(product(a3,product(a12,a7)),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[518]) ).
tff(520,plain,
product(product(a3,product(a12,a7)),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a12,a7),product(a12,a7))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[519]) ).
tff(521,plain,
product(product(product(a1,a2),product(a1,a2)),a6) = product(product(a3,a3),product(product(a12,a7),a3)),
inference(monotonicity,[status(thm)],[51,67]) ).
tff(522,plain,
product(product(a3,a3),product(product(a12,a7),a3)) = product(product(product(a1,a2),product(a1,a2)),a6),
inference(symmetry,[status(thm)],[521]) ).
tff(523,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a5,a5) = a5 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(524,plain,
product(a5,a5) = a5,
inference(unit_resolution,[status(thm)],[523,7]) ).
tff(525,plain,
a5 = product(a5,a5),
inference(symmetry,[status(thm)],[524]) ).
tff(526,plain,
a5 = product(product(a3,a4),product(a3,a4)),
inference(transitivity,[status(thm)],[525,493]) ).
tff(527,plain,
product(a5,a4) = product(product(product(a3,a4),product(a3,a4)),a4),
inference(monotonicity,[status(thm)],[526]) ).
tff(528,plain,
product(a5,a4) = product(a3,a3),
inference(transitivity,[status(thm)],[527,484,477,51]) ).
tff(529,plain,
product(product(a5,a4),a6) = product(product(a3,a3),product(product(a12,a7),a3)),
inference(monotonicity,[status(thm)],[528,67]) ).
tff(530,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a5,a4),a6) = product(product(a5,a6),product(a4,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(531,plain,
product(product(a5,a4),a6) = product(product(a5,a6),product(a4,a6)),
inference(unit_resolution,[status(thm)],[530,22]) ).
tff(532,plain,
product(product(a5,a6),product(a4,a6)) = product(product(a5,a4),a6),
inference(symmetry,[status(thm)],[531]) ).
tff(533,plain,
product(product(a5,a6),product(a4,a6)) = product(product(product(a1,a2),product(a1,a2)),a6),
inference(transitivity,[status(thm)],[532,529,522]) ).
tff(534,plain,
product(product(product(a5,a6),product(a4,a6)),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a1,a2),product(a1,a2)),a6),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[533]) ).
tff(535,plain,
product(product(product(product(a1,a2),product(a1,a2)),a6),product(product(a1,a2),product(a1,a2))) = product(product(product(a5,a6),product(a4,a6)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[534]) ).
tff(536,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(a1,a2)),a6),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a6,product(product(a1,a2),product(a1,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(537,plain,
product(product(product(product(a1,a2),product(a1,a2)),a6),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a6,product(product(a1,a2),product(a1,a2)))),
inference(unit_resolution,[status(thm)],[536,22]) ).
tff(538,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a6,product(product(a1,a2),product(a1,a2)))) = product(product(product(product(a1,a2),product(a1,a2)),a6),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[537]) ).
tff(539,plain,
product(product(product(a12,a7),a3),product(product(a12,a7),a3)) = product(product(a13,a8),product(a13,a8)),
inference(monotonicity,[status(thm)],[108,108]) ).
tff(540,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a12,a7),product(a12,a7)),a3) = product(product(product(a12,a7),a3),product(product(a12,a7),a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(541,plain,
product(product(product(a12,a7),product(a12,a7)),a3) = product(product(product(a12,a7),a3),product(product(a12,a7),a3)),
inference(unit_resolution,[status(thm)],[540,22]) ).
tff(542,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))) = product(product(product(a12,a7),product(a12,a7)),a3),
inference(monotonicity,[status(thm)],[134]) ).
tff(543,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))) = product(product(a12,a7),a3),
inference(transitivity,[status(thm)],[542,541,539,161,160,66,62,54]) ).
tff(544,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(product(a12,a7),a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[543,51]) ).
tff(545,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a12,a7),product(a12,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(546,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a12,a7),product(a12,a7)),
inference(unit_resolution,[status(thm)],[545,89]) ).
tff(547,plain,
product(product(a12,a7),product(a12,a7)) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[546]) ).
tff(548,plain,
product(a12,a7) = product(a6,product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[307,306,319,322,547,544,69]) ).
tff(549,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a1,a2),product(a1,a2))) = product(product(a3,a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[51,51]) ).
tff(550,plain,
product(product(a3,a3),product(a3,a3)) = product(product(product(a1,a2),product(a1,a2)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[549]) ).
tff(551,plain,
product(a3,a3) = product(a1,a2),
inference(transitivity,[status(thm)],[71,49]) ).
tff(552,plain,
product(product(a3,a3),product(a3,a3)) = product(product(a1,a2),product(a1,a2)),
inference(monotonicity,[status(thm)],[551,551]) ).
tff(553,plain,
product(product(a1,a2),product(a1,a2)) = product(product(a3,a3),product(a3,a3)),
inference(symmetry,[status(thm)],[552]) ).
tff(554,plain,
a3 = product(product(product(a1,a2),product(a1,a2)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[241,50,553,550]) ).
tff(555,plain,
product(a3,product(a12,a7)) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a6,product(product(a1,a2),product(a1,a2)))),
inference(monotonicity,[status(thm)],[554,548]) ).
tff(556,plain,
product(a3,product(a12,a7)) = product(product(product(a5,a6),product(a4,a6)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[555,538,535]) ).
tff(557,plain,
product(product(a3,product(a12,a7)),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a5,a6),product(a4,a6)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[556]) ).
tff(558,plain,
product(product(product(product(a5,a6),product(a4,a6)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(product(a3,product(a12,a7)),product(product(a5,a6),product(a5,a6))),
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(product(a5,a6),product(a4,a6)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(560,plain,
product(product(product(product(a5,a6),product(a4,a6)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[559,22]) ).
tff(561,plain,
product(product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a5,a6),product(a4,a6)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[560]) ).
tff(562,plain,
product(product(a12,a12),product(a14,a12)) = product(a12,product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[192,93]) ).
tff(563,plain,
product(a12,product(product(a6,a7),product(a6,a7))) = product(product(a12,a12),product(a14,a12)),
inference(symmetry,[status(thm)],[562]) ).
tff(564,plain,
product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))) = product(a10,product(product(a4,a7),product(a4,a7))),
inference(monotonicity,[status(thm)],[272]) ).
tff(565,plain,
product(a10,product(product(a4,a7),product(a4,a7))) = product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),
inference(symmetry,[status(thm)],[564]) ).
tff(566,plain,
product(product(a4,a7),product(a4,a7)) = a11,
inference(transitivity,[status(thm)],[261,287]) ).
tff(567,plain,
a10 = product(a10,a10),
inference(symmetry,[status(thm)],[270]) ).
tff(568,plain,
product(a10,product(product(a4,a7),product(a4,a7))) = product(product(a10,a10),a11),
inference(monotonicity,[status(thm)],[567,566]) ).
tff(569,plain,
product(product(a10,a10),a11) = product(a10,product(product(a4,a7),product(a4,a7))),
inference(symmetry,[status(thm)],[568]) ).
tff(570,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a10,a10),a11) = product(product(a10,a11),product(a10,a11)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(571,plain,
product(product(a10,a10),a11) = product(product(a10,a11),product(a10,a11)),
inference(unit_resolution,[status(thm)],[570,22]) ).
tff(572,plain,
product(product(a10,a11),product(a10,a11)) = product(product(a10,a10),a11),
inference(symmetry,[status(thm)],[571]) ).
tff(573,plain,
a12 = product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),
inference(transitivity,[status(thm)],[193,177,572,569,565]) ).
tff(574,plain,
product(a12,product(product(a6,a7),product(a6,a7))) = product(product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[573]) ).
tff(575,plain,
product(product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),product(product(a6,a7),product(a6,a7))) = product(a12,product(product(a6,a7),product(a6,a7))),
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(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7))),product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(577,plain,
product(product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7))),product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[576,22]) ).
tff(578,plain,
product(product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7))),product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[577]) ).
tff(579,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))) = product(product(a11,a11),a2),
inference(monotonicity,[status(thm)],[261,197]) ).
tff(580,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))) = product(product(a4,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[579,289]) ).
tff(581,plain,
product(product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7))),product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a9,a1),product(a9,a1)),a2),product(product(a4,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[198,580]) ).
tff(582,plain,
product(product(product(product(a9,a1),product(a9,a1)),a2),product(product(a4,a7),product(a6,a7))) = product(product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7))),product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7)))),
inference(symmetry,[status(thm)],[581]) ).
tff(583,plain,
product(product(product(a15,a8),product(a13,a8)),a7) = product(product(a4,a6),a7),
inference(monotonicity,[status(thm)],[453]) ).
tff(584,plain,
product(product(a4,a6),a7) = product(product(product(a15,a8),product(a13,a8)),a7),
inference(symmetry,[status(thm)],[583]) ).
tff(585,plain,
product(product(a4,a7),product(a6,a7)) = product(product(a4,a6),a7),
inference(symmetry,[status(thm)],[36]) ).
tff(586,plain,
product(product(a4,a7),product(a6,a7)) = product(product(product(a15,a8),product(a13,a8)),a7),
inference(transitivity,[status(thm)],[585,584]) ).
tff(587,plain,
product(product(product(a9,a1),product(a9,a1)),a2) = product(a7,a7),
inference(transitivity,[status(thm)],[222,225,239,251,142,145,76]) ).
tff(588,plain,
product(product(product(product(a9,a1),product(a9,a1)),a2),product(product(a4,a7),product(a6,a7))) = product(product(a7,a7),product(product(product(a15,a8),product(a13,a8)),a7)),
inference(monotonicity,[status(thm)],[587,586]) ).
tff(589,plain,
product(product(a7,a7),product(product(product(a15,a8),product(a13,a8)),a7)) = product(product(product(product(a9,a1),product(a9,a1)),a2),product(product(a4,a7),product(a6,a7))),
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(a7,product(product(a15,a8),product(a13,a8))),a7) = product(product(a7,a7),product(product(product(a15,a8),product(a13,a8)),a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(591,plain,
product(product(a7,product(product(a15,a8),product(a13,a8))),a7) = product(product(a7,a7),product(product(product(a15,a8),product(a13,a8)),a7)),
inference(unit_resolution,[status(thm)],[590,22]) ).
tff(592,plain,
product(a7,product(product(a15,a8),product(a13,a8))) = product(product(a5,a6),product(a4,a6)),
inference(monotonicity,[status(thm)],[40,453]) ).
tff(593,plain,
product(product(a5,a6),product(a4,a6)) = product(a7,product(product(a15,a8),product(a13,a8))),
inference(symmetry,[status(thm)],[592]) ).
tff(594,plain,
product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6))) = product(product(a7,product(product(a15,a8),product(a13,a8))),a7),
inference(monotonicity,[status(thm)],[593,77]) ).
tff(595,plain,
product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6))) = product(product(a12,a12),product(a14,a12)),
inference(transitivity,[status(thm)],[594,591,589,582,578,575,563]) ).
tff(596,plain,
product(product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a12,a12),product(a14,a12)),product(a3,product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[595,294]) ).
tff(597,plain,
product(product(product(a12,a12),product(a14,a12)),product(a3,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[596]) ).
tff(598,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[260]) ).
tff(599,plain,
product(a3,product(product(a5,a6),product(a5,a6))) = product(product(a4,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[257,598,284,289]) ).
tff(600,plain,
product(product(product(a12,a12),product(a14,a12)),product(a3,product(product(a5,a6),product(a5,a6)))) = product(product(product(a12,a12),product(a14,a12)),product(product(a4,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[599]) ).
tff(601,plain,
product(product(product(a12,a12),product(a14,a12)),product(product(a4,a7),product(a6,a7))) = product(product(product(a12,a12),product(a14,a12)),product(a3,product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[600]) ).
tff(602,plain,
product(product(a11,a11),a2) = product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[579]) ).
tff(603,plain,
product(product(a4,a7),product(a6,a7)) = product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),
inference(transitivity,[status(thm)],[290,602]) ).
tff(604,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))) = product(a12,product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[341]) ).
tff(605,plain,
product(a12,product(product(a6,a7),product(a6,a7))) = product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[604]) ).
tff(606,plain,
product(product(a12,a12),product(a14,a12)) = product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),
inference(transitivity,[status(thm)],[562,605]) ).
tff(607,plain,
product(product(product(a12,a12),product(a14,a12)),product(product(a4,a7),product(a6,a7))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7)))),
inference(monotonicity,[status(thm)],[606,603]) ).
tff(608,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a12,a12),product(a14,a12)),product(product(a4,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[607]) ).
tff(609,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(610,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[609,22]) ).
tff(611,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),product(product(a4,a7),product(a4,a7))) = product(product(a9,a1),product(a9,a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(612,plain,
product(product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),product(product(a4,a7),product(a4,a7))) = product(product(a9,a1),product(a9,a1)),
inference(unit_resolution,[status(thm)],[611,89]) ).
tff(613,plain,
product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))) = product(a10,a11),
inference(transitivity,[status(thm)],[564,568,571,178,192,176]) ).
tff(614,plain,
product(product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),product(product(a4,a7),product(a4,a7))) = product(product(a10,a11),product(a11,a11)),
inference(monotonicity,[status(thm)],[613,261]) ).
tff(615,plain,
product(product(a10,a11),product(a11,a11)) = product(product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),product(product(a4,a7),product(a4,a7))),
inference(symmetry,[status(thm)],[614]) ).
tff(616,plain,
product(product(a10,a11),product(a10,a11)) = product(a10,a11),
inference(transitivity,[status(thm)],[178,192,176]) ).
tff(617,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))) = product(product(a10,a11),product(a11,a11)),
inference(monotonicity,[status(thm)],[616,261]) ).
tff(618,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))) = product(product(a9,a1),product(a9,a1)),
inference(transitivity,[status(thm)],[617,615,612]) ).
tff(619,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),product(product(a6,a7),product(a6,a7))) = product(product(product(a9,a1),product(a9,a1)),a2),
inference(monotonicity,[status(thm)],[618,197]) ).
tff(620,plain,
product(product(product(a9,a1),product(a9,a1)),a2) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[619]) ).
tff(621,plain,
product(a5,a5) = product(product(product(a1,a2),product(a1,a2)),a4),
inference(transitivity,[status(thm)],[493,482,479]) ).
tff(622,plain,
product(product(a5,a5),a6) = product(product(product(product(a1,a2),product(a1,a2)),a4),a6),
inference(monotonicity,[status(thm)],[621]) ).
tff(623,plain,
product(product(product(product(a1,a2),product(a1,a2)),a4),a6) = product(product(a5,a5),a6),
inference(symmetry,[status(thm)],[622]) ).
tff(624,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(a1,a2)),a4),a6) = product(product(product(product(a1,a2),product(a1,a2)),a6),product(a4,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(625,plain,
product(product(product(product(a1,a2),product(a1,a2)),a4),a6) = product(product(product(product(a1,a2),product(a1,a2)),a6),product(a4,a6)),
inference(unit_resolution,[status(thm)],[624,22]) ).
tff(626,plain,
product(product(product(product(a1,a2),product(a1,a2)),a6),product(a4,a6)) = product(product(product(product(a1,a2),product(a1,a2)),a4),a6),
inference(symmetry,[status(thm)],[625]) ).
tff(627,plain,
product(product(a3,a3),product(product(a12,a7),a3)) = product(product(a5,a4),a6),
inference(symmetry,[status(thm)],[529]) ).
tff(628,plain,
product(product(product(a1,a2),product(a1,a2)),a6) = product(product(a5,a6),product(a4,a6)),
inference(transitivity,[status(thm)],[521,627,531]) ).
tff(629,plain,
product(product(product(product(a1,a2),product(a1,a2)),a6),product(a4,a6)) = product(product(product(a5,a6),product(a4,a6)),product(product(a15,a8),product(a13,a8))),
inference(monotonicity,[status(thm)],[628,122]) ).
tff(630,plain,
product(product(product(a5,a6),product(a4,a6)),product(product(a15,a8),product(a13,a8))) = product(product(product(product(a1,a2),product(a1,a2)),a6),product(a4,a6)),
inference(symmetry,[status(thm)],[629]) ).
tff(631,plain,
product(a1,a1) = product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),
inference(transitivity,[status(thm)],[207,277,274]) ).
tff(632,plain,
product(product(a1,a1),a2) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[631,200]) ).
tff(633,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))) = product(product(a1,a1),a2),
inference(symmetry,[status(thm)],[632]) ).
tff(634,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(635,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[634,22]) ).
tff(636,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[635]) ).
tff(637,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a4,a7),product(a6,a7)),product(product(product(a9,a1),product(a9,a1)),a2)),
inference(monotonicity,[status(thm)],[580,198]) ).
tff(638,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(product(a9,a1),product(a9,a1)),a2)) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))),
inference(symmetry,[status(thm)],[637]) ).
tff(639,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(product(a9,a1),product(a9,a1)),a2)) = product(product(product(product(a15,a8),product(a13,a8)),a7),product(a7,a7)),
inference(monotonicity,[status(thm)],[586,587]) ).
tff(640,plain,
product(product(product(product(a15,a8),product(a13,a8)),a7),product(a7,a7)) = product(product(product(a4,a7),product(a6,a7)),product(product(product(a9,a1),product(a9,a1)),a2)),
inference(symmetry,[status(thm)],[639]) ).
tff(641,plain,
product(product(a4,a6),a7) = product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[454]) ).
tff(642,plain,
product(product(product(a15,a8),product(a13,a8)),a7) = product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[583,641]) ).
tff(643,plain,
product(product(product(product(a15,a8),product(a13,a8)),a7),product(a7,a7)) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[642,41]) ).
tff(644,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a15,a8),product(a13,a8)),a7),product(a7,a7)),
inference(symmetry,[status(thm)],[643]) ).
tff(645,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a15,a8),product(a13,a8)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(646,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a15,a8),product(a13,a8)),
inference(unit_resolution,[status(thm)],[645,89]) ).
tff(647,plain,
product(product(a15,a8),product(a13,a8)) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[646]) ).
tff(648,plain,
product(product(a15,a8),product(a13,a8)) = product(product(a1,a2),product(a1,a2)),
inference(transitivity,[status(thm)],[647,644,640,638,636,633,228]) ).
tff(649,plain,
product(product(product(a5,a6),product(a4,a6)),product(product(a15,a8),product(a13,a8))) = product(product(product(a5,a6),product(a4,a6)),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[648]) ).
tff(650,plain,
product(product(product(a5,a6),product(a4,a6)),product(product(a1,a2),product(a1,a2))) = product(product(product(a5,a6),product(a4,a6)),product(product(a15,a8),product(a13,a8))),
inference(symmetry,[status(thm)],[649]) ).
tff(651,plain,
product(a6,product(product(a1,a2),product(a1,a2))) = product(product(a15,a8),product(a13,a8)),
inference(transitivity,[status(thm)],[68,103,106,116]) ).
tff(652,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a1,a2),product(a1,a2))) = product(product(a1,a2),product(a1,a2)),
inference(transitivity,[status(thm)],[549,552]) ).
tff(653,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a6,product(product(a1,a2),product(a1,a2)))) = product(product(product(a1,a2),product(a1,a2)),product(product(a15,a8),product(a13,a8))),
inference(monotonicity,[status(thm)],[652,651]) ).
tff(654,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a15,a8),product(a13,a8))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a1,a2),product(a1,a2))),product(a6,product(product(a1,a2),product(a1,a2)))),
inference(symmetry,[status(thm)],[653]) ).
tff(655,plain,
product(product(a1,a2),product(a1,a2)) = product(a4,a6),
inference(transitivity,[status(thm)],[255,632,635,637,639,643,646,453]) ).
tff(656,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a15,a8),product(a13,a8))) = product(product(a4,a6),product(a4,a6)),
inference(monotonicity,[status(thm)],[655,453]) ).
tff(657,plain,
product(product(a4,a6),product(a4,a6)) = product(product(product(a1,a2),product(a1,a2)),product(product(a15,a8),product(a13,a8))),
inference(symmetry,[status(thm)],[656]) ).
tff(658,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a4,a4),a6) = product(product(a4,a6),product(a4,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(659,plain,
product(product(a4,a4),a6) = product(product(a4,a6),product(a4,a6)),
inference(unit_resolution,[status(thm)],[658,22]) ).
tff(660,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a4,a4) = a4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(661,plain,
product(a4,a4) = a4,
inference(unit_resolution,[status(thm)],[660,7]) ).
tff(662,plain,
product(a4,a4) = product(a15,a8),
inference(transitivity,[status(thm)],[661,121]) ).
tff(663,plain,
product(product(a4,a4),a6) = product(product(a15,a8),product(a13,a8)),
inference(monotonicity,[status(thm)],[662,66]) ).
tff(664,plain,
product(product(a15,a8),product(a13,a8)) = product(product(a4,a4),a6),
inference(symmetry,[status(thm)],[663]) ).
tff(665,plain,
product(product(product(a11,a10),product(a11,a10)),product(product(a11,a10),product(a11,a10))) = product(a1,a1),
inference(monotonicity,[status(thm)],[209,209]) ).
tff(666,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))) = product(product(a11,a10),product(a11,a10)),
inference(transitivity,[status(thm)],[273,276]) ).
tff(667,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a11,a10),product(a11,a10))) = product(product(product(a11,a10),product(a11,a10)),product(product(a11,a10),product(a11,a10))),
inference(monotonicity,[status(thm)],[666]) ).
tff(668,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a11,a10),product(a11,a10))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a11,a10),product(a11,a10))),product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(669,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a11,a10),product(a11,a10))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a11,a10),product(a11,a10))),product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10)))),
inference(unit_resolution,[status(thm)],[668,22]) ).
tff(670,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a11,a10),product(a11,a10))),product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10)))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a11,a10),product(a11,a10))),
inference(symmetry,[status(thm)],[669]) ).
tff(671,plain,
product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10))) = product(product(a10,a10),product(a11,a10)),
inference(monotonicity,[status(thm)],[271,281]) ).
tff(672,plain,
product(product(a10,a10),product(a11,a10)) = product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10))),
inference(symmetry,[status(thm)],[671]) ).
tff(673,plain,
product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))) = product(a10,a10),
inference(transitivity,[status(thm)],[216,219,271]) ).
tff(674,plain,
product(product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),product(product(a11,a10),product(a11,a10))) = product(product(a10,a10),product(a11,a10)),
inference(monotonicity,[status(thm)],[673,281]) ).
tff(675,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),product(product(a11,a10),product(a11,a10))) = product(product(a8,a2),product(a8,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(676,plain,
product(product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),product(product(a11,a10),product(a11,a10))) = product(product(a8,a2),product(a8,a2)),
inference(unit_resolution,[status(thm)],[675,89]) ).
tff(677,plain,
product(product(a8,a2),product(a8,a2)) = product(product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),product(product(a11,a10),product(a11,a10))),
inference(symmetry,[status(thm)],[676]) ).
tff(678,plain,
product(product(a8,a2),product(a8,a2)) = product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10))),
inference(transitivity,[status(thm)],[677,674,672]) ).
tff(679,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a11,a10),product(a11,a10))) = product(a11,product(product(a11,a10),product(a11,a10))),
inference(monotonicity,[status(thm)],[566]) ).
tff(680,plain,
product(a11,product(product(a11,a10),product(a11,a10))) = product(product(product(a4,a7),product(a4,a7)),product(product(a11,a10),product(a11,a10))),
inference(symmetry,[status(thm)],[679]) ).
tff(681,plain,
product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a8,a2),product(a8,a2))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a11,a10),product(a11,a10))),product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10)))),
inference(monotonicity,[status(thm)],[680,678]) ).
tff(682,plain,
product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a8,a2),product(a8,a2))) = product(a1,a1),
inference(transitivity,[status(thm)],[681,670,667,665]) ).
tff(683,plain,
product(product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))) = product(product(a1,a1),a2),
inference(monotonicity,[status(thm)],[682,197]) ).
tff(684,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))) = product(product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))),product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(685,plain,
product(product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))) = product(product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))),product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[684,22]) ).
tff(686,plain,
product(product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))),product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[685]) ).
tff(687,plain,
product(product(a8,a2),product(a2,a2)) = product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[237]) ).
tff(688,plain,
product(product(a7,a3),product(a7,a3)) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[243]) ).
tff(689,plain,
product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2))) = product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7))),
inference(transitivity,[status(thm)],[135,138,688,248,687]) ).
tff(690,plain,
product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))) = product(product(a11,product(product(a11,a10),product(a11,a10))),a2),
inference(monotonicity,[status(thm)],[197]) ).
tff(691,plain,
product(product(a11,product(product(a11,a10),product(a11,a10))),a2) = product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[690]) ).
tff(692,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a11,product(product(a11,a10),product(a11,a10))),a2) = product(product(a11,a2),product(product(product(a11,a10),product(a11,a10)),a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(693,plain,
product(product(a11,product(product(a11,a10),product(a11,a10))),a2) = product(product(a11,a2),product(product(product(a11,a10),product(a11,a10)),a2)),
inference(unit_resolution,[status(thm)],[692,22]) ).
tff(694,plain,
product(product(a11,a2),product(product(product(a11,a10),product(a11,a10)),a2)) = product(product(a11,product(product(a11,a10),product(a11,a10))),a2),
inference(symmetry,[status(thm)],[693]) ).
tff(695,plain,
product(product(product(a11,a10),product(a11,a10)),a2) = product(product(a1,a1),a2),
inference(monotonicity,[status(thm)],[208]) ).
tff(696,plain,
product(product(product(a11,a10),product(a11,a10)),a2) = product(a1,a2),
inference(transitivity,[status(thm)],[695,228,51,71,49]) ).
tff(697,plain,
product(product(a11,a2),product(product(product(a11,a10),product(a11,a10)),a2)) = product(product(a11,a2),product(a1,a2)),
inference(monotonicity,[status(thm)],[696]) ).
tff(698,plain,
product(product(a11,a2),product(a1,a2)) = product(product(a11,a2),product(product(product(a11,a10),product(a11,a10)),a2)),
inference(symmetry,[status(thm)],[697]) ).
tff(699,plain,
product(product(a1,a2),product(a1,a2)) = product(a1,a2),
inference(transitivity,[status(thm)],[51,71,49]) ).
tff(700,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))) = product(product(a11,a2),product(a1,a2)),
inference(monotonicity,[status(thm)],[34,699]) ).
tff(701,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))) = product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))),
inference(transitivity,[status(thm)],[700,698,694,691]) ).
tff(702,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2)))) = product(product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))),product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7)))),
inference(monotonicity,[status(thm)],[701,689]) ).
tff(703,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(704,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2)))),
inference(unit_resolution,[status(thm)],[703,22]) ).
tff(705,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a15,a8),product(a13,a8)),a7),product(a7,a7)),
inference(monotonicity,[status(thm)],[586,76]) ).
tff(706,plain,
product(product(product(product(a15,a8),product(a13,a8)),a7),product(a7,a7)) = product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[705]) ).
tff(707,plain,
product(a4,a6) = product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[122,647,644,706]) ).
tff(708,plain,
product(product(a4,a6),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[707]) ).
tff(709,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a4,a6),product(product(a1,a2),product(a1,a2))) = product(product(a4,product(product(a1,a2),product(a1,a2))),product(a6,product(product(a1,a2),product(a1,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(710,plain,
product(product(a4,a6),product(product(a1,a2),product(a1,a2))) = product(product(a4,product(product(a1,a2),product(a1,a2))),product(a6,product(product(a1,a2),product(a1,a2)))),
inference(unit_resolution,[status(thm)],[709,22]) ).
tff(711,plain,
product(product(a4,product(product(a1,a2),product(a1,a2))),product(a6,product(product(a1,a2),product(a1,a2)))) = product(product(a4,a6),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[710]) ).
tff(712,plain,
product(product(a15,a8),product(a13,a8)) = product(a6,product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[117,107,104,69]) ).
tff(713,plain,
product(product(a14,a3),product(a7,a3)) = product(product(a14,a7),a3),
inference(symmetry,[status(thm)],[114]) ).
tff(714,plain,
product(a15,a8) = product(product(a14,a3),product(a7,a3)),
inference(symmetry,[status(thm)],[112]) ).
tff(715,plain,
a4 = product(product(a14,a7),a3),
inference(transitivity,[status(thm)],[121,714,713]) ).
tff(716,plain,
product(a4,product(product(a1,a2),product(a1,a2))) = product(product(product(a14,a7),a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[715,51]) ).
tff(717,plain,
product(product(product(a14,a7),a3),product(a3,a3)) = product(a4,product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[716]) ).
tff(718,plain,
product(product(product(product(a14,a7),a3),product(a3,a3)),product(product(a15,a8),product(a13,a8))) = product(product(a4,product(product(a1,a2),product(a1,a2))),product(a6,product(product(a1,a2),product(a1,a2)))),
inference(monotonicity,[status(thm)],[717,712]) ).
tff(719,plain,
product(product(a1,a2),product(a1,a2)) = product(product(a15,a8),product(a13,a8)),
inference(transitivity,[status(thm)],[255,632,635,637,639,643,646]) ).
tff(720,plain,
product(product(a4,product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a14,a7),a3),product(a3,a3)),product(product(a15,a8),product(a13,a8))),
inference(monotonicity,[status(thm)],[716,719]) ).
tff(721,plain,
a3 = product(product(a1,a2),product(a1,a2)),
inference(transitivity,[status(thm)],[241,50]) ).
tff(722,plain,
product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))) = product(product(product(a14,a7),product(a14,a7)),a3),
inference(monotonicity,[status(thm)],[134]) ).
tff(723,plain,
product(product(product(a14,a7),product(a14,a7)),a3) = product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[722]) ).
tff(724,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a14,a7),product(a14,a7)),a3) = product(product(product(a14,a7),a3),product(product(a14,a7),a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(725,plain,
product(product(product(a14,a7),product(a14,a7)),a3) = product(product(product(a14,a7),a3),product(product(a14,a7),a3)),
inference(unit_resolution,[status(thm)],[724,22]) ).
tff(726,plain,
product(product(product(a14,a7),a3),product(product(a14,a7),a3)) = product(product(product(a14,a7),product(a14,a7)),a3),
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
product(a15,a8) = product(product(a14,a7),a3),
inference(transitivity,[status(thm)],[714,713]) ).
tff(728,plain,
product(product(a15,a8),product(a15,a8)) = product(product(product(a14,a7),a3),product(product(a14,a7),a3)),
inference(monotonicity,[status(thm)],[727,727]) ).
tff(729,plain,
product(a4,a4) = product(product(a15,a8),product(a15,a8)),
inference(monotonicity,[status(thm)],[121,121]) ).
tff(730,plain,
a4 = product(a4,a4),
inference(symmetry,[status(thm)],[661]) ).
tff(731,plain,
product(product(a14,a7),a3) = product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[114,112,120,730,729,728,726,723]) ).
tff(732,plain,
product(product(product(a14,a7),a3),product(a3,a3)) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[731,50]) ).
tff(733,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(product(a14,a7),a3),product(a3,a3)),
inference(symmetry,[status(thm)],[732]) ).
tff(734,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a14,a7),product(a14,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(735,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a14,a7),product(a14,a7)),
inference(unit_resolution,[status(thm)],[734,89]) ).
tff(736,plain,
product(product(a14,a7),product(a14,a7)) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[735]) ).
tff(737,plain,
product(product(a14,a7),product(a14,a7)) = product(a4,product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[736,733,717]) ).
tff(738,plain,
product(product(product(a14,a7),product(a14,a7)),a3) = product(product(a4,product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[737,721]) ).
tff(739,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a15,a15),a8) = product(product(a15,a8),product(a15,a8)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(740,plain,
product(product(a15,a15),a8) = product(product(a15,a8),product(a15,a8)),
inference(unit_resolution,[status(thm)],[739,22]) ).
tff(741,plain,
a15 = product(a14,a3),
inference(symmetry,[status(thm)],[111]) ).
tff(742,plain,
product(a15,a15) = product(product(a14,a3),product(a14,a3)),
inference(monotonicity,[status(thm)],[741,741]) ).
tff(743,plain,
product(product(a14,a3),product(a14,a3)) = product(a15,a15),
inference(symmetry,[status(thm)],[742]) ).
tff(744,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a14,a14),a3) = product(product(a14,a3),product(a14,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(745,plain,
product(product(a14,a14),a3) = product(product(a14,a3),product(a14,a3)),
inference(unit_resolution,[status(thm)],[744,22]) ).
tff(746,plain,
product(product(a14,a12),product(a12,a12)) = product(product(a2,a2),a12),
inference(monotonicity,[status(thm)],[231,192]) ).
tff(747,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a14,a12),a12) = product(product(a14,a12),product(a12,a12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(748,plain,
product(product(a14,a12),a12) = product(product(a14,a12),product(a12,a12)),
inference(unit_resolution,[status(thm)],[747,22]) ).
tff(749,plain,
product(product(a14,a12),a12) = product(a14,a14),
inference(transitivity,[status(thm)],[748,746,24,15]) ).
tff(750,plain,
product(product(product(a14,a12),a12),a3) = product(product(a14,a14),a3),
inference(monotonicity,[status(thm)],[749]) ).
tff(751,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a14,a12),a12),a3) = product(product(product(a14,a12),a3),product(a12,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(752,plain,
product(product(product(a14,a12),a12),a3) = product(product(product(a14,a12),a3),product(a12,a3)),
inference(unit_resolution,[status(thm)],[751,22]) ).
tff(753,plain,
product(product(product(a14,a12),a3),product(a12,a3)) = product(product(product(a14,a12),a12),a3),
inference(symmetry,[status(thm)],[752]) ).
tff(754,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a14,a12),a3) = product(product(a14,a3),product(a12,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(755,plain,
product(product(a14,a12),a3) = product(product(a14,a3),product(a12,a3)),
inference(unit_resolution,[status(thm)],[754,22]) ).
tff(756,plain,
product(product(a14,a3),product(a12,a3)) = product(product(a14,a12),a3),
inference(symmetry,[status(thm)],[755]) ).
tff(757,plain,
product(a15,a13) = product(product(a14,a3),product(a12,a3)),
inference(monotonicity,[status(thm)],[741,152]) ).
tff(758,plain,
product(a15,a13) = product(product(a14,a12),a3),
inference(transitivity,[status(thm)],[757,756]) ).
tff(759,plain,
product(product(a15,a13),a13) = product(product(product(a14,a12),a3),product(a12,a3)),
inference(monotonicity,[status(thm)],[758,152]) ).
tff(760,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a15,a13),a13) = product(product(a15,a13),product(a13,a13)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(761,plain,
product(product(a15,a13),a13) = product(product(a15,a13),product(a13,a13)),
inference(unit_resolution,[status(thm)],[760,22]) ).
tff(762,plain,
product(product(a15,a13),product(a13,a13)) = product(product(a15,a13),a13),
inference(symmetry,[status(thm)],[761]) ).
tff(763,plain,
product(product(a14,a3),product(a12,a3)) = product(a15,a13),
inference(symmetry,[status(thm)],[757]) ).
tff(764,plain,
product(product(product(a14,a3),product(a12,a3)),product(product(a12,a3),product(a12,a3))) = product(product(a15,a13),product(a13,a13)),
inference(monotonicity,[status(thm)],[763,156]) ).
tff(765,plain,
product(product(product(a14,a3),product(a12,a3)),product(product(a12,a3),product(a12,a3))) = product(a15,a15),
inference(transitivity,[status(thm)],[764,762,759,753,750,745,743]) ).
tff(766,plain,
product(product(product(product(a14,a3),product(a12,a3)),product(product(a12,a3),product(a12,a3))),a8) = product(product(a15,a15),a8),
inference(monotonicity,[status(thm)],[765]) ).
tff(767,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a14,a3),product(a12,a3)),product(product(a12,a3),product(a12,a3))),a8) = product(product(product(product(a14,a3),product(a12,a3)),a8),product(product(product(a12,a3),product(a12,a3)),a8)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(768,plain,
product(product(product(product(a14,a3),product(a12,a3)),product(product(a12,a3),product(a12,a3))),a8) = product(product(product(product(a14,a3),product(a12,a3)),a8),product(product(product(a12,a3),product(a12,a3)),a8)),
inference(unit_resolution,[status(thm)],[767,22]) ).
tff(769,plain,
product(product(product(product(a14,a3),product(a12,a3)),a8),product(product(product(a12,a3),product(a12,a3)),a8)) = product(product(product(product(a14,a3),product(a12,a3)),product(product(a12,a3),product(a12,a3))),a8),
inference(symmetry,[status(thm)],[768]) ).
tff(770,plain,
product(product(product(a12,a3),product(a12,a3)),a8) = product(product(a13,a13),a8),
inference(monotonicity,[status(thm)],[156]) ).
tff(771,plain,
product(product(a13,a13),a8) = product(product(product(a12,a3),product(a12,a3)),a8),
inference(symmetry,[status(thm)],[770]) ).
tff(772,plain,
product(product(a13,a8),product(a13,a8)) = product(product(a13,a13),a8),
inference(symmetry,[status(thm)],[163]) ).
tff(773,plain,
product(a6,a6) = product(product(a13,a8),product(a13,a8)),
inference(symmetry,[status(thm)],[161]) ).
tff(774,plain,
a6 = product(a6,a6),
inference(symmetry,[status(thm)],[160]) ).
tff(775,plain,
product(a13,a8) = product(product(product(a12,a3),product(a12,a3)),a8),
inference(transitivity,[status(thm)],[65,774,773,772,771]) ).
tff(776,plain,
product(product(product(product(a14,a3),product(a12,a3)),a8),product(a13,a8)) = product(product(product(product(a14,a3),product(a12,a3)),a8),product(product(product(a12,a3),product(a12,a3)),a8)),
inference(monotonicity,[status(thm)],[775]) ).
tff(777,plain,
product(product(product(a14,a3),product(a12,a3)),a8) = product(product(a15,a13),a8),
inference(monotonicity,[status(thm)],[763]) ).
tff(778,plain,
product(product(a15,a13),a8) = product(product(product(a14,a3),product(a12,a3)),a8),
inference(symmetry,[status(thm)],[777]) ).
tff(779,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a15,a13),a8) = product(product(a15,a8),product(a13,a8)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(780,plain,
product(product(a15,a13),a8) = product(product(a15,a8),product(a13,a8)),
inference(unit_resolution,[status(thm)],[779,22]) ).
tff(781,plain,
product(product(a15,a8),product(a13,a8)) = product(product(a15,a13),a8),
inference(symmetry,[status(thm)],[780]) ).
tff(782,plain,
product(a4,a6) = product(product(product(a14,a3),product(a12,a3)),a8),
inference(transitivity,[status(thm)],[122,781,778]) ).
tff(783,plain,
product(product(a4,a6),a6) = product(product(product(product(a14,a3),product(a12,a3)),a8),product(a13,a8)),
inference(monotonicity,[status(thm)],[782,66]) ).
tff(784,plain,
product(a6,product(product(a1,a2),product(a1,a2))) = product(a4,a6),
inference(transitivity,[status(thm)],[68,103,106,116,453]) ).
tff(785,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),a6) = product(product(a4,a6),a6),
inference(monotonicity,[status(thm)],[784]) ).
tff(786,plain,
product(product(a6,a7),product(a7,a7)) = a6,
inference(transitivity,[status(thm)],[348,371,100]) ).
tff(787,plain,
product(product(a12,a7),product(a12,a7)) = product(a6,product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[547,544,69]) ).
tff(788,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a7,a7))) = product(product(a6,product(product(a1,a2),product(a1,a2))),a6),
inference(monotonicity,[status(thm)],[787,786]) ).
tff(789,plain,
product(product(product(a6,a7),product(a6,a7)),a7) = product(product(a6,a7),product(a7,a7)),
inference(symmetry,[status(thm)],[348]) ).
tff(790,plain,
product(product(a14,a7),product(a12,a7)) = product(product(a14,a12),a7),
inference(symmetry,[status(thm)],[73]) ).
tff(791,plain,
product(a14,a7) = product(a14,product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[45]) ).
tff(792,plain,
product(a14,product(product(a5,a6),product(a5,a6))) = product(a14,a7),
inference(symmetry,[status(thm)],[791]) ).
tff(793,plain,
a14 = product(a14,a14),
inference(symmetry,[status(thm)],[9]) ).
tff(794,plain,
a14 = product(product(a2,a12),product(a2,a12)),
inference(transitivity,[status(thm)],[793,14]) ).
tff(795,plain,
product(a14,product(product(a5,a6),product(a5,a6))) = product(product(product(a2,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[794]) ).
tff(796,plain,
product(product(product(a2,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))) = product(a14,product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[795]) ).
tff(797,plain,
product(product(a14,a14),a7) = product(product(product(a2,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[14,45]) ).
tff(798,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a14,a14),a7) = product(product(a14,a7),product(a14,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(799,plain,
product(product(a14,a14),a7) = product(product(a14,a7),product(a14,a7)),
inference(unit_resolution,[status(thm)],[798,22]) ).
tff(800,plain,
product(product(a14,a7),product(a14,a7)) = product(product(a14,a14),a7),
inference(symmetry,[status(thm)],[799]) ).
tff(801,plain,
product(product(a14,a7),product(a14,a7)) = product(a14,a7),
inference(transitivity,[status(thm)],[800,797,796,792]) ).
tff(802,plain,
product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))) = product(product(a14,a7),product(a12,a7)),
inference(monotonicity,[status(thm)],[801,324]) ).
tff(803,plain,
product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))) = product(product(a6,a7),product(a7,a7)),
inference(transitivity,[status(thm)],[802,790,74,94,789]) ).
tff(804,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))) = product(product(a12,a7),product(a12,a7)),
inference(monotonicity,[status(thm)],[324,324]) ).
tff(805,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))),product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7)))) = product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a7,a7))),
inference(monotonicity,[status(thm)],[804,803]) ).
tff(806,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a12,a7),product(a12,a7)),product(product(a14,a7),product(a14,a7))),product(product(a12,a7),product(a12,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))),product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(807,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a14,a7),product(a14,a7))),product(product(a12,a7),product(a12,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))),product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7)))),
inference(unit_resolution,[status(thm)],[806,22]) ).
tff(808,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a14,a7),product(a14,a7))) = product(product(a12,a7),product(a14,a7)),
inference(monotonicity,[status(thm)],[324,801]) ).
tff(809,plain,
product(product(a12,a7),product(a14,a7)) = product(product(product(a12,a7),product(a12,a7)),product(product(a14,a7),product(a14,a7))),
inference(symmetry,[status(thm)],[808]) ).
tff(810,plain,
product(product(product(a12,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a14,a7),product(a14,a7))),product(product(a12,a7),product(a12,a7))),
inference(monotonicity,[status(thm)],[809]) ).
tff(811,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a12,a14),a7) = product(product(a12,a7),product(a14,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(812,plain,
product(product(a12,a14),a7) = product(product(a12,a7),product(a14,a7)),
inference(unit_resolution,[status(thm)],[811,22]) ).
tff(813,plain,
product(product(a12,a14),a7) = product(product(a12,a14),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[45]) ).
tff(814,plain,
product(product(a12,a14),product(product(a5,a6),product(a5,a6))) = product(product(a12,a14),a7),
inference(symmetry,[status(thm)],[813]) ).
tff(815,plain,
product(a12,a14) = product(product(a12,a12),product(a2,a12)),
inference(monotonicity,[status(thm)],[193,13]) ).
tff(816,plain,
product(product(a12,a12),product(a2,a12)) = product(a12,a14),
inference(symmetry,[status(thm)],[815]) ).
tff(817,plain,
product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))) = product(product(a12,a14),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[816]) ).
tff(818,plain,
product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))) = product(product(a12,a7),product(a14,a7)),
inference(transitivity,[status(thm)],[817,814,812]) ).
tff(819,plain,
product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a12,a7))) = product(product(product(a12,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))),
inference(monotonicity,[status(thm)],[818]) ).
tff(820,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))) = product(product(a12,a7),product(a12,a7)),
inference(transitivity,[status(thm)],[319,322]) ).
tff(821,plain,
product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a12,a7))),
inference(monotonicity,[status(thm)],[820]) ).
tff(822,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(823,plain,
product(product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[822,22]) ).
tff(824,plain,
product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))) = product(product(a12,a14),product(product(a10,a11),product(a10,a11))),
inference(monotonicity,[status(thm)],[816]) ).
tff(825,plain,
product(product(a12,a14),product(product(a10,a11),product(a10,a11))) = product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[824]) ).
tff(826,plain,
product(product(a12,a14),product(product(a10,a11),product(a10,a11))) = product(product(a12,a14),a12),
inference(monotonicity,[status(thm)],[341]) ).
tff(827,plain,
product(product(a12,a14),a12) = product(product(a12,a14),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[826]) ).
tff(828,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a12,a14),a12) = product(product(a12,a12),product(a14,a12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(829,plain,
product(product(a12,a14),a12) = product(product(a12,a12),product(a14,a12)),
inference(unit_resolution,[status(thm)],[828,22]) ).
tff(830,plain,
product(product(a12,a12),product(a14,a12)) = product(product(a12,a14),a12),
inference(symmetry,[status(thm)],[829]) ).
tff(831,plain,
product(product(a12,a12),product(a14,a12)) = product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),
inference(transitivity,[status(thm)],[830,827,825]) ).
tff(832,plain,
product(product(product(a12,a12),product(a14,a12)),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[831]) ).
tff(833,plain,
product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7))) = product(product(a5,a6),product(a5,a6)),
inference(transitivity,[status(thm)],[198,222,225,239,251,142,145]) ).
tff(834,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))) = product(product(a12,a12),product(a14,a12)),
inference(transitivity,[status(thm)],[604,563]) ).
tff(835,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a12,a12),product(a14,a12)),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[834,833]) ).
tff(836,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a10,a11),product(a10,a11)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(837,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[836,22]) ).
tff(838,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a9,a1),product(a9,a1))) = product(product(a10,a11),a10),
inference(monotonicity,[status(thm)],[616,272]) ).
tff(839,plain,
product(product(a10,a11),a10) = product(product(product(a10,a11),product(a10,a11)),product(product(a9,a1),product(a9,a1))),
inference(symmetry,[status(thm)],[838]) ).
tff(840,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a10,a11),a10) = product(product(a10,a10),product(a11,a10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(841,plain,
product(product(a10,a11),a10) = product(product(a10,a10),product(a11,a10)),
inference(unit_resolution,[status(thm)],[840,22]) ).
tff(842,plain,
product(product(a10,a10),product(a11,a10)) = product(product(a10,a11),a10),
inference(symmetry,[status(thm)],[841]) ).
tff(843,plain,
product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10))) = product(product(product(a10,a11),product(a10,a11)),product(product(a9,a1),product(a9,a1))),
inference(transitivity,[status(thm)],[671,842,839]) ).
tff(844,plain,
product(product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[843]) ).
tff(845,plain,
a9 = product(a9,a9),
inference(symmetry,[status(thm)],[235]) ).
tff(846,plain,
product(a8,a2) = product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10))),
inference(transitivity,[status(thm)],[212,845,214,677,674,672]) ).
tff(847,plain,
product(product(a8,a2),product(a2,a2)) = product(product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[846,79]) ).
tff(848,plain,
product(a8,a8) = product(a7,a3),
inference(transitivity,[status(thm)],[128,126]) ).
tff(849,plain,
product(product(a8,a8),product(a8,a8)) = product(product(a7,a3),product(a7,a3)),
inference(monotonicity,[status(thm)],[848,848]) ).
tff(850,plain,
product(product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))) = product(product(a8,a2),product(a2,a2)),
inference(symmetry,[status(thm)],[847]) ).
tff(851,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[844]) ).
tff(852,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a9,a1),product(a9,a1))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[837]) ).
tff(853,plain,
product(product(product(a12,a12),product(a14,a12)),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),product(product(product(a9,a1),product(a9,a1)),product(product(a6,a7),product(a6,a7)))),
inference(symmetry,[status(thm)],[835]) ).
tff(854,plain,
product(product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),product(product(a5,a6),product(a5,a6))) = product(product(product(a12,a12),product(a14,a12)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[832]) ).
tff(855,plain,
product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[823]) ).
tff(856,plain,
product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a12,a7))) = product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[821]) ).
tff(857,plain,
product(product(product(a12,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))) = product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a12,a7))),
inference(symmetry,[status(thm)],[819]) ).
tff(858,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a14,a7),product(a14,a7))),product(product(a12,a7),product(a12,a7))) = product(product(product(a12,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))),
inference(symmetry,[status(thm)],[810]) ).
tff(859,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))),product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7)))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a14,a7),product(a14,a7))),product(product(a12,a7),product(a12,a7))),
inference(symmetry,[status(thm)],[807]) ).
tff(860,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a7,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))),product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7)))),
inference(symmetry,[status(thm)],[805]) ).
tff(861,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),a6) = product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a7,a7))),
inference(symmetry,[status(thm)],[788]) ).
tff(862,plain,
product(product(a4,a6),a6) = product(product(a6,product(product(a1,a2),product(a1,a2))),a6),
inference(symmetry,[status(thm)],[785]) ).
tff(863,plain,
product(product(product(product(a14,a3),product(a12,a3)),a8),product(a13,a8)) = product(product(a4,a6),a6),
inference(symmetry,[status(thm)],[783]) ).
tff(864,plain,
product(product(product(product(a14,a3),product(a12,a3)),a8),product(product(product(a12,a3),product(a12,a3)),a8)) = product(product(product(product(a14,a3),product(a12,a3)),a8),product(a13,a8)),
inference(symmetry,[status(thm)],[776]) ).
tff(865,plain,
product(product(a15,a15),a8) = product(product(product(product(a14,a3),product(a12,a3)),product(product(a12,a3),product(a12,a3))),a8),
inference(symmetry,[status(thm)],[766]) ).
tff(866,plain,
product(product(a15,a8),product(a15,a8)) = product(product(a15,a15),a8),
inference(symmetry,[status(thm)],[740]) ).
tff(867,plain,
product(a15,a8) = product(a8,a8),
inference(transitivity,[status(thm)],[120,730,729,866,865,768,864,863,862,861,860,859,858,857,856,855,854,853,852,851,850,249,243,130]) ).
tff(868,plain,
product(product(a15,a8),product(a8,a8)) = product(product(a8,a8),product(a8,a8)),
inference(monotonicity,[status(thm)],[867]) ).
tff(869,plain,
product(product(a15,a8),product(a15,a8)) = product(a4,a4),
inference(symmetry,[status(thm)],[729]) ).
tff(870,plain,
product(product(product(a14,a3),product(a14,a3)),product(product(a7,a3),product(a7,a3))) = product(product(a15,a15),a8),
inference(monotonicity,[status(thm)],[743,164]) ).
tff(871,plain,
product(product(product(a14,a3),product(a14,a3)),product(product(a7,a3),product(a7,a3))) = product(a15,a8),
inference(transitivity,[status(thm)],[870,740,869,661,121]) ).
tff(872,plain,
product(product(product(product(a14,a3),product(a14,a3)),product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))) = product(product(a15,a8),product(a8,a8)),
inference(monotonicity,[status(thm)],[871,130]) ).
tff(873,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a14,a3),product(a14,a3)),product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))) = product(product(a14,a3),product(a14,a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(874,plain,
product(product(product(product(a14,a3),product(a14,a3)),product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))) = product(product(a14,a3),product(a14,a3)),
inference(unit_resolution,[status(thm)],[873,89]) ).
tff(875,plain,
product(product(a14,a3),product(a14,a3)) = product(product(product(product(a14,a3),product(a14,a3)),product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))),
inference(symmetry,[status(thm)],[874]) ).
tff(876,plain,
( ~ ! [X: $i] : ( product(X,X) = X )
| ( product(a15,a15) = a15 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(877,plain,
product(a15,a15) = a15,
inference(unit_resolution,[status(thm)],[876,7]) ).
tff(878,plain,
a15 = product(a15,a15),
inference(symmetry,[status(thm)],[877]) ).
tff(879,plain,
a15 = a14,
inference(transitivity,[status(thm)],[878,742,875,872,868,849,688,248,847,844,837,835,832,823,821,819,810,807,805,788,785,783,776,769,766,740,728,726,738,720,718,711,708,704,702,686,683,632,635,637,639,643,646,664,659,657,654,538,535,650,630,626,623,488,146,143,252,240,226,223,620,610,608,601,597,561,558,520,517,515,513,510,506,457,452,450,444,346,331,328,316,304,190,187,172,151,149,301,299,293,196,24,15,9]) ).
tff(880,plain,
product(a8,a8) = product(a15,a8),
inference(transitivity,[status(thm)],[129,688,248,847,844,837,835,832,823,821,819,810,807,805,788,785,783,776,769,766,740,869,661,121]) ).
tff(881,plain,
product(product(a13,a8),product(a8,a8)) = product(product(a13,a8),product(a15,a8)),
inference(monotonicity,[status(thm)],[880]) ).
tff(882,plain,
product(product(a13,a8),product(a15,a8)) = product(product(a13,a8),product(a8,a8)),
inference(symmetry,[status(thm)],[881]) ).
tff(883,plain,
product(product(a13,a8),product(a15,a8)) = product(product(product(a12,a7),a3),product(product(a14,a7),a3)),
inference(monotonicity,[status(thm)],[389,727]) ).
tff(884,plain,
product(product(product(a12,a7),a3),product(product(a14,a7),a3)) = product(product(a13,a8),product(a15,a8)),
inference(symmetry,[status(thm)],[883]) ).
tff(885,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(a12,a7),product(a14,a7)),a3) = product(product(product(a12,a7),a3),product(product(a14,a7),a3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(886,plain,
product(product(product(a12,a7),product(a14,a7)),a3) = product(product(product(a12,a7),a3),product(product(a14,a7),a3)),
inference(unit_resolution,[status(thm)],[885,22]) ).
tff(887,plain,
a3 = product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[241,50,255,632,635,637,639,706]) ).
tff(888,plain,
product(product(a12,a14),product(product(a5,a6),product(a5,a6))) = product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[817]) ).
tff(889,plain,
product(product(a12,a7),product(a14,a7)) = product(product(a12,a14),a7),
inference(symmetry,[status(thm)],[812]) ).
tff(890,plain,
product(product(a12,a7),product(a14,a7)) = product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[889,813,888]) ).
tff(891,plain,
product(product(product(a12,a7),product(a14,a7)),a3) = product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[890,887]) ).
tff(892,plain,
product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a12,a7),product(a14,a7)),a3),
inference(symmetry,[status(thm)],[891]) ).
tff(893,plain,
product(product(product(a12,a7),a3),product(a3,a3)) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[544]) ).
tff(894,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))) = product(product(a12,a7),product(a12,a7)),
inference(transitivity,[status(thm)],[705,643,646,117,107,104,893,546]) ).
tff(895,plain,
product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a12,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))),
inference(monotonicity,[status(thm)],[818,894]) ).
tff(896,plain,
product(product(product(a12,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))) = product(product(product(product(a12,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[895]) ).
tff(897,plain,
product(product(product(a14,a7),a3),product(product(a14,a7),a3)) = product(product(a15,a8),product(a15,a8)),
inference(symmetry,[status(thm)],[728]) ).
tff(898,plain,
product(product(a4,product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(product(a14,a7),product(a14,a7)),a3),
inference(symmetry,[status(thm)],[738]) ).
tff(899,plain,
product(product(product(product(a14,a7),a3),product(a3,a3)),product(product(a15,a8),product(a13,a8))) = product(product(a4,product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[720]) ).
tff(900,plain,
product(product(a4,product(product(a1,a2),product(a1,a2))),product(a6,product(product(a1,a2),product(a1,a2)))) = product(product(product(product(a14,a7),a3),product(a3,a3)),product(product(a15,a8),product(a13,a8))),
inference(symmetry,[status(thm)],[718]) ).
tff(901,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a1,a2),product(a1,a2))) = product(product(a4,a6),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[708]) ).
tff(902,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2)))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[704]) ).
tff(903,plain,
product(product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a6,a7),product(a6,a7))),product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),product(product(product(a5,a6),product(a5,a6)),product(product(a1,a2),product(a1,a2)))),
inference(symmetry,[status(thm)],[702]) ).
tff(904,plain,
product(product(a1,a1),a2) = product(product(product(a11,product(product(a11,a10),product(a11,a10))),product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[683]) ).
tff(905,plain,
product(product(a4,a6),product(a4,a6)) = product(product(a4,a4),a6),
inference(symmetry,[status(thm)],[659]) ).
tff(906,plain,
product(product(a5,a6),product(a5,a6)) = product(product(a5,a5),a6),
inference(symmetry,[status(thm)],[488]) ).
tff(907,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7))),product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[610]) ).
tff(908,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a12,a7),product(a12,a7))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[517]) ).
tff(909,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a10,a11),product(a10,a11))),product(product(product(a5,a6),product(a5,a6)),product(product(a10,a11),product(a10,a11)))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[452]) ).
tff(910,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2)))) = product(product(a6,product(product(a7,a3),product(a7,a3))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[151]) ).
tff(911,plain,
product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) = product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[301]) ).
tff(912,plain,
product(product(a2,a12),product(a2,a12)) = product(product(a2,a2),a12),
inference(symmetry,[status(thm)],[24]) ).
tff(913,plain,
a14 = a13,
inference(transitivity,[status(thm)],[793,14,912,195,292,298,911,148,910,171,186,189,303,315,327,330,345,443,449,909,456,505,509,512,514,908,519,557,560,596,600,607,907,619,222,225,239,251,142,145,906,622,625,629,649,534,537,653,656,905,663,647,644,640,638,636,633,904,685,903,902,901,710,900,899,898,725,897,866,865,768,864,863,862,861,860,859,858,896,892,886,884,882,168,158,156,154]) ).
tff(914,plain,
product(product(product(a12,a7),a3),product(product(a14,a7),a3)) = product(product(product(a12,a7),product(a14,a7)),a3),
inference(symmetry,[status(thm)],[886]) ).
tff(915,plain,
product(product(a12,a3),product(a12,a3)) = product(product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a7,a3))),product(product(a7,a3),product(a7,a3))),
inference(symmetry,[status(thm)],[158]) ).
tff(916,plain,
a13 = a12,
inference(transitivity,[status(thm)],[184,155,915,167,881,883,914,891,895,810,807,805,788,785,783,776,769,766,740,728,726,738,720,718,711,708,704,702,686,683,632,635,637,639,643,646,664,659,657,654,538,535,650,630,626,623,488,146,143,252,240,226,223,620,610,608,601,597,561,558,520,517,515,513,510,506,457,452,450,444,346,331,328,316,304,178,192]) ).
tff(917,plain,
a4 = product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[730,729,728,726,723]) ).
tff(918,plain,
product(a4,a7) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[917,45]) ).
tff(919,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(a4,a7),
inference(symmetry,[status(thm)],[918]) ).
tff(920,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(921,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[920,22]) ).
tff(922,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[921]) ).
tff(923,plain,
product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))) = product(product(a14,a7),product(a7,a7)),
inference(monotonicity,[status(thm)],[801,76]) ).
tff(924,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a14,a7),product(a7,a7)),product(a3,product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[923,294]) ).
tff(925,plain,
product(product(product(a14,a7),product(a7,a7)),product(a3,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[924]) ).
tff(926,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a2,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a2,a12),product(a2,a12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(927,plain,
product(product(product(product(a2,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a2,a12),product(a2,a12)),
inference(unit_resolution,[status(thm)],[926,89]) ).
tff(928,plain,
product(a14,a7) = product(product(product(a2,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[791,795]) ).
tff(929,plain,
product(product(a14,a7),product(a7,a7)) = product(product(product(product(a2,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[928,41]) ).
tff(930,plain,
product(product(a14,a7),product(a7,a7)) = product(product(a2,a12),product(a2,a12)),
inference(transitivity,[status(thm)],[929,927]) ).
tff(931,plain,
product(product(product(a14,a7),product(a7,a7)),product(a3,product(product(a5,a6),product(a5,a6)))) = product(product(product(a2,a12),product(a2,a12)),product(a3,product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[930]) ).
tff(932,plain,
product(product(product(a2,a12),product(a2,a12)),product(a3,product(product(a5,a6),product(a5,a6)))) = product(product(product(a14,a7),product(a7,a7)),product(a3,product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[931]) ).
tff(933,plain,
product(product(product(a2,a12),product(a2,a12)),product(a3,product(product(a5,a6),product(a5,a6)))) = product(product(product(a2,a12),product(a2,a12)),product(product(a4,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[599]) ).
tff(934,plain,
product(product(product(a2,a12),product(a2,a12)),product(product(a4,a7),product(a6,a7))) = product(product(product(a2,a12),product(a2,a12)),product(a3,product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[933]) ).
tff(935,plain,
product(product(product(product(a2,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a14,a7),product(a7,a7)),
inference(symmetry,[status(thm)],[929]) ).
tff(936,plain,
product(product(a2,a12),product(a2,a12)) = product(product(product(product(a2,a12),product(a2,a12)),product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[927]) ).
tff(937,plain,
product(product(a2,a12),product(a2,a12)) = product(product(a14,a7),product(a7,a7)),
inference(transitivity,[status(thm)],[936,935]) ).
tff(938,plain,
product(product(product(a2,a12),product(a2,a12)),product(product(a4,a7),product(a6,a7))) = product(product(product(a14,a7),product(a7,a7)),product(product(a4,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[937]) ).
tff(939,plain,
product(product(product(a14,a7),product(a7,a7)),product(product(a4,a7),product(a6,a7))) = product(product(product(a2,a12),product(a2,a12)),product(product(a4,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[938]) ).
tff(940,plain,
product(product(a4,a7),product(a6,a7)) = product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[585,641]) ).
tff(941,plain,
product(product(a14,a7),product(a7,a7)) = product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[923]) ).
tff(942,plain,
product(product(product(a14,a7),product(a7,a7)),product(product(a4,a7),product(a6,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[941,940]) ).
tff(943,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a14,a7),product(a7,a7)),product(product(a4,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[942]) ).
tff(944,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a14,a7),product(a14,a7)),product(product(a15,a8),product(a13,a8))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(945,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a15,a8),product(a13,a8))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[944,22]) ).
tff(946,plain,
a7 = product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[44,41,146,143,133]) ).
tff(947,plain,
product(a12,a3) = product(product(a12,a3),product(a12,a3)),
inference(transitivity,[status(thm)],[60,184,155]) ).
tff(948,plain,
product(product(a14,a3),product(a12,a3)) = product(a15,product(product(a12,a3),product(a12,a3))),
inference(monotonicity,[status(thm)],[111,947]) ).
tff(949,plain,
product(a15,product(product(a12,a3),product(a12,a3))) = product(product(a14,a3),product(a12,a3)),
inference(symmetry,[status(thm)],[948]) ).
tff(950,plain,
a15 = product(product(a14,a3),product(a14,a3)),
inference(transitivity,[status(thm)],[878,742]) ).
tff(951,plain,
product(a15,product(product(a12,a3),product(a12,a3))) = product(product(product(a14,a3),product(a14,a3)),product(product(a12,a3),product(a12,a3))),
inference(monotonicity,[status(thm)],[950]) ).
tff(952,plain,
product(product(product(a14,a3),product(a14,a3)),product(product(a12,a3),product(a12,a3))) = product(a15,product(product(a12,a3),product(a12,a3))),
inference(symmetry,[status(thm)],[951]) ).
tff(953,plain,
product(product(product(a14,a3),product(a14,a3)),product(product(a12,a3),product(a12,a3))) = product(product(a15,a15),a13),
inference(monotonicity,[status(thm)],[743,386]) ).
tff(954,plain,
product(product(a15,a15),a13) = product(product(product(a14,a3),product(a14,a3)),product(product(a12,a3),product(a12,a3))),
inference(symmetry,[status(thm)],[953]) ).
tff(955,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a15,a15),a13) = product(product(a15,a13),product(a15,a13)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(956,plain,
product(product(a15,a15),a13) = product(product(a15,a13),product(a15,a13)),
inference(unit_resolution,[status(thm)],[955,22]) ).
tff(957,plain,
product(product(a15,a13),product(a15,a13)) = product(product(a15,a15),a13),
inference(symmetry,[status(thm)],[956]) ).
tff(958,plain,
product(product(a15,a13),product(a15,a13)) = product(product(a14,a12),a3),
inference(transitivity,[status(thm)],[957,954,952,949,756]) ).
tff(959,plain,
product(product(product(a15,a13),product(a15,a13)),product(product(a1,a2),product(a1,a2))) = product(product(product(a14,a12),a3),product(a3,a3)),
inference(monotonicity,[status(thm)],[958,51]) ).
tff(960,plain,
product(product(product(a14,a12),a3),product(a3,a3)) = product(product(product(a15,a13),product(a15,a13)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[959]) ).
tff(961,plain,
product(product(product(a6,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))) = product(product(a2,a2),product(a1,a2)),
inference(monotonicity,[status(thm)],[78,699]) ).
tff(962,plain,
product(product(a2,a2),product(a1,a2)) = product(product(product(a6,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[961]) ).
tff(963,plain,
product(product(a2,a12),a12) = product(a14,a12),
inference(symmetry,[status(thm)],[92]) ).
tff(964,plain,
a2 = product(product(a2,a12),a12),
inference(symmetry,[status(thm)],[91]) ).
tff(965,plain,
product(a2,a2) = product(a14,a12),
inference(transitivity,[status(thm)],[81,964,963]) ).
tff(966,plain,
product(product(a2,a2),product(a1,a2)) = product(product(a14,a12),a3),
inference(monotonicity,[status(thm)],[965,48]) ).
tff(967,plain,
product(product(a14,a12),a3) = product(product(a2,a2),product(a1,a2)),
inference(symmetry,[status(thm)],[966]) ).
tff(968,plain,
product(product(a14,a12),a3) = product(product(product(a6,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[967,962]) ).
tff(969,plain,
product(product(product(a14,a12),a3),product(a3,a3)) = product(product(product(product(a6,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[968,50]) ).
tff(970,plain,
product(product(product(product(a6,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(product(a14,a12),a3),product(a3,a3)),
inference(symmetry,[status(thm)],[969]) ).
tff(971,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a6,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a6,a7),product(a6,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(972,plain,
product(product(product(product(a6,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(a6,a7),product(a6,a7)),
inference(unit_resolution,[status(thm)],[971,89]) ).
tff(973,plain,
product(product(a6,a7),product(a6,a7)) = product(product(product(product(a6,a7),product(a6,a7)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[972]) ).
tff(974,plain,
product(product(a6,a7),product(a6,a7)) = product(product(product(a15,a13),product(a15,a13)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[973,970,960]) ).
tff(975,plain,
product(product(product(a6,a7),product(a6,a7)),a7) = product(product(product(product(a15,a13),product(a15,a13)),product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2)))),
inference(monotonicity,[status(thm)],[974,946]) ).
tff(976,plain,
product(product(product(product(a15,a13),product(a15,a13)),product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2)))) = product(product(product(a6,a7),product(a6,a7)),a7),
inference(symmetry,[status(thm)],[975]) ).
tff(977,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a15,a13),product(a15,a13)),product(product(a7,a3),product(a7,a3))),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a15,a13),product(a15,a13)),product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(978,plain,
product(product(product(product(a15,a13),product(a15,a13)),product(product(a7,a3),product(a7,a3))),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a15,a13),product(a15,a13)),product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2)))),
inference(unit_resolution,[status(thm)],[977,22]) ).
tff(979,plain,
product(product(product(a14,a3),product(a12,a3)),a8) = product(a4,a6),
inference(transitivity,[status(thm)],[777,780,453]) ).
tff(980,plain,
product(product(product(product(a14,a3),product(a12,a3)),a8),product(product(product(a14,a3),product(a12,a3)),a8)) = product(product(a4,a6),product(a4,a6)),
inference(monotonicity,[status(thm)],[979,979]) ).
tff(981,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a14,a3),product(a12,a3)),product(product(a14,a3),product(a12,a3))),a8) = product(product(product(product(a14,a3),product(a12,a3)),a8),product(product(product(a14,a3),product(a12,a3)),a8)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(982,plain,
product(product(product(product(a14,a3),product(a12,a3)),product(product(a14,a3),product(a12,a3))),a8) = product(product(product(product(a14,a3),product(a12,a3)),a8),product(product(product(a14,a3),product(a12,a3)),a8)),
inference(unit_resolution,[status(thm)],[981,22]) ).
tff(983,plain,
product(product(product(a14,a3),product(a12,a3)),product(product(a14,a3),product(a12,a3))) = product(product(a15,a13),product(a15,a13)),
inference(monotonicity,[status(thm)],[763,763]) ).
tff(984,plain,
product(product(a15,a13),product(a15,a13)) = product(product(product(a14,a3),product(a12,a3)),product(product(a14,a3),product(a12,a3))),
inference(symmetry,[status(thm)],[983]) ).
tff(985,plain,
product(product(product(a15,a13),product(a15,a13)),product(product(a7,a3),product(a7,a3))) = product(product(product(product(a14,a3),product(a12,a3)),product(product(a14,a3),product(a12,a3))),a8),
inference(monotonicity,[status(thm)],[984,164]) ).
tff(986,plain,
product(product(product(a15,a13),product(a15,a13)),product(product(a7,a3),product(a7,a3))) = product(a4,a6),
inference(transitivity,[status(thm)],[985,982,980,905,663,453]) ).
tff(987,plain,
product(product(product(product(a15,a13),product(a15,a13)),product(product(a7,a3),product(a7,a3))),product(product(a1,a2),product(a1,a2))) = product(product(a4,a6),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[986]) ).
tff(988,plain,
product(product(a4,a6),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a15,a13),product(a15,a13)),product(product(a7,a3),product(a7,a3))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[987]) ).
tff(989,plain,
product(product(a14,a7),product(a14,a7)) = product(product(product(a14,a7),a3),product(a3,a3)),
inference(transitivity,[status(thm)],[736,733]) ).
tff(990,plain,
product(product(product(a14,a7),product(a14,a7)),product(product(a15,a8),product(a13,a8))) = product(product(product(product(a14,a7),a3),product(a3,a3)),product(product(a15,a8),product(a13,a8))),
inference(monotonicity,[status(thm)],[989]) ).
tff(991,plain,
product(product(product(a14,a7),product(a14,a7)),product(product(a15,a8),product(a13,a8))) = a6,
inference(transitivity,[status(thm)],[990,718,711,988,978,976,371,100]) ).
tff(992,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a15,a8),product(a13,a8))),product(product(a5,a6),product(a5,a6))) = product(a6,a7),
inference(monotonicity,[status(thm)],[991,77]) ).
tff(993,plain,
product(a6,a7) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a15,a8),product(a13,a8))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[992]) ).
tff(994,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a1,a2),product(a1,a2))) = product(product(a4,a6),product(product(a1,a2),product(a1,a2))),
inference(monotonicity,[status(thm)],[453]) ).
tff(995,plain,
product(product(a4,a6),product(product(a1,a2),product(a1,a2))) = product(product(product(a15,a8),product(a13,a8)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[994]) ).
tff(996,plain,
product(product(product(product(a15,a13),product(a15,a13)),product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2)))) = product(product(product(product(a15,a13),product(a15,a13)),product(product(a7,a3),product(a7,a3))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[978]) ).
tff(997,plain,
a6 = product(product(product(a15,a8),product(a13,a8)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[101,98,975,996,987,995]) ).
tff(998,plain,
product(a6,a7) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[997,45]) ).
tff(999,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(a6,a7),
inference(symmetry,[status(thm)],[998]) ).
tff(1000,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a15,a8),product(a13,a8)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1001,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1000,22]) ).
tff(1002,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a1,a2),product(a1,a2))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1001]) ).
tff(1003,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a4,a7),product(a6,a7)),product(a3,product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[455,294]) ).
tff(1004,plain,
product(product(product(a4,a7),product(a6,a7)),product(a3,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[1003]) ).
tff(1005,plain,
product(a3,product(product(a5,a6),product(a5,a6))) = product(a11,a2),
inference(transitivity,[status(thm)],[257,598,284,289,34]) ).
tff(1006,plain,
product(product(product(a4,a7),product(a6,a7)),product(a3,product(product(a5,a6),product(a5,a6)))) = product(product(a11,a2),product(a11,a2)),
inference(monotonicity,[status(thm)],[34,1005]) ).
tff(1007,plain,
product(product(a11,a2),product(a11,a2)) = product(product(product(a4,a7),product(a6,a7)),product(a3,product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[1006]) ).
tff(1008,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a11,a11),a2) = product(product(a11,a2),product(a11,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1009,plain,
product(product(a11,a11),a2) = product(product(a11,a2),product(a11,a2)),
inference(unit_resolution,[status(thm)],[1008,22]) ).
tff(1010,plain,
a12 = a11,
inference(transitivity,[status(thm)],[193,177,190,187,172,151,149,125,36,290,1009,1007,1004,1002,999,993,945,943,939,934,932,925,922,919,31]) ).
tff(1011,plain,
product(a7,product(product(a15,a8),product(a13,a8))) = product(product(product(a1,a2),product(a1,a2)),a6),
inference(transitivity,[status(thm)],[592,532,529,522]) ).
tff(1012,plain,
product(product(a7,product(product(a15,a8),product(a13,a8))),a7) = product(product(product(product(a1,a2),product(a1,a2)),a6),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1011,45]) ).
tff(1013,plain,
product(product(product(product(a1,a2),product(a1,a2)),a6),product(product(a5,a6),product(a5,a6))) = product(product(a7,product(product(a15,a8),product(a13,a8))),a7),
inference(symmetry,[status(thm)],[1012]) ).
tff(1014,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(a1,a2)),a6),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1015,plain,
product(product(product(product(a1,a2),product(a1,a2)),a6),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1014,22]) ).
tff(1016,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a1,a2),product(a1,a2)),a6),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1015]) ).
tff(1017,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[97]) ).
tff(1018,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[1017]) ).
tff(1019,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(a1,a2)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1020,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[1019,22]) ).
tff(1021,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1020]) ).
tff(1022,plain,
product(product(a7,a7),product(a6,a7)) = product(a7,product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[43,347]) ).
tff(1023,plain,
product(a7,product(product(a6,a7),product(a6,a7))) = product(product(a7,a7),product(a6,a7)),
inference(symmetry,[status(thm)],[1022]) ).
tff(1024,plain,
product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7))) = product(a7,product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[77]) ).
tff(1025,plain,
product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7))) = product(product(a7,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[1024,1023]) ).
tff(1026,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7))) = product(product(a1,a2),product(a2,a2)),
inference(monotonicity,[status(thm)],[699,78]) ).
tff(1027,plain,
product(product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a1,a2),product(a2,a2)),product(product(a7,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1026,1025]) ).
tff(1028,plain,
product(product(product(a1,a2),product(a2,a2)),product(product(a7,a7),product(a6,a7))) = product(product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))),
inference(symmetry,[status(thm)],[1027]) ).
tff(1029,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(a6,a7),product(a6,a7))) = product(product(a11,a10),product(a11,a10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1030,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(a6,a7),product(a6,a7))) = product(product(a11,a10),product(a11,a10)),
inference(unit_resolution,[status(thm)],[1029,89]) ).
tff(1031,plain,
product(a1,a2) = product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),
inference(transitivity,[status(thm)],[48,241,50,255,254]) ).
tff(1032,plain,
product(product(a1,a2),product(a2,a2)) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1031,79]) ).
tff(1033,plain,
product(product(a1,a2),product(a2,a2)) = a1,
inference(transitivity,[status(thm)],[1032,1030,208,202]) ).
tff(1034,plain,
product(product(product(a8,a2),product(a8,a2)),product(product(a1,a2),product(a2,a2))) = product(product(a9,a9),a1),
inference(monotonicity,[status(thm)],[215,1033]) ).
tff(1035,plain,
product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))) = product(product(a8,a2),product(a8,a2)),
inference(transitivity,[status(thm)],[246,245]) ).
tff(1036,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a8,a2),product(a8,a2)),product(product(a1,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[1035,1026]) ).
tff(1037,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1038,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[1037,22]) ).
tff(1039,plain,
product(a7,product(product(a6,a7),product(a6,a7))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[946]) ).
tff(1040,plain,
product(product(a7,a7),product(a6,a7)) = product(a10,a10),
inference(transitivity,[status(thm)],[1022,1039,1038,1036,1034,219,271]) ).
tff(1041,plain,
product(product(a1,a2),product(a2,a2)) = product(a11,a10),
inference(transitivity,[status(thm)],[1032,1030,208,202,206]) ).
tff(1042,plain,
product(product(product(a1,a2),product(a2,a2)),product(product(a7,a7),product(a6,a7))) = product(product(a11,a10),product(a10,a10)),
inference(monotonicity,[status(thm)],[1041,1040]) ).
tff(1043,plain,
product(product(a11,a10),product(a10,a10)) = product(product(product(a1,a2),product(a2,a2)),product(product(a7,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1042]) ).
tff(1044,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a9,a1),product(a9,a1))) = product(product(a11,a10),product(a10,a10)),
inference(symmetry,[status(thm)],[280]) ).
tff(1045,plain,
product(product(a4,a7),product(a4,a7)) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),product(product(a9,a1),product(a9,a1))),
inference(symmetry,[status(thm)],[263]) ).
tff(1046,plain,
product(a11,a11) = product(product(a4,a7),product(a4,a7)),
inference(symmetry,[status(thm)],[261]) ).
tff(1047,plain,
product(a11,a11) = product(product(a12,a12),product(a14,a12)),
inference(transitivity,[status(thm)],[1046,1045,1044,1043,1028,1021,1018,1016,1013,591,589,582,578,575,563]) ).
tff(1048,plain,
product(a10,a11) = product(product(a10,a11),product(a10,a11)),
inference(transitivity,[status(thm)],[175,193,177]) ).
tff(1049,plain,
product(product(a10,a11),product(a11,a11)) = product(product(product(a10,a11),product(a10,a11)),product(product(a12,a12),product(a14,a12))),
inference(monotonicity,[status(thm)],[1048,1047]) ).
tff(1050,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a12,a12),product(a14,a12))) = product(product(a10,a11),product(a11,a11)),
inference(symmetry,[status(thm)],[1049]) ).
tff(1051,plain,
product(product(a10,a11),product(a10,a11)) = product(product(a4,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[190,187,172,151,149,125,36]) ).
tff(1052,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a12,a12),product(a14,a12))) = product(product(product(a4,a7),product(a6,a7)),product(product(a12,a12),product(a14,a12))),
inference(monotonicity,[status(thm)],[1051]) ).
tff(1053,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a12,a12),product(a14,a12))) = product(product(product(a10,a11),product(a10,a11)),product(product(a12,a12),product(a14,a12))),
inference(symmetry,[status(thm)],[1052]) ).
tff(1054,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a12,a12),product(a14,a12))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7)))),
inference(monotonicity,[status(thm)],[603,606]) ).
tff(1055,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a4,a7),product(a6,a7)),product(product(a12,a12),product(a14,a12))),
inference(symmetry,[status(thm)],[1054]) ).
tff(1056,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a4,a7),product(a4,a7)),product(product(a10,a11),product(a10,a11))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1057,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a10,a11),product(a10,a11))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[1056,22]) ).
tff(1058,plain,
product(a1,a11) = product(product(a11,a10),a11),
inference(monotonicity,[status(thm)],[206]) ).
tff(1059,plain,
product(product(a11,a10),a11) = product(a1,a11),
inference(symmetry,[status(thm)],[1058]) ).
tff(1060,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a11,a10),a11) = product(product(a11,a11),product(a10,a11)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1061,plain,
product(product(a11,a10),a11) = product(product(a11,a11),product(a10,a11)),
inference(unit_resolution,[status(thm)],[1060,22]) ).
tff(1062,plain,
product(product(a11,a11),product(a10,a11)) = product(product(a11,a10),a11),
inference(symmetry,[status(thm)],[1061]) ).
tff(1063,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a10,a11),product(a10,a11))) = product(product(a11,a11),product(a10,a11)),
inference(monotonicity,[status(thm)],[261,616]) ).
tff(1064,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a10,a11),product(a10,a11))) = product(a1,a11),
inference(transitivity,[status(thm)],[1063,1062,1059]) ).
tff(1065,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a10,a11),product(a10,a11))),product(product(a6,a7),product(a6,a7))) = product(product(a1,a11),a2),
inference(monotonicity,[status(thm)],[1064,197]) ).
tff(1066,plain,
product(product(a1,a11),a2) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a10,a11),product(a10,a11))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1065]) ).
tff(1067,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,a11),a2) = product(product(a1,a2),product(a11,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1068,plain,
product(product(a1,a11),a2) = product(product(a1,a2),product(a11,a2)),
inference(unit_resolution,[status(thm)],[1067,22]) ).
tff(1069,plain,
product(product(a1,a2),product(a11,a2)) = product(product(a1,a11),a2),
inference(symmetry,[status(thm)],[1068]) ).
tff(1070,plain,
product(a1,a2) = product(product(a15,a8),product(a13,a8)),
inference(transitivity,[status(thm)],[48,241,50,255,632,635,637,639,643,646]) ).
tff(1071,plain,
product(product(a1,a2),product(a11,a2)) = product(product(product(a15,a8),product(a13,a8)),product(product(a4,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1070,33]) ).
tff(1072,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a4,a7),product(a6,a7))) = product(product(a1,a2),product(a11,a2)),
inference(symmetry,[status(thm)],[1071]) ).
tff(1073,plain,
product(product(a15,a8),product(a13,a8)) = product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[647,644,706]) ).
tff(1074,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a4,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1073]) ).
tff(1075,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a6,a7))) = product(product(product(a15,a8),product(a13,a8)),product(product(a4,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1074]) ).
tff(1076,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[940]) ).
tff(1077,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1076]) ).
tff(1078,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1079,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1078,22]) ).
tff(1080,plain,
product(product(product(a14,a7),product(a14,a7)),a6) = product(product(a4,product(product(a1,a2),product(a1,a2))),a6),
inference(monotonicity,[status(thm)],[737]) ).
tff(1081,plain,
product(product(a4,product(product(a1,a2),product(a1,a2))),a6) = product(product(product(a14,a7),product(a14,a7)),a6),
inference(symmetry,[status(thm)],[1080]) ).
tff(1082,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a4,product(product(a1,a2),product(a1,a2))),a6) = product(product(a4,a6),product(product(product(a1,a2),product(a1,a2)),a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1083,plain,
product(product(a4,product(product(a1,a2),product(a1,a2))),a6) = product(product(a4,a6),product(product(product(a1,a2),product(a1,a2)),a6)),
inference(unit_resolution,[status(thm)],[1082,22]) ).
tff(1084,plain,
product(product(a4,a6),product(product(product(a1,a2),product(a1,a2)),a6)) = product(product(a4,product(product(a1,a2),product(a1,a2))),a6),
inference(symmetry,[status(thm)],[1083]) ).
tff(1085,plain,
product(product(a4,a6),product(product(product(a1,a2),product(a1,a2)),a6)) = product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a4,a6))),
inference(monotonicity,[status(thm)],[122,628]) ).
tff(1086,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a4,a6))) = product(product(a4,a6),product(product(product(a1,a2),product(a1,a2)),a6)),
inference(symmetry,[status(thm)],[1085]) ).
tff(1087,plain,
product(product(product(a5,a6),product(a5,a6)),product(product(a15,a8),product(a13,a8))) = product(a7,product(product(a15,a8),product(a13,a8))),
inference(monotonicity,[status(thm)],[77]) ).
tff(1088,plain,
product(a7,product(product(a15,a8),product(a13,a8))) = product(product(product(a5,a6),product(a5,a6)),product(product(a15,a8),product(a13,a8))),
inference(symmetry,[status(thm)],[1087]) ).
tff(1089,plain,
product(product(a5,a6),product(a4,a6)) = product(product(product(a5,a6),product(a5,a6)),product(product(a15,a8),product(a13,a8))),
inference(transitivity,[status(thm)],[593,1088]) ).
tff(1090,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a15,a8),product(a13,a8))) = product(product(a4,a6),product(a4,a6)),
inference(monotonicity,[status(thm)],[453,453]) ).
tff(1091,plain,
product(product(a4,a6),product(a4,a6)) = product(product(product(a15,a8),product(a13,a8)),product(product(a15,a8),product(a13,a8))),
inference(symmetry,[status(thm)],[1090]) ).
tff(1092,plain,
product(product(a15,a8),product(a13,a8)) = product(product(product(a15,a8),product(a13,a8)),product(product(a15,a8),product(a13,a8))),
inference(transitivity,[status(thm)],[664,659,1091]) ).
tff(1093,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a4,a6))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a15,a8),product(a13,a8))),product(product(product(a5,a6),product(a5,a6)),product(product(a15,a8),product(a13,a8)))),
inference(monotonicity,[status(thm)],[1092,1089]) ).
tff(1094,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a15,a8),product(a13,a8))),product(product(product(a5,a6),product(a5,a6)),product(product(a15,a8),product(a13,a8)))) = product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a4,a6))),
inference(symmetry,[status(thm)],[1093]) ).
tff(1095,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a15,a8),product(a13,a8))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a15,a8),product(a13,a8))),product(product(product(a5,a6),product(a5,a6)),product(product(a15,a8),product(a13,a8)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1096,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a15,a8),product(a13,a8))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a15,a8),product(a13,a8))),product(product(product(a5,a6),product(a5,a6)),product(product(a15,a8),product(a13,a8)))),
inference(unit_resolution,[status(thm)],[1095,22]) ).
tff(1097,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a15,a8),product(a13,a8))) = product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))),
inference(monotonicity,[status(thm)],[455]) ).
tff(1098,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6))),product(product(a15,a8),product(a13,a8))),
inference(symmetry,[status(thm)],[1097]) ).
tff(1099,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))) = product(product(product(a14,a7),product(a14,a7)),a6),
inference(transitivity,[status(thm)],[1098,1096,1094,1086,1084,1081]) ).
tff(1100,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a14,a7),product(a14,a7)),a6),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1099]) ).
tff(1101,plain,
product(product(product(product(a14,a7),product(a14,a7)),a6),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1100]) ).
tff(1102,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a14,a7),product(a14,a7)),a6),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1103,plain,
product(product(product(product(a14,a7),product(a14,a7)),a6),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1102,22]) ).
tff(1104,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a14,a7),product(a14,a7)),a6),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1103]) ).
tff(1105,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[97]) ).
tff(1106,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[1105]) ).
tff(1107,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(a14,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[923]) ).
tff(1108,plain,
product(product(product(a14,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1107]) ).
tff(1109,plain,
product(product(a14,a7),product(a7,a7)) = a14,
inference(transitivity,[status(thm)],[929,927,15,9]) ).
tff(1110,plain,
product(product(product(a14,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))) = product(a14,product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1109]) ).
tff(1111,plain,
product(a14,product(product(a6,a7),product(a6,a7))) = product(product(product(a14,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1110]) ).
tff(1112,plain,
product(product(a6,a7),product(a6,a7)) = product(a14,a12),
inference(transitivity,[status(thm)],[78,81,964,963]) ).
tff(1113,plain,
product(a14,product(product(a6,a7),product(a6,a7))) = product(product(product(a2,a12),product(a2,a12)),product(a14,a12)),
inference(monotonicity,[status(thm)],[794,1112]) ).
tff(1114,plain,
product(product(product(a2,a12),product(a2,a12)),product(a14,a12)) = product(a14,product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1113]) ).
tff(1115,plain,
product(product(product(a6,a7),product(a6,a7)),a12) = product(product(a2,a2),a12),
inference(monotonicity,[status(thm)],[78]) ).
tff(1116,plain,
product(product(a2,a2),a12) = product(product(product(a6,a7),product(a6,a7)),a12),
inference(symmetry,[status(thm)],[1115]) ).
tff(1117,plain,
product(product(a2,a12),product(a2,a12)) = product(product(product(a6,a7),product(a6,a7)),a12),
inference(transitivity,[status(thm)],[912,1116]) ).
tff(1118,plain,
product(product(product(a2,a12),product(a2,a12)),product(a14,a12)) = product(product(product(product(a6,a7),product(a6,a7)),a12),product(a14,a12)),
inference(monotonicity,[status(thm)],[1117]) ).
tff(1119,plain,
product(product(product(product(a6,a7),product(a6,a7)),a12),product(a14,a12)) = product(product(product(a2,a12),product(a2,a12)),product(a14,a12)),
inference(symmetry,[status(thm)],[1118]) ).
tff(1120,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,a7),product(a6,a7)),a14),a12) = product(product(product(product(a6,a7),product(a6,a7)),a12),product(a14,a12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1121,plain,
product(product(product(product(a6,a7),product(a6,a7)),a14),a12) = product(product(product(product(a6,a7),product(a6,a7)),a12),product(a14,a12)),
inference(unit_resolution,[status(thm)],[1120,22]) ).
tff(1122,plain,
product(product(product(a2,a12),product(a2,a12)),product(product(a12,a12),product(a2,a12))) = product(product(product(a2,a12),product(a2,a12)),product(a12,a14)),
inference(monotonicity,[status(thm)],[816]) ).
tff(1123,plain,
product(product(product(a2,a12),product(a2,a12)),product(a12,a14)) = product(product(product(a2,a12),product(a2,a12)),product(product(a12,a12),product(a2,a12))),
inference(symmetry,[status(thm)],[1122]) ).
tff(1124,plain,
product(product(product(a2,a12),product(a2,a12)),product(a12,a14)) = product(product(a14,a14),product(a12,a14)),
inference(monotonicity,[status(thm)],[15]) ).
tff(1125,plain,
product(product(a14,a14),product(a12,a14)) = product(product(product(a2,a12),product(a2,a12)),product(a12,a14)),
inference(symmetry,[status(thm)],[1124]) ).
tff(1126,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a14,a12),a14) = product(product(a14,a14),product(a12,a14)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1127,plain,
product(product(a14,a12),a14) = product(product(a14,a14),product(a12,a14)),
inference(unit_resolution,[status(thm)],[1126,22]) ).
tff(1128,plain,
product(product(a14,a12),a14) = product(product(a14,a12),product(product(a2,a12),product(a2,a12))),
inference(monotonicity,[status(thm)],[794]) ).
tff(1129,plain,
product(product(a14,a12),product(product(a2,a12),product(a2,a12))) = product(product(a14,a12),a14),
inference(symmetry,[status(thm)],[1128]) ).
tff(1130,plain,
product(product(product(a6,a7),product(a6,a7)),a14) = product(product(a14,a12),product(product(a2,a12),product(a2,a12))),
inference(monotonicity,[status(thm)],[1112,794]) ).
tff(1131,plain,
product(product(product(a6,a7),product(a6,a7)),a14) = product(product(product(a2,a12),product(a2,a12)),product(product(a12,a12),product(a2,a12))),
inference(transitivity,[status(thm)],[1130,1129,1127,1125,1123]) ).
tff(1132,plain,
product(product(product(product(a6,a7),product(a6,a7)),a14),a12) = product(product(product(product(a2,a12),product(a2,a12)),product(product(a12,a12),product(a2,a12))),product(product(a10,a11),product(a10,a11))),
inference(monotonicity,[status(thm)],[1131,305]) ).
tff(1133,plain,
product(product(product(product(a2,a12),product(a2,a12)),product(product(a12,a12),product(a2,a12))),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a6,a7),product(a6,a7)),a14),a12),
inference(symmetry,[status(thm)],[1132]) ).
tff(1134,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a2,a12),product(a2,a12)),product(product(a12,a12),product(a2,a12))),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a2,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1135,plain,
product(product(product(product(a2,a12),product(a2,a12)),product(product(a12,a12),product(a2,a12))),product(product(a10,a11),product(a10,a11))) = product(product(product(product(a2,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11)))),
inference(unit_resolution,[status(thm)],[1134,22]) ).
tff(1136,plain,
product(product(product(product(a2,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11)))) = product(product(product(product(a2,a12),product(a2,a12)),product(product(a12,a12),product(a2,a12))),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[1135]) ).
tff(1137,plain,
product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))) = product(product(a12,a12),product(a14,a12)),
inference(transitivity,[status(thm)],[824,826,829]) ).
tff(1138,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a2,a12),a12) = product(product(a2,a12),product(a12,a12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1139,plain,
product(product(a2,a12),a12) = product(product(a2,a12),product(a12,a12)),
inference(unit_resolution,[status(thm)],[1138,22]) ).
tff(1140,plain,
product(product(a2,a12),product(a12,a12)) = product(product(a2,a12),a12),
inference(symmetry,[status(thm)],[1139]) ).
tff(1141,plain,
product(product(a2,a12),product(a2,a12)) = product(a2,a12),
inference(transitivity,[status(thm)],[15,9,13]) ).
tff(1142,plain,
product(product(product(a2,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))) = product(product(a2,a12),product(a12,a12)),
inference(monotonicity,[status(thm)],[1141,178]) ).
tff(1143,plain,
product(product(product(a2,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))) = product(product(a6,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[1142,1140,91,82,79]) ).
tff(1144,plain,
product(product(product(product(a2,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11)))) = product(product(product(a6,a7),product(a6,a7)),product(product(a12,a12),product(a14,a12))),
inference(monotonicity,[status(thm)],[1143,1137]) ).
tff(1145,plain,
product(product(product(a6,a7),product(a6,a7)),product(product(a12,a12),product(a14,a12))) = product(product(product(product(a2,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11))),product(product(product(a12,a12),product(a2,a12)),product(product(a10,a11),product(a10,a11)))),
inference(symmetry,[status(thm)],[1144]) ).
tff(1146,plain,
product(product(a7,product(product(a15,a8),product(a13,a8))),a7) = product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[594]) ).
tff(1147,plain,
product(product(a7,a7),product(product(product(a15,a8),product(a13,a8)),a7)) = product(product(a7,product(product(a15,a8),product(a13,a8))),a7),
inference(symmetry,[status(thm)],[591]) ).
tff(1148,plain,
product(product(a12,a12),product(a14,a12)) = product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[562,574,577,581,588,1147,1146]) ).
tff(1149,plain,
product(product(product(a6,a7),product(a6,a7)),product(product(a12,a12),product(a14,a12))) = product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[297,1148]) ).
tff(1150,plain,
product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a6,a7),product(a6,a7)),product(product(a12,a12),product(a14,a12))),
inference(symmetry,[status(thm)],[1149]) ).
tff(1151,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,product(product(a5,a6),product(a4,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1152,plain,
product(product(a6,product(product(a5,a6),product(a4,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1151,22]) ).
tff(1153,plain,
product(product(product(a12,a7),product(a12,a7)),a6) = product(product(a6,product(product(a1,a2),product(a1,a2))),a6),
inference(monotonicity,[status(thm)],[787]) ).
tff(1154,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),a6) = product(product(product(a12,a7),product(a12,a7)),a6),
inference(symmetry,[status(thm)],[1153]) ).
tff(1155,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,product(product(a1,a2),product(a1,a2))),a6) = product(product(a6,a6),product(product(product(a1,a2),product(a1,a2)),a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1156,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),a6) = product(product(a6,a6),product(product(product(a1,a2),product(a1,a2)),a6)),
inference(unit_resolution,[status(thm)],[1155,22]) ).
tff(1157,plain,
product(product(a6,a6),product(product(product(a1,a2),product(a1,a2)),a6)) = product(product(a6,product(product(a1,a2),product(a1,a2))),a6),
inference(symmetry,[status(thm)],[1156]) ).
tff(1158,plain,
product(a6,product(product(a5,a6),product(a4,a6))) = product(product(a6,a6),product(product(product(a1,a2),product(a1,a2)),a6)),
inference(monotonicity,[status(thm)],[774,533]) ).
tff(1159,plain,
product(a6,product(product(a5,a6),product(a4,a6))) = product(product(product(a12,a7),product(a12,a7)),a6),
inference(transitivity,[status(thm)],[1158,1157,1154]) ).
tff(1160,plain,
product(product(a6,product(product(a5,a6),product(a4,a6))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a12,a7),product(a12,a7)),a6),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1159]) ).
tff(1161,plain,
product(product(product(product(a12,a7),product(a12,a7)),a6),product(product(a5,a6),product(a5,a6))) = product(product(a6,product(product(a5,a6),product(a4,a6))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1160]) ).
tff(1162,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a12,a7),product(a12,a7)),a6),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1163,plain,
product(product(product(product(a12,a7),product(a12,a7)),a6),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1162,22]) ).
tff(1164,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a12,a7),product(a12,a7)),a6),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1163]) ).
tff(1165,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[97]) ).
tff(1166,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(a6,product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[1165]) ).
tff(1167,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(a12,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[325]) ).
tff(1168,plain,
product(product(product(a12,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1167]) ).
tff(1169,plain,
product(product(a12,a7),product(a7,a7)) = a12,
inference(transitivity,[status(thm)],[309,312,178,192]) ).
tff(1170,plain,
product(product(product(a12,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))) = product(a12,product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1169]) ).
tff(1171,plain,
product(a12,product(product(a6,a7),product(a6,a7))) = product(product(product(a12,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1170]) ).
tff(1172,plain,
a11 = product(a11,a11),
inference(symmetry,[status(thm)],[287]) ).
tff(1173,plain,
a11 = a10,
inference(transitivity,[status(thm)],[1172,1046,1045,1044,1043,1028,1021,1018,1016,1013,591,589,582,578,575,1171,1168,1166,1164,1161,1152,1150,1145,1136,1133,1121,1119,1114,1111,1108,1106,1104,1101,1079,1077,1075,1072,1069,1066,1057,1055,1053,1050,615,612,271,270]) ).
tff(1174,plain,
product(product(a10,a10),product(a11,a10)) = product(product(product(product(a8,a2),product(a8,a2)),product(product(a11,a10),product(a11,a10))),product(product(a11,a10),product(a11,a10))),
inference(symmetry,[status(thm)],[674]) ).
tff(1175,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))) = product(a7,product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1039]) ).
tff(1176,plain,
product(product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1038]) ).
tff(1177,plain,
product(product(product(a8,a2),product(a8,a2)),product(product(a1,a2),product(a2,a2))) = product(product(product(product(a7,a3),product(a7,a3)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))),
inference(symmetry,[status(thm)],[1036]) ).
tff(1178,plain,
product(product(a9,a9),a1) = product(product(product(a8,a2),product(a8,a2)),product(product(a1,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[1034]) ).
tff(1179,plain,
a10 = product(product(a7,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[567,268,220,1178,1177,1176,1175,1023]) ).
tff(1180,plain,
product(product(a10,a11),a10) = product(product(product(a10,a11),product(a10,a11)),product(product(a7,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1048,1179]) ).
tff(1181,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a7,a7),product(a6,a7))) = product(product(a10,a11),a10),
inference(symmetry,[status(thm)],[1180]) ).
tff(1182,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a7,a7),product(a6,a7))) = product(product(product(a4,a7),product(a6,a7)),product(product(a7,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1051]) ).
tff(1183,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a7,a7),product(a6,a7))) = product(product(product(a10,a11),product(a10,a11)),product(product(a7,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1182]) ).
tff(1184,plain,
product(a7,product(product(a6,a7),product(a6,a7))) = product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1024]) ).
tff(1185,plain,
product(product(a7,a7),product(a6,a7)) = product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7))),
inference(transitivity,[status(thm)],[1022,1184]) ).
tff(1186,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a7,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))),
inference(monotonicity,[status(thm)],[603,1185]) ).
tff(1187,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a4,a7),product(a6,a7)),product(product(a7,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1186]) ).
tff(1188,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1189,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[1188,22]) ).
tff(1190,plain,
( ~ ! [Y: $i,X: $i] : ( product(product(X,Y),Y) = X )
| ( product(product(a4,product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = a4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1191,plain,
product(product(a4,product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))) = a4,
inference(unit_resolution,[status(thm)],[1190,89]) ).
tff(1192,plain,
product(product(a4,a7),product(a7,a7)) = product(product(a4,product(product(a5,a6),product(a5,a6))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[459,41]) ).
tff(1193,plain,
product(product(a4,a7),product(a4,a7)) = product(a4,a7),
inference(transitivity,[status(thm)],[261,287,32]) ).
tff(1194,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6))) = product(product(a4,a7),product(a7,a7)),
inference(monotonicity,[status(thm)],[1193,76]) ).
tff(1195,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6))) = a4,
inference(transitivity,[status(thm)],[1194,1192,1191]) ).
tff(1196,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(a4,product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1195]) ).
tff(1197,plain,
product(a4,product(product(a6,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1196]) ).
tff(1198,plain,
product(a4,product(product(a6,a7),product(a6,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[917]) ).
tff(1199,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))) = product(a4,product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1198]) ).
tff(1200,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1201,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[1200,22]) ).
tff(1202,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1201]) ).
tff(1203,plain,
product(product(a6,a7),product(a6,a7)) = product(a6,a7),
inference(transitivity,[status(thm)],[78,81,28]) ).
tff(1204,plain,
product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))) = product(product(a14,a7),product(a6,a7)),
inference(monotonicity,[status(thm)],[801,1203]) ).
tff(1205,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a14,a7),product(a6,a7)),product(product(a1,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[1204,1026]) ).
tff(1206,plain,
product(product(product(a14,a7),product(a6,a7)),product(product(a1,a2),product(a2,a2))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))),
inference(symmetry,[status(thm)],[1205]) ).
tff(1207,plain,
product(a12,a7) = product(product(a15,a8),product(a13,a8)),
inference(transitivity,[status(thm)],[307,306,319,322,547,544,103,106,116]) ).
tff(1208,plain,
product(product(a12,a7),product(a6,a7)) = product(product(product(a15,a8),product(a13,a8)),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1207,347]) ).
tff(1209,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a6,a7),product(a6,a7))) = product(product(a12,a7),product(a6,a7)),
inference(symmetry,[status(thm)],[1208]) ).
tff(1210,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1073]) ).
tff(1211,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(a15,a8),product(a13,a8)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1210]) ).
tff(1212,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1213,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[1212,22]) ).
tff(1214,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1213]) ).
tff(1215,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a4,a6),a6) = product(product(a4,a6),product(a6,a6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1216,plain,
product(product(a4,a6),a6) = product(product(a4,a6),product(a6,a6)),
inference(unit_resolution,[status(thm)],[1215,22]) ).
tff(1217,plain,
product(product(a4,a6),product(a6,a6)) = product(product(a4,a6),a6),
inference(symmetry,[status(thm)],[1216]) ).
tff(1218,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a13,a8),product(a13,a8))) = product(product(a4,a6),product(a6,a6)),
inference(monotonicity,[status(thm)],[453,161]) ).
tff(1219,plain,
product(product(product(a15,a8),product(a13,a8)),product(product(a13,a8),product(a13,a8))) = a4,
inference(transitivity,[status(thm)],[1218,1217,783,776,769,766,740,869,661]) ).
tff(1220,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a13,a8),product(a13,a8))),a7) = product(a4,a7),
inference(monotonicity,[status(thm)],[1219]) ).
tff(1221,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a15,a8),product(a13,a8)),product(product(a13,a8),product(a13,a8))),a7) = product(product(product(product(a15,a8),product(a13,a8)),a7),product(product(product(a13,a8),product(a13,a8)),a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1222,plain,
product(product(product(product(a15,a8),product(a13,a8)),product(product(a13,a8),product(a13,a8))),a7) = product(product(product(product(a15,a8),product(a13,a8)),a7),product(product(product(a13,a8),product(a13,a8)),a7)),
inference(unit_resolution,[status(thm)],[1221,22]) ).
tff(1223,plain,
product(product(product(product(a15,a8),product(a13,a8)),a7),product(product(product(a13,a8),product(a13,a8)),a7)) = product(product(product(product(a15,a8),product(a13,a8)),product(product(a13,a8),product(a13,a8))),a7),
inference(symmetry,[status(thm)],[1222]) ).
tff(1224,plain,
product(product(product(a13,a8),product(a13,a8)),a7) = product(product(a6,a6),a7),
inference(monotonicity,[status(thm)],[161]) ).
tff(1225,plain,
product(product(a6,a6),a7) = product(product(product(a13,a8),product(a13,a8)),a7),
inference(symmetry,[status(thm)],[1224]) ).
tff(1226,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,a6),a7) = product(product(a6,a7),product(a6,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1227,plain,
product(product(a6,a6),a7) = product(product(a6,a7),product(a6,a7)),
inference(unit_resolution,[status(thm)],[1226,22]) ).
tff(1228,plain,
product(product(a6,a7),product(a6,a7)) = product(product(a6,a6),a7),
inference(symmetry,[status(thm)],[1227]) ).
tff(1229,plain,
product(a6,a7) = product(product(product(a13,a8),product(a13,a8)),a7),
inference(transitivity,[status(thm)],[27,82,79,1228,1225]) ).
tff(1230,plain,
product(product(product(product(a15,a8),product(a13,a8)),a7),product(a6,a7)) = product(product(product(product(a15,a8),product(a13,a8)),a7),product(product(product(a13,a8),product(a13,a8)),a7)),
inference(monotonicity,[status(thm)],[1229]) ).
tff(1231,plain,
product(a2,a2) = product(a6,a7),
inference(transitivity,[status(thm)],[81,28]) ).
tff(1232,plain,
product(a11,a2) = product(product(product(a15,a8),product(a13,a8)),a7),
inference(transitivity,[status(thm)],[33,585,584]) ).
tff(1233,plain,
product(product(a11,a2),product(a2,a2)) = product(product(product(product(a15,a8),product(a13,a8)),a7),product(a6,a7)),
inference(monotonicity,[status(thm)],[1232,1231]) ).
tff(1234,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a6,a7),product(a6,a7))) = product(product(a11,a2),product(a2,a2)),
inference(monotonicity,[status(thm)],[34,78]) ).
tff(1235,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a6,a7),product(a6,a7))) = product(product(a4,a7),product(a4,a7)),
inference(transitivity,[status(thm)],[1234,1233,1230,1223,1220,31,1172,1046]) ).
tff(1236,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a4,a7),product(a4,a7)),product(product(a7,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1235,1025]) ).
tff(1237,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a7,a7),product(a6,a7))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))),
inference(symmetry,[status(thm)],[1236]) ).
tff(1238,plain,
product(product(a11,a11),a10) = product(product(product(a4,a7),product(a4,a7)),product(product(a7,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1046,1179]) ).
tff(1239,plain,
product(product(a1,a2),product(a2,a2)) = product(product(a12,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[1032,1030,277,1238,1237,1214,1211,1209]) ).
tff(1240,plain,
product(product(product(a14,a7),product(a6,a7)),product(product(a1,a2),product(a2,a2))) = product(product(product(a14,a7),product(a6,a7)),product(product(a12,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1239]) ).
tff(1241,plain,
product(product(product(a14,a7),product(a6,a7)),product(product(a12,a7),product(a6,a7))) = product(product(product(a14,a7),product(a6,a7)),product(product(a1,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[1240]) ).
tff(1242,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7))) = product(product(a12,a7),product(a6,a7)),
inference(monotonicity,[status(thm)],[324,1203]) ).
tff(1243,plain,
product(product(a12,a7),product(a6,a7)) = product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1242]) ).
tff(1244,plain,
product(product(a14,a7),product(a6,a7)) = product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1204]) ).
tff(1245,plain,
product(product(product(a14,a7),product(a6,a7)),product(product(a12,a7),product(a6,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7)))),
inference(monotonicity,[status(thm)],[1244,1243]) ).
tff(1246,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a14,a7),product(a6,a7)),product(product(a12,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1245]) ).
tff(1247,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1248,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[1247,22]) ).
tff(1249,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))),product(product(a6,a7),product(a6,a7))) = product(product(product(a6,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[803]) ).
tff(1250,plain,
product(product(product(a6,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1249]) ).
tff(1251,plain,
product(product(product(a6,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))) = product(a6,product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[786]) ).
tff(1252,plain,
product(a6,product(product(a6,a7),product(a6,a7))) = product(product(product(a6,a7),product(a7,a7)),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1251]) ).
tff(1253,plain,
product(product(product(a12,a7),product(a12,a7)),a3) = product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[542]) ).
tff(1254,plain,
product(product(product(a12,a7),a3),product(product(a12,a7),a3)) = product(product(product(a12,a7),product(a12,a7)),a3),
inference(symmetry,[status(thm)],[541]) ).
tff(1255,plain,
product(product(a13,a8),product(a13,a8)) = product(product(product(a12,a7),a3),product(product(a12,a7),a3)),
inference(symmetry,[status(thm)],[539]) ).
tff(1256,plain,
a6 = product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[774,773,1255,1254,1253]) ).
tff(1257,plain,
product(a6,product(product(a6,a7),product(a6,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1256]) ).
tff(1258,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))) = product(a6,product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1257]) ).
tff(1259,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1260,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[1259,22]) ).
tff(1261,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a1,a2),product(a1,a2))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1260]) ).
tff(1262,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a12,a7),product(a6,a7)),product(product(a1,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[1242,1026]) ).
tff(1263,plain,
product(product(product(a12,a7),product(a6,a7)),product(product(a1,a2),product(a2,a2))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a1,a2),product(a1,a2)),product(product(a6,a7),product(a6,a7)))),
inference(symmetry,[status(thm)],[1262]) ).
tff(1264,plain,
product(product(a1,a2),product(a2,a2)) = product(product(a11,a10),product(a11,a10)),
inference(transitivity,[status(thm)],[1032,1030]) ).
tff(1265,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a7,a7),product(a6,a7))) = product(product(a11,a11),a10),
inference(symmetry,[status(thm)],[1238]) ).
tff(1266,plain,
product(product(a12,a7),product(a6,a7)) = product(product(a11,a10),product(a11,a10)),
inference(transitivity,[status(thm)],[1208,1210,1213,1236,1265,276]) ).
tff(1267,plain,
product(product(product(a12,a7),product(a6,a7)),product(product(a1,a2),product(a2,a2))) = product(product(product(a11,a10),product(a11,a10)),product(product(a11,a10),product(a11,a10))),
inference(monotonicity,[status(thm)],[1266,1264]) ).
tff(1268,plain,
product(product(product(a11,a10),product(a11,a10)),product(product(a11,a10),product(a11,a10))) = product(product(product(a12,a7),product(a6,a7)),product(product(a1,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[1267]) ).
tff(1269,plain,
product(a1,a1) = product(product(product(a11,a10),product(a11,a10)),product(product(a11,a10),product(a11,a10))),
inference(symmetry,[status(thm)],[665]) ).
tff(1270,plain,
product(product(product(a4,a7),product(a4,a7)),product(product(a7,a7),product(a6,a7))) = product(product(a4,product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[460,471]) ).
tff(1271,plain,
product(product(a4,product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a4,a7),product(a4,a7)),product(product(a7,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1270]) ).
tff(1272,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a4,product(product(a5,a6),product(a6,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a4,product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1273,plain,
product(product(a4,product(product(a5,a6),product(a6,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a4,product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1272,22]) ).
tff(1274,plain,
product(a4,product(product(a5,a6),product(a6,a6))) = product(a4,product(product(a3,a4),product(a3,a4))),
inference(monotonicity,[status(thm)],[499]) ).
tff(1275,plain,
product(product(a4,product(product(a5,a6),product(a6,a6))),product(product(a5,a6),product(a5,a6))) = product(product(a4,product(product(a3,a4),product(a3,a4))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1274]) ).
tff(1276,plain,
product(product(a4,product(product(a3,a4),product(a3,a4))),product(product(a5,a6),product(a5,a6))) = product(product(a4,product(product(a5,a6),product(a6,a6))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1275]) ).
tff(1277,plain,
product(product(product(a14,a7),product(a14,a7)),a4) = product(product(a4,product(product(a1,a2),product(a1,a2))),a4),
inference(monotonicity,[status(thm)],[737]) ).
tff(1278,plain,
product(product(a4,product(product(a1,a2),product(a1,a2))),a4) = product(product(product(a14,a7),product(a14,a7)),a4),
inference(symmetry,[status(thm)],[1277]) ).
tff(1279,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a4,product(product(a1,a2),product(a1,a2))),a4) = product(product(a4,a4),product(product(product(a1,a2),product(a1,a2)),a4)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1280,plain,
product(product(a4,product(product(a1,a2),product(a1,a2))),a4) = product(product(a4,a4),product(product(product(a1,a2),product(a1,a2)),a4)),
inference(unit_resolution,[status(thm)],[1279,22]) ).
tff(1281,plain,
product(product(a4,a4),product(product(product(a1,a2),product(a1,a2)),a4)) = product(product(a4,product(product(a1,a2),product(a1,a2))),a4),
inference(symmetry,[status(thm)],[1280]) ).
tff(1282,plain,
product(a4,product(product(a3,a4),product(a3,a4))) = product(product(a4,a4),product(product(product(a1,a2),product(a1,a2)),a4)),
inference(monotonicity,[status(thm)],[730,483]) ).
tff(1283,plain,
product(a4,product(product(a3,a4),product(a3,a4))) = product(product(product(a14,a7),product(a14,a7)),a4),
inference(transitivity,[status(thm)],[1282,1281,1278]) ).
tff(1284,plain,
product(product(a4,product(product(a3,a4),product(a3,a4))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a14,a7),product(a14,a7)),a4),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1283]) ).
tff(1285,plain,
product(product(product(product(a14,a7),product(a14,a7)),a4),product(product(a5,a6),product(a5,a6))) = product(product(a4,product(product(a3,a4),product(a3,a4))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1284]) ).
tff(1286,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a14,a7),product(a14,a7)),a4),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1287,plain,
product(product(product(product(a14,a7),product(a14,a7)),a4),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1286,22]) ).
tff(1288,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a14,a7),product(a14,a7)),a4),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1287]) ).
tff(1289,plain,
product(a4,product(product(a5,a6),product(a5,a6))) = product(product(a4,a7),product(a4,a7)),
inference(transitivity,[status(thm)],[458,31,1172,1046]) ).
tff(1290,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a4,a7))),
inference(monotonicity,[status(thm)],[1289]) ).
tff(1291,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a4,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[1290]) ).
tff(1292,plain,
product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))) = product(product(a2,a12),product(a2,a12)),
inference(transitivity,[status(thm)],[923,929,927]) ).
tff(1293,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a4,a7))) = product(product(product(a2,a12),product(a2,a12)),product(product(a4,a7),product(a4,a7))),
inference(monotonicity,[status(thm)],[1292]) ).
tff(1294,plain,
product(product(product(a2,a12),product(a2,a12)),product(product(a4,a7),product(a4,a7))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a4,a7))),
inference(symmetry,[status(thm)],[1293]) ).
tff(1295,plain,
product(product(product(a6,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))) = product(product(a2,a2),a12),
inference(monotonicity,[status(thm)],[78,341]) ).
tff(1296,plain,
product(product(a2,a2),a12) = product(product(product(a6,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[1295]) ).
tff(1297,plain,
product(product(a2,a12),product(a2,a12)) = product(product(product(a6,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))),
inference(transitivity,[status(thm)],[912,1296]) ).
tff(1298,plain,
product(product(product(a2,a12),product(a2,a12)),product(product(a4,a7),product(a4,a7))) = product(product(product(product(a6,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))),product(product(a4,a7),product(a4,a7))),
inference(monotonicity,[status(thm)],[1297]) ).
tff(1299,plain,
product(product(product(product(a6,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))),product(product(a4,a7),product(a4,a7))) = product(product(product(a2,a12),product(a2,a12)),product(product(a4,a7),product(a4,a7))),
inference(symmetry,[status(thm)],[1298]) ).
tff(1300,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a6,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))),product(product(a4,a7),product(a4,a7))) = product(product(product(product(a6,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))),product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1301,plain,
product(product(product(product(a6,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))),product(product(a4,a7),product(a4,a7))) = product(product(product(product(a6,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))),product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7)))),
inference(unit_resolution,[status(thm)],[1300,22]) ).
tff(1302,plain,
product(product(product(product(a6,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))),product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7)))) = product(product(product(product(a6,a7),product(a6,a7)),product(product(a10,a11),product(a10,a11))),product(product(a4,a7),product(a4,a7))),
inference(symmetry,[status(thm)],[1301]) ).
tff(1303,plain,
product(a6,a7) = product(a2,a2),
inference(transitivity,[status(thm)],[27,82]) ).
tff(1304,plain,
product(product(a6,a7),product(a4,a7)) = product(product(a2,a2),a11),
inference(monotonicity,[status(thm)],[1303,31]) ).
tff(1305,plain,
product(product(a2,a2),a11) = product(product(a6,a7),product(a4,a7)),
inference(symmetry,[status(thm)],[1304]) ).
tff(1306,plain,
product(product(product(a6,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))) = product(product(a2,a2),a11),
inference(monotonicity,[status(thm)],[78,566]) ).
tff(1307,plain,
product(product(product(a6,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))) = product(product(a6,a7),product(a4,a7)),
inference(transitivity,[status(thm)],[1306,1305]) ).
tff(1308,plain,
product(product(product(product(a6,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))),product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7)))) = product(product(product(a6,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),
inference(monotonicity,[status(thm)],[1307,618]) ).
tff(1309,plain,
product(product(product(a6,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))) = product(product(product(product(a6,a7),product(a6,a7)),product(product(a4,a7),product(a4,a7))),product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7)))),
inference(symmetry,[status(thm)],[1308]) ).
tff(1310,plain,
product(product(a9,a1),product(a9,a1)) = product(product(a7,a7),product(a6,a7)),
inference(transitivity,[status(thm)],[220,1178,1177,1176,1175,1023]) ).
tff(1311,plain,
product(product(product(a6,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))) = product(product(product(a6,a7),product(a4,a7)),product(product(a7,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1310]) ).
tff(1312,plain,
product(product(product(a6,a7),product(a4,a7)),product(product(a7,a7),product(a6,a7))) = product(product(product(a6,a7),product(a4,a7)),product(product(a9,a1),product(a9,a1))),
inference(symmetry,[status(thm)],[1311]) ).
tff(1313,plain,
product(a6,a4) = product(product(a13,a8),product(a15,a8)),
inference(monotonicity,[status(thm)],[66,121]) ).
tff(1314,plain,
product(product(a13,a8),product(a15,a8)) = product(a6,a4),
inference(symmetry,[status(thm)],[1313]) ).
tff(1315,plain,
product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a5,a6))) = product(product(a6,a4),a7),
inference(monotonicity,[status(thm)],[1314,77]) ).
tff(1316,plain,
product(product(a6,a4),a7) = product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1315]) ).
tff(1317,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,a4),a7) = product(product(a6,a7),product(a4,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1318,plain,
product(product(a6,a4),a7) = product(product(a6,a7),product(a4,a7)),
inference(unit_resolution,[status(thm)],[1317,22]) ).
tff(1319,plain,
product(product(a6,a7),product(a4,a7)) = product(product(a6,a4),a7),
inference(symmetry,[status(thm)],[1318]) ).
tff(1320,plain,
product(product(a6,a7),product(a4,a7)) = product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[1319,1316]) ).
tff(1321,plain,
product(product(product(a6,a7),product(a4,a7)),product(product(a7,a7),product(a6,a7))) = product(product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[1320,471]) ).
tff(1322,plain,
product(product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a6,a7),product(a4,a7)),product(product(a7,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1321]) ).
tff(1323,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a6,a6))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1324,plain,
product(product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a6,a6))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1323,22]) ).
tff(1325,plain,
product(product(product(a12,a7),product(a12,a7)),a4) = product(product(a6,product(product(a1,a2),product(a1,a2))),a4),
inference(monotonicity,[status(thm)],[787]) ).
tff(1326,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),a4) = product(product(product(a12,a7),product(a12,a7)),a4),
inference(symmetry,[status(thm)],[1325]) ).
tff(1327,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a6,product(product(a1,a2),product(a1,a2))),a4) = product(product(a6,a4),product(product(product(a1,a2),product(a1,a2)),a4)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1328,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),a4) = product(product(a6,a4),product(product(product(a1,a2),product(a1,a2)),a4)),
inference(unit_resolution,[status(thm)],[1327,22]) ).
tff(1329,plain,
product(product(a6,a4),product(product(product(a1,a2),product(a1,a2)),a4)) = product(product(a6,product(product(a1,a2),product(a1,a2))),a4),
inference(symmetry,[status(thm)],[1328]) ).
tff(1330,plain,
product(a3,a4) = product(product(product(a1,a2),product(a1,a2)),a4),
inference(transitivity,[status(thm)],[491,525,493,482,479]) ).
tff(1331,plain,
product(product(a6,a4),product(a3,a4)) = product(product(a6,a4),product(product(product(a1,a2),product(a1,a2)),a4)),
inference(monotonicity,[status(thm)],[1330]) ).
tff(1332,plain,
product(product(a5,a6),product(a6,a6)) = product(a3,a4),
inference(transitivity,[status(thm)],[464,461,498,486,494,524,492]) ).
tff(1333,plain,
product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a6,a6))) = product(product(a6,a4),product(a3,a4)),
inference(monotonicity,[status(thm)],[1314,1332]) ).
tff(1334,plain,
product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a6,a6))) = product(product(product(a12,a7),product(a12,a7)),a4),
inference(transitivity,[status(thm)],[1333,1331,1329,1326]) ).
tff(1335,plain,
product(product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a6,a6))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a12,a7),product(a12,a7)),a4),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1334]) ).
tff(1336,plain,
product(product(product(product(a12,a7),product(a12,a7)),a4),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a6,a6))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1335]) ).
tff(1337,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a12,a7),product(a12,a7)),a4),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1338,plain,
product(product(product(product(a12,a7),product(a12,a7)),a4),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1337,22]) ).
tff(1339,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a12,a7),product(a12,a7)),a4),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1338]) ).
tff(1340,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a4,a7))),
inference(monotonicity,[status(thm)],[1289]) ).
tff(1341,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a4,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(a4,product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[1340]) ).
tff(1342,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))) = product(a10,a11),
inference(transitivity,[status(thm)],[325,309,312,178,192,176]) ).
tff(1343,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a4,a7))) = product(product(a10,a11),product(a11,a11)),
inference(monotonicity,[status(thm)],[1342,261]) ).
tff(1344,plain,
product(product(a10,a11),product(a11,a11)) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a4,a7),product(a4,a7))),
inference(symmetry,[status(thm)],[1343]) ).
tff(1345,plain,
product(product(a9,a1),product(a9,a1)) = product(product(product(product(a9,a1),product(a9,a1)),product(product(a4,a7),product(a4,a7))),product(product(a4,a7),product(a4,a7))),
inference(symmetry,[status(thm)],[612]) ).
tff(1346,plain,
a10 = a9,
inference(transitivity,[status(thm)],[567,268,1345,614,1344,1341,1339,1336,1324,1322,1312,1309,1302,1299,1294,1291,1288,1285,1276,1273,1271,1265,276,208,1269,1268,1263,1261,1258,1252,1250,1248,1246,1241,1206,1202,1199,1197,1189,1187,1183,1181,841,1174,676,215,235]) ).
tff(1347,plain,
product(product(a11,a2),product(a11,a2)) = product(product(a11,a11),a2),
inference(symmetry,[status(thm)],[1009]) ).
tff(1348,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a15,a8),product(a13,a8))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[945]) ).
tff(1349,plain,
product(product(a6,product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a4,a6)),product(product(a5,a6),product(a5,a6)))) = product(product(a6,product(product(a5,a6),product(a4,a6))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1152]) ).
tff(1350,plain,
product(product(product(product(a6,a7),product(a6,a7)),a12),product(a14,a12)) = product(product(product(product(a6,a7),product(a6,a7)),a14),a12),
inference(symmetry,[status(thm)],[1121]) ).
tff(1351,plain,
product(product(product(product(a4,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a15,a8),product(a13,a8)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1079]) ).
tff(1352,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a10,a11),product(a10,a11)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a10,a11),product(a10,a11))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1057]) ).
tff(1353,plain,
product(product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a13,a8),product(a15,a8)),product(product(a5,a6),product(a6,a6))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1324]) ).
tff(1354,plain,
product(product(a4,product(product(a5,a6),product(a5,a6))),product(product(product(a5,a6),product(a6,a6)),product(product(a5,a6),product(a5,a6)))) = product(product(a4,product(product(a5,a6),product(a6,a6))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1273]) ).
tff(1355,plain,
product(product(product(product(a14,a7),product(a14,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a12,a7),product(a12,a7)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a14,a7),product(a14,a7)),product(product(a12,a7),product(a12,a7))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1248]) ).
tff(1356,plain,
product(product(product(product(a4,a7),product(a4,a7)),product(product(a6,a7),product(a6,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1189]) ).
tff(1357,plain,
a9 = a8,
inference(transitivity,[status(thm)],[845,214,677,674,842,1180,1182,1186,1356,1196,1198,1201,1205,1240,1245,1355,1249,1251,1257,1260,1262,1267,665,207,277,1238,1270,1354,1275,1284,1287,1290,1293,1298,1301,1308,1311,1321,1353,1335,1338,1340,1343,1049,1052,1054,1352,1065,1068,1071,1074,1076,1351,1100,1103,1105,1107,1110,1113,1118,1350,1132,1135,1144,1149,1349,1160,1163,1165,1167,1170,574,577,581,588,1147,1012,1015,1017,1020,1027,1042,280,263,261,287,32,918,921,924,931,933,938,942,1348,992,998,1001,1003,1006,1347,289,585,124,148,910,171,186,189,303,315,327,330,345,443,449,909,456,505,509,512,514,908,519,557,560,596,600,607,907,619,222,225,239,251,142,145,906,622,625,629,649,534,537,653,656,905,663,647,644,640,638,636,633,904,685,903,902,901,710,900,899,898,725,897,866,865,768,864,863,862,861,860,859,858,857,856,855,854,853,852,851,850,249,243,130,128]) ).
tff(1358,plain,
a8 = a7,
inference(transitivity,[status(thm)],[140,129,688,248,847,844,837,835,832,823,821,819,810,807,805,788,785,783,776,769,766,740,728,726,738,720,718,711,708,704,702,686,683,632,635,637,639,643,646,664,659,657,654,538,535,650,630,626,623,488,76,43]) ).
tff(1359,plain,
a7 = a6,
inference(transitivity,[status(thm)],[44,41,906,622,625,629,649,534,537,653,656,905,663,647,644,640,638,636,633,904,685,903,902,901,988,978,976,371,100]) ).
tff(1360,plain,
a6 = product(product(a6,a7),product(a7,a7)),
inference(transitivity,[status(thm)],[101,98,789]) ).
tff(1361,plain,
product(a7,a6) = product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a7,a7))),
inference(monotonicity,[status(thm)],[45,1360]) ).
tff(1362,plain,
product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a7,a7))) = product(a7,a6),
inference(symmetry,[status(thm)],[1361]) ).
tff(1363,plain,
product(product(product(a6,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))) = product(product(product(a6,a7),product(a6,a7)),a7),
inference(monotonicity,[status(thm)],[77]) ).
tff(1364,plain,
product(product(product(a6,a7),product(a6,a7)),a7) = product(product(product(a6,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1363]) ).
tff(1365,plain,
product(product(a6,a7),product(a7,a7)) = product(product(product(a6,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[348,1364]) ).
tff(1366,plain,
product(product(product(a5,a6),product(a5,a6)),product(product(a5,a6),product(a5,a6))) = product(product(a7,a7),product(a7,a7)),
inference(monotonicity,[status(thm)],[76,76]) ).
tff(1367,plain,
product(product(a7,a7),product(a7,a7)) = product(product(product(a5,a6),product(a5,a6)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1366]) ).
tff(1368,plain,
product(a7,a7) = product(a5,a6),
inference(transitivity,[status(thm)],[43,40]) ).
tff(1369,plain,
product(product(a7,a7),product(a7,a7)) = product(product(a5,a6),product(a5,a6)),
inference(monotonicity,[status(thm)],[1368,1368]) ).
tff(1370,plain,
product(product(a5,a6),product(a5,a6)) = product(product(a7,a7),product(a7,a7)),
inference(symmetry,[status(thm)],[1369]) ).
tff(1371,plain,
product(product(a5,a6),product(a5,a6)) = product(product(product(a5,a6),product(a5,a6)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[1370,1367]) ).
tff(1372,plain,
product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a7,a7))) = product(product(product(product(a5,a6),product(a5,a6)),product(product(a5,a6),product(a5,a6))),product(product(product(a6,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[1371,1365]) ).
tff(1373,plain,
product(product(product(product(a5,a6),product(a5,a6)),product(product(a5,a6),product(a5,a6))),product(product(product(a6,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a7,a7))),
inference(symmetry,[status(thm)],[1372]) ).
tff(1374,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a5,a6),product(a5,a6)),product(product(a5,a6),product(a5,a6))),product(product(product(a6,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1375,plain,
product(product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a5,a6),product(a5,a6)),product(product(a5,a6),product(a5,a6))),product(product(product(a6,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1374,22]) ).
tff(1376,plain,
product(product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7))),product(product(a5,a6),product(a5,a6))) = product(product(product(a7,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1025]) ).
tff(1377,plain,
product(product(product(a7,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1376]) ).
tff(1378,plain,
product(product(a7,a7),product(a6,a7)) = product(product(a9,a1),product(a9,a1)),
inference(transitivity,[status(thm)],[1022,1039,1038,1036,1034,219]) ).
tff(1379,plain,
product(product(product(a7,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))) = product(product(product(a9,a1),product(a9,a1)),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1378]) ).
tff(1380,plain,
product(product(product(a9,a1),product(a9,a1)),product(product(a5,a6),product(a5,a6))) = product(product(product(a7,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1379]) ).
tff(1381,plain,
product(product(a10,a11),product(a11,a11)) = product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),
inference(symmetry,[status(thm)],[617]) ).
tff(1382,plain,
product(product(a9,a1),product(a9,a1)) = product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),
inference(transitivity,[status(thm)],[1345,614,1381]) ).
tff(1383,plain,
product(product(product(a9,a1),product(a9,a1)),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1382]) ).
tff(1384,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),product(product(a5,a6),product(a5,a6))) = product(product(product(a9,a1),product(a9,a1)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1383]) ).
tff(1385,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1386,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1385,22]) ).
tff(1387,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a4,a7),product(a4,a7))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1386]) ).
tff(1388,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))) = product(a6,product(product(a1,a2),product(a1,a2))),
inference(transitivity,[status(thm)],[319,322,547,544,69]) ).
tff(1389,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6)))) = product(product(a6,product(product(a1,a2),product(a1,a2))),a4),
inference(monotonicity,[status(thm)],[1388,1195]) ).
tff(1390,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),a4) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(product(a4,a7),product(a4,a7)),product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[1389]) ).
tff(1391,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),a4) = product(product(a4,a6),a4),
inference(monotonicity,[status(thm)],[784]) ).
tff(1392,plain,
product(product(a4,a6),a4) = product(product(a6,product(product(a1,a2),product(a1,a2))),a4),
inference(symmetry,[status(thm)],[1391]) ).
tff(1393,plain,
a4 = product(a8,a8),
inference(transitivity,[status(thm)],[730,729,866,865,768,864,863,862,861,860,859,858,857,856,855,854,853,852,851,850,249,243,130]) ).
tff(1394,plain,
product(product(a4,a6),a4) = product(product(product(product(a14,a3),product(a12,a3)),a8),product(a8,a8)),
inference(monotonicity,[status(thm)],[782,1393]) ).
tff(1395,plain,
product(product(product(product(a14,a3),product(a12,a3)),a8),product(a8,a8)) = product(product(a4,a6),a4),
inference(symmetry,[status(thm)],[1394]) ).
tff(1396,plain,
product(product(product(a14,a3),product(a12,a3)),a8) = product(a3,a3),
inference(transitivity,[status(thm)],[777,780,647,644,640,638,636,633,228,51]) ).
tff(1397,plain,
product(product(product(product(a14,a3),product(a12,a3)),a8),product(a8,a8)) = product(product(a3,a3),product(a7,a3)),
inference(monotonicity,[status(thm)],[1396,848]) ).
tff(1398,plain,
product(product(a3,a3),product(a7,a3)) = product(product(product(product(a14,a3),product(a12,a3)),a8),product(a8,a8)),
inference(symmetry,[status(thm)],[1397]) ).
tff(1399,plain,
product(a7,a3) = product(product(a8,a2),product(a2,a2)),
inference(transitivity,[status(thm)],[57,140,129,688,248]) ).
tff(1400,plain,
product(product(a3,a3),product(a7,a3)) = product(product(product(a1,a2),product(a1,a2)),product(product(a8,a2),product(a2,a2))),
inference(monotonicity,[status(thm)],[50,1399]) ).
tff(1401,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a8,a2),product(a2,a2))) = product(product(a3,a3),product(a7,a3)),
inference(symmetry,[status(thm)],[1400]) ).
tff(1402,plain,
product(product(a1,a2),product(a1,a2)) = product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),
inference(transitivity,[status(thm)],[255,254]) ).
tff(1403,plain,
product(product(product(a1,a2),product(a1,a2)),product(product(a8,a2),product(a2,a2))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7)))),
inference(monotonicity,[status(thm)],[1402,687]) ).
tff(1404,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7)))) = product(product(product(a1,a2),product(a1,a2)),product(product(a8,a2),product(a2,a2))),
inference(symmetry,[status(thm)],[1403]) ).
tff(1405,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a11,a10),product(a11,a10)),product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1406,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7)))),
inference(unit_resolution,[status(thm)],[1405,22]) ).
tff(1407,plain,
product(product(product(a11,a10),product(a11,a10)),product(product(a8,a2),product(a8,a2))) = product(a1,product(product(a8,a2),product(a8,a2))),
inference(monotonicity,[status(thm)],[209]) ).
tff(1408,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))) = product(product(a1,product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))),
inference(monotonicity,[status(thm)],[1407]) ).
tff(1409,plain,
product(product(a1,product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1408]) ).
tff(1410,plain,
product(product(product(a8,a2),product(a8,a2)),a1) = product(product(a9,a9),a1),
inference(monotonicity,[status(thm)],[215]) ).
tff(1411,plain,
product(product(product(a8,a2),product(a8,a2)),a1) = product(a10,a10),
inference(transitivity,[status(thm)],[1410,219,271]) ).
tff(1412,plain,
product(a1,a1) = product(a11,a10),
inference(transitivity,[status(thm)],[202,206]) ).
tff(1413,plain,
product(product(a1,a1),product(product(product(a8,a2),product(a8,a2)),a1)) = product(product(a11,a10),product(a10,a10)),
inference(monotonicity,[status(thm)],[1412,1411]) ).
tff(1414,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a1,product(product(a8,a2),product(a8,a2))),a1) = product(product(a1,a1),product(product(product(a8,a2),product(a8,a2)),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1415,plain,
product(product(a1,product(product(a8,a2),product(a8,a2))),a1) = product(product(a1,a1),product(product(product(a8,a2),product(a8,a2)),a1)),
inference(unit_resolution,[status(thm)],[1414,22]) ).
tff(1416,plain,
product(product(a1,product(product(a8,a2),product(a8,a2))),product(product(a11,a10),product(a11,a10))) = product(product(a1,product(product(a8,a2),product(a8,a2))),a1),
inference(monotonicity,[status(thm)],[209]) ).
tff(1417,plain,
product(product(a1,product(product(a8,a2),product(a8,a2))),product(product(a11,a10),product(a11,a10))) = a11,
inference(transitivity,[status(thm)],[1416,1415,1413,280,263,261,287]) ).
tff(1418,plain,
product(product(product(a1,product(product(a8,a2),product(a8,a2))),product(product(a11,a10),product(a11,a10))),product(product(a11,a10),product(a11,a10))) = product(a11,product(product(a11,a10),product(a11,a10))),
inference(monotonicity,[status(thm)],[1417]) ).
tff(1419,plain,
product(product(a1,product(product(a8,a2),product(a8,a2))),a1) = product(product(a1,product(product(a8,a2),product(a8,a2))),product(product(a11,a10),product(a11,a10))),
inference(symmetry,[status(thm)],[1416]) ).
tff(1420,plain,
product(product(a1,a1),product(product(product(a8,a2),product(a8,a2)),a1)) = product(product(a1,product(product(a8,a2),product(a8,a2))),a1),
inference(symmetry,[status(thm)],[1415]) ).
tff(1421,plain,
product(product(a11,a10),product(a10,a10)) = product(product(a1,a1),product(product(product(a8,a2),product(a8,a2)),a1)),
inference(symmetry,[status(thm)],[1413]) ).
tff(1422,plain,
product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))) = product(product(a1,product(product(a8,a2),product(a8,a2))),product(product(a11,a10),product(a11,a10))),
inference(transitivity,[status(thm)],[282,1421,1420,1419]) ).
tff(1423,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))),product(product(a11,a10),product(a11,a10))) = product(product(product(a1,product(product(a8,a2),product(a8,a2))),product(product(a11,a10),product(a11,a10))),product(product(a11,a10),product(a11,a10))),
inference(monotonicity,[status(thm)],[1422]) ).
tff(1424,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))),product(product(a11,a10),product(a11,a10))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a11,a10),product(a11,a10))),product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1425,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))),product(product(a11,a10),product(a11,a10))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a11,a10),product(a11,a10))),product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10)))),
inference(unit_resolution,[status(thm)],[1424,22]) ).
tff(1426,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a11,a10),product(a11,a10))),product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10)))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a9,a1),product(a9,a1))),product(product(a11,a10),product(a11,a10))),
inference(symmetry,[status(thm)],[1425]) ).
tff(1427,plain,
a1 = product(product(product(a11,a10),product(a11,a10)),product(product(a11,a10),product(a11,a10))),
inference(transitivity,[status(thm)],[278,1269]) ).
tff(1428,plain,
product(a1,product(product(a8,a2),product(a8,a2))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a11,a10),product(a11,a10))),product(product(product(a9,a1),product(a9,a1)),product(product(a11,a10),product(a11,a10)))),
inference(monotonicity,[status(thm)],[1427,678]) ).
tff(1429,plain,
product(a1,product(product(a8,a2),product(a8,a2))) = product(a11,product(product(a11,a10),product(a11,a10))),
inference(transitivity,[status(thm)],[1428,1426,1423,1418]) ).
tff(1430,plain,
product(product(a1,product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))) = product(product(a11,product(product(a11,a10),product(a11,a10))),a2),
inference(monotonicity,[status(thm)],[1429,197]) ).
tff(1431,plain,
product(product(a11,product(product(a11,a10),product(a11,a10))),a2) = product(product(a1,product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1430]) ).
tff(1432,plain,
product(product(a11,a2),product(a1,a2)) = product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))),
inference(monotonicity,[status(thm)],[33,1070]) ).
tff(1433,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))) = product(product(a11,a2),product(a1,a2)),
inference(symmetry,[status(thm)],[1432]) ).
tff(1434,plain,
product(product(a15,a8),product(a13,a8)) = product(a12,a7),
inference(transitivity,[status(thm)],[117,107,104,893,546,323,320,318,317]) ).
tff(1435,plain,
product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))) = product(product(product(product(a15,a8),product(a13,a8)),a7),product(a12,a7)),
inference(monotonicity,[status(thm)],[586,1434]) ).
tff(1436,plain,
product(product(product(product(a15,a8),product(a13,a8)),a7),product(a12,a7)) = product(product(product(a4,a7),product(a6,a7)),product(product(a15,a8),product(a13,a8))),
inference(symmetry,[status(thm)],[1435]) ).
tff(1437,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a15,a8),product(a13,a8)),a12),a7) = product(product(product(product(a15,a8),product(a13,a8)),a7),product(a12,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1438,plain,
product(product(product(product(a15,a8),product(a13,a8)),a12),a7) = product(product(product(product(a15,a8),product(a13,a8)),a7),product(a12,a7)),
inference(unit_resolution,[status(thm)],[1437,22]) ).
tff(1439,plain,
product(product(product(a10,a11),product(a10,a11)),product(a7,a12)) = product(product(a12,a12),product(a7,a12)),
inference(symmetry,[status(thm)],[441]) ).
tff(1440,plain,
product(product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2))),product(product(product(a7,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2)))) = product(product(product(a10,a11),product(a10,a11)),product(a7,a12)),
inference(symmetry,[status(thm)],[440]) ).
tff(1441,plain,
product(product(product(product(a12,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a12,a3),product(a12,a3)),product(product(a7,a3),product(a12,a3))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[413]) ).
tff(1442,plain,
product(product(a6,product(product(a12,a3),product(a12,a3))),product(product(a1,a2),product(a1,a2))) = product(product(product(product(a12,a12),product(a7,a12)),product(product(a1,a2),product(a1,a2))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[397]) ).
tff(1443,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2)))) = product(product(a6,product(product(a12,a3),product(a12,a3))),product(product(a1,a2),product(a1,a2))),
inference(symmetry,[status(thm)],[385]) ).
tff(1444,plain,
product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a10,a11),product(a10,a11))) = product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(product(a12,a3),product(a12,a3)),product(product(a1,a2),product(a1,a2)))),
inference(symmetry,[status(thm)],[383]) ).
tff(1445,plain,
product(product(a6,product(product(a10,a11),product(a10,a11))),product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11)))) = product(product(a6,product(product(a1,a2),product(a1,a2))),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[379]) ).
tff(1446,plain,
product(product(product(a2,a12),product(a7,a12)),product(a3,product(product(a10,a11),product(a10,a11)))) = product(product(a6,product(product(a10,a11),product(a10,a11))),product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11)))),
inference(symmetry,[status(thm)],[377]) ).
tff(1447,plain,
product(product(product(product(a6,a7),product(a7,a7)),product(product(a10,a11),product(a10,a11))),product(product(product(a1,a2),product(a1,a2)),product(product(a10,a11),product(a10,a11)))) = product(product(product(a2,a12),product(a7,a12)),product(a3,product(product(a10,a11),product(a10,a11)))),
inference(symmetry,[status(thm)],[370]) ).
tff(1448,plain,
product(product(product(a15,a8),product(a13,a8)),a12) = product(product(product(product(a6,a7),product(a7,a7)),product(product(a1,a2),product(a1,a2))),product(product(a10,a11),product(a10,a11))),
inference(symmetry,[status(thm)],[352]) ).
tff(1449,plain,
product(product(product(a15,a8),product(a13,a8)),a12) = product(product(a12,a12),product(a7,a12)),
inference(transitivity,[status(thm)],[1448,354,1447,1446,1445,1444,1443,1442,1441,415,1440,1439]) ).
tff(1450,plain,
product(product(product(product(a15,a8),product(a13,a8)),a12),a7) = product(product(product(a12,a12),product(a7,a12)),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1449,45]) ).
tff(1451,plain,
product(product(product(a12,a12),product(a7,a12)),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a15,a8),product(a13,a8)),a12),a7),
inference(symmetry,[status(thm)],[1450]) ).
tff(1452,plain,
product(product(product(a5,a6),product(a5,a6)),a12) = product(a7,a12),
inference(symmetry,[status(thm)],[436]) ).
tff(1453,plain,
product(product(a7,a12),product(a7,a12)) = product(a7,a12),
inference(transitivity,[status(thm)],[445,334,1452]) ).
tff(1454,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(a7,a12),product(a7,a12))) = product(product(product(a10,a11),product(a10,a11)),product(a7,a12)),
inference(monotonicity,[status(thm)],[1453]) ).
tff(1455,plain,
product(product(product(a10,a11),product(a10,a11)),product(a7,a12)) = product(product(product(a10,a11),product(a10,a11)),product(product(a7,a12),product(a7,a12))),
inference(symmetry,[status(thm)],[1454]) ).
tff(1456,plain,
product(product(a12,a12),product(a7,a12)) = product(product(product(a10,a11),product(a10,a11)),product(product(a7,a12),product(a7,a12))),
inference(transitivity,[status(thm)],[441,1455]) ).
tff(1457,plain,
product(product(product(a12,a12),product(a7,a12)),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a7,a12),product(a7,a12))),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1456]) ).
tff(1458,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a7,a12),product(a7,a12))),product(product(a5,a6),product(a5,a6))) = product(product(product(a12,a12),product(a7,a12)),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1457]) ).
tff(1459,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a10,a11),product(a10,a11)),product(product(a7,a12),product(a7,a12))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(product(a7,a12),product(a7,a12)),product(product(a5,a6),product(a5,a6)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1460,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a7,a12),product(a7,a12))),product(product(a5,a6),product(a5,a6))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(product(a7,a12),product(a7,a12)),product(product(a5,a6),product(a5,a6)))),
inference(unit_resolution,[status(thm)],[1459,22]) ).
tff(1461,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(product(a7,a12),product(a7,a12)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a7,a12),product(a7,a12))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1460]) ).
tff(1462,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(a7,a12),a7) = product(product(a7,a7),product(a12,a7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1463,plain,
product(product(a7,a12),a7) = product(product(a7,a7),product(a12,a7)),
inference(unit_resolution,[status(thm)],[1462,22]) ).
tff(1464,plain,
product(product(a7,a12),a7) = product(product(a7,a12),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[45]) ).
tff(1465,plain,
product(product(a7,a12),product(product(a5,a6),product(a5,a6))) = product(product(a7,a12),a7),
inference(symmetry,[status(thm)],[1464]) ).
tff(1466,plain,
product(product(product(a7,a12),product(a7,a12)),product(product(a5,a6),product(a5,a6))) = product(product(a7,a12),product(product(a5,a6),product(a5,a6))),
inference(monotonicity,[status(thm)],[1453]) ).
tff(1467,plain,
product(product(product(a7,a12),product(a7,a12)),product(product(a5,a6),product(a5,a6))) = product(product(a7,a7),product(a12,a7)),
inference(transitivity,[status(thm)],[1466,1465,1463]) ).
tff(1468,plain,
product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(product(a7,a12),product(a7,a12)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a12,a7),product(a12,a7)),product(product(a7,a7),product(a12,a7))),
inference(monotonicity,[status(thm)],[820,1467]) ).
tff(1469,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a7,a7),product(a12,a7))) = product(product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),product(product(product(a7,a12),product(a7,a12)),product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[1468]) ).
tff(1470,plain,
product(product(product(a5,a6),product(a5,a6)),product(product(a12,a7),product(a12,a7))) = product(product(a7,a7),product(a12,a7)),
inference(monotonicity,[status(thm)],[76,324]) ).
tff(1471,plain,
product(product(a7,a7),product(a12,a7)) = product(product(product(a5,a6),product(a5,a6)),product(product(a12,a7),product(a12,a7))),
inference(symmetry,[status(thm)],[1470]) ).
tff(1472,plain,
product(product(a12,a7),product(a12,a7)) = product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))),
inference(symmetry,[status(thm)],[804]) ).
tff(1473,plain,
product(product(product(a12,a7),product(a12,a7)),product(product(a7,a7),product(a12,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a12,a7),product(a12,a7)))),
inference(monotonicity,[status(thm)],[1472,1471]) ).
tff(1474,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a12,a7),product(a12,a7)))) = product(product(product(a12,a7),product(a12,a7)),product(product(a7,a7),product(a12,a7))),
inference(symmetry,[status(thm)],[1473]) ).
tff(1475,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) )
| ( product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a12,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a12,a7),product(a12,a7)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1476,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a12,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a12,a7),product(a12,a7)))),
inference(unit_resolution,[status(thm)],[1475,22]) ).
tff(1477,plain,
product(product(a12,a7),product(a12,a7)) = product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6))),
inference(transitivity,[status(thm)],[323,320]) ).
tff(1478,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a12,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6)))),
inference(monotonicity,[status(thm)],[1477]) ).
tff(1479,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a12,a7))),
inference(symmetry,[status(thm)],[1478]) ).
tff(1480,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6)))) = product(product(product(a12,a7),product(a7,a7)),product(product(a12,a7),product(a12,a7))),
inference(monotonicity,[status(thm)],[325,820]) ).
tff(1481,plain,
product(product(product(a12,a7),product(a7,a7)),product(product(a12,a7),product(a12,a7))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(product(a10,a11),product(a10,a11)),product(product(a5,a6),product(a5,a6)))),
inference(symmetry,[status(thm)],[1480]) ).
tff(1482,plain,
product(product(a12,a7),product(a7,a7)) = product(product(a10,a11),product(a10,a11)),
inference(transitivity,[status(thm)],[309,312]) ).
tff(1483,plain,
product(product(product(a12,a7),product(a7,a7)),product(product(a12,a7),product(a12,a7))) = product(product(product(a10,a11),product(a10,a11)),product(a12,a7)),
inference(monotonicity,[status(thm)],[1482,324]) ).
tff(1484,plain,
product(product(product(a10,a11),product(a10,a11)),product(a12,a7)) = product(product(product(a12,a7),product(a7,a7)),product(product(a12,a7),product(a12,a7))),
inference(symmetry,[status(thm)],[1483]) ).
tff(1485,plain,
product(a12,a7) = product(product(product(a12,a7),a3),product(a3,a3)),
inference(transitivity,[status(thm)],[307,306,319,322,547,544]) ).
tff(1486,plain,
product(product(product(a10,a11),product(a10,a11)),product(a12,a7)) = product(product(product(a10,a11),product(a10,a11)),product(product(product(a12,a7),a3),product(a3,a3))),
inference(monotonicity,[status(thm)],[1485]) ).
tff(1487,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(product(a12,a7),a3),product(a3,a3))) = product(product(product(a10,a11),product(a10,a11)),product(a12,a7)),
inference(symmetry,[status(thm)],[1486]) ).
tff(1488,plain,
product(product(product(a12,a7),a3),product(a3,a3)) = product(product(a15,a8),product(a13,a8)),
inference(transitivity,[status(thm)],[103,106,116]) ).
tff(1489,plain,
product(product(product(a10,a11),product(a10,a11)),product(product(product(a12,a7),a3),product(a3,a3))) = product(a12,product(product(a15,a8),product(a13,a8))),
inference(monotonicity,[status(thm)],[341,1488]) ).
tff(1490,plain,
product(a12,product(product(a15,a8),product(a13,a8))) = product(product(product(a10,a11),product(a10,a11)),product(product(product(a12,a7),a3),product(a3,a3))),
inference(symmetry,[status(thm)],[1489]) ).
tff(1491,plain,
product(product(a15,a8),product(a13,a8)) = a3,
inference(transitivity,[status(thm)],[647,644,640,638,636,633,228,51,71]) ).
tff(1492,plain,
product(a12,product(product(a15,a8),product(a13,a8))) = product(product(a12,a12),a3),
inference(monotonicity,[status(thm)],[193,1491]) ).
tff(1493,plain,
product(product(a12,a12),a3) = product(a12,product(product(a15,a8),product(a13,a8))),
inference(symmetry,[status(thm)],[1492]) ).
tff(1494,plain,
a6 = a5,
inference(transitivity,[status(thm)],[101,98,975,996,987,710,900,899,898,725,897,866,865,768,864,863,862,861,860,859,858,896,892,886,884,882,168,158,183,1493,1490,1487,1484,1481,1479,1476,1474,1469,1461,1458,1451,1438,1436,1433,698,694,1431,1409,1406,1404,1401,1398,1395,1392,1390,1387,1384,1380,1377,1375,1373,1362,498,486,494,524]) ).
tff(1495,plain,
product(product(product(product(a12,a7),product(a12,a7)),product(product(a12,a7),product(a12,a7))),product(product(product(a5,a6),product(a5,a6)),product(product(a12,a7),product(a12,a7)))) = product(product(product(product(a12,a7),product(a12,a7)),product(product(a5,a6),product(a5,a6))),product(product(a12,a7),product(a12,a7))),
inference(symmetry,[status(thm)],[1476]) ).
tff(1496,plain,
product(product(product(product(a15,a8),product(a13,a8)),a7),product(a12,a7)) = product(product(product(product(a15,a8),product(a13,a8)),a12),a7),
inference(symmetry,[status(thm)],[1438]) ).
tff(1497,plain,
product(product(product(product(a11,a10),product(a11,a10)),product(product(a6,a7),product(a6,a7))),product(product(product(a8,a2),product(a8,a2)),product(product(a6,a7),product(a6,a7)))) = product(product(product(product(a11,a10),product(a11,a10)),product(product(a8,a2),product(a8,a2))),product(product(a6,a7),product(a6,a7))),
inference(symmetry,[status(thm)],[1406]) ).
tff(1498,plain,
product(product(product(product(a5,a6),product(a5,a6)),product(product(a5,a6),product(a5,a6))),product(product(product(a6,a7),product(a6,a7)),product(product(a5,a6),product(a5,a6)))) = product(product(product(product(a5,a6),product(a5,a6)),product(product(a6,a7),product(a6,a7))),product(product(a5,a6),product(a5,a6))),
inference(symmetry,[status(thm)],[1375]) ).
tff(1499,plain,
product(product(a3,a4),product(a3,a4)) = product(product(product(product(a3,a4),product(a3,a4)),a6),a6),
inference(symmetry,[status(thm)],[486]) ).
tff(1500,plain,
a5 = a4,
inference(transitivity,[status(thm)],[525,493,1499,497,1361,1372,1498,1376,1379,1383,1386,1389,1391,1394,1397,1400,1403,1497,1408,1430,693,697,1432,1435,1496,1450,1457,1460,1468,1473,1495,1478,1480,1483,1486,1489,1492,182,915,167,881,883,914,891,895,810,807,805,788,785,783,776,769,766,740,869,661]) ).
tff(1501,plain,
a4 = a3,
inference(transitivity,[status(thm)],[730,729,728,726,738,720,718,711,708,704,702,686,683,228,51,71]) ).
tff(1502,plain,
a3 = a2,
inference(transitivity,[status(thm)],[241,50,255,632,635,637,639,643,646,664,659,657,654,538,535,650,630,626,623,488,146,143,252,240,226,223,620,610,608,601,597,561,558,520,517,515,513,510,506,457,452,450,444,346,331,328,316,304,190,187,172,151,149,125,36,290,1009,1007,1004,1002,999,27]) ).
tff(1503,plain,
a2 = a1,
inference(transitivity,[status(thm)],[28,993,945,943,939,934,932,925,922,919,31,1172,1046,1045,1044,1043,1028,1021,1018,1016,1013,591,589,582,578,575,1171,1168,1166,1164,1161,1152,1150,1145,1136,1133,1121,1119,1114,1111,1108,1106,1104,1101,1079,1077,1075,1072,1069,1066,1057,1055,1053,1050,1344,1341,1339,1336,1324,1322,1312,1309,1302,1299,1294,1291,1288,1285,1276,1273,1271,1265,276,208,202]) ).
tff(1504,plain,
tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15) = tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14),
inference(monotonicity,[status(thm)],[1503,1502,1501,1500,1494,1359,1358,1357,1346,1173,1010,916,913,879]) ).
tff(1505,plain,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(symmetry,[status(thm)],[1504]) ).
tff(1506,plain,
( ( tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15) )
<=> ( tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1507,axiom,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(1508,plain,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(modus_ponens,[status(thm)],[1507,1506]) ).
tff(1509,plain,
$false,
inference(unit_resolution,[status(thm)],[1508,1505]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : TOP053-1 : TPTP v9.0.0. Released v8.1.0.
% 0.12/0.12 % 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 14:05:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.55/3.73 % SZS status Unsatisfiable
% 3.55/3.73 % SZS output start Proof
% See solution above
% 3.74/3.90 % E exiting
%------------------------------------------------------------------------------