%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG007-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 04:57:45 AM UTC 2025
% Result : Unsatisfiable 7.58s 7.75s
% Output : Proof 7.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 116
% Syntax : Number of formulae : 632 ( 520 unt; 0 typ; 0 def)
% Number of atoms : 750 ( 746 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 224 ( 109 ~; 105 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 344 ( 337 !; 0 ?; 344 :)
% Comments :
%------------------------------------------------------------------------------
tff(difference_type,type,
difference: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
<=> ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
<=> ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
<=> ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_3_simplified) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,c),difference(b,c)) = difference(difference(a,difference(b,c)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
difference(difference(a,c),difference(b,c)) = difference(difference(a,difference(b,c)),c),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
difference(difference(a,difference(b,c)),c) = difference(difference(a,c),difference(b,c)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [Y: $i,X: $i] :
refl(( ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
<=> ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
<=> ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
<=> ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_2) ).
tff(15,plain,
! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(a,difference(b,c)),difference(difference(a,a),b)),difference(difference(difference(a,difference(b,c)),difference(difference(a,a),b)),a)) = difference(a,difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
difference(difference(difference(a,difference(b,c)),difference(difference(a,a),b)),difference(difference(difference(a,difference(b,c)),difference(difference(a,a),b)),a)) = difference(a,difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(( ( difference(X,difference(Y,X)) = X )
<=> ( difference(X,difference(Y,X)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
<=> ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
<=> ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_1) ).
tff(24,plain,
! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(difference(a,a),b),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b))) = difference(difference(a,a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
difference(difference(difference(a,a),b),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b))) = difference(difference(a,a),b),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(b,difference(difference(a,a),b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
difference(b,difference(difference(a,a),b)) = b,
inference(unit_resolution,[status(thm)],[29,26]) ).
tff(31,plain,
b = difference(b,difference(difference(a,a),b)),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
difference(b,c) = difference(difference(b,difference(difference(a,a),b)),c),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
difference(difference(b,difference(difference(a,a),b)),c) = difference(b,c),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(difference(a,a),b)),c) = difference(difference(b,c),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
difference(difference(b,difference(difference(a,a),b)),c) = difference(difference(b,c),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[34,7]) ).
tff(36,plain,
difference(difference(b,c),difference(difference(a,a),b)) = difference(difference(b,difference(difference(a,a),b)),c),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
difference(difference(b,c),difference(difference(a,a),b)) = difference(b,c),
inference(transitivity,[status(thm)],[36,33]) ).
tff(38,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)) = difference(difference(b,c),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
difference(difference(b,c),difference(difference(a,a),b)) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
difference(difference(difference(a,a),b),difference(difference(b,c),difference(difference(a,a),b))) = difference(difference(difference(a,a),b),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,b),a) = difference(difference(a,a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
difference(difference(a,b),a) = difference(difference(a,a),b),
inference(unit_resolution,[status(thm)],[41,7]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(a,difference(difference(a,b),a)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
difference(a,difference(difference(a,b),a)) = a,
inference(unit_resolution,[status(thm)],[43,26]) ).
tff(45,plain,
a = difference(a,difference(difference(a,b),a)),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
difference(a,b) = difference(difference(a,difference(difference(a,b),a)),b),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
difference(difference(a,difference(difference(a,b),a)),b) = difference(a,b),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,b),difference(difference(a,b),a)) = difference(difference(a,difference(difference(a,b),a)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
difference(difference(a,b),difference(difference(a,b),a)) = difference(difference(a,difference(difference(a,b),a)),b),
inference(unit_resolution,[status(thm)],[48,7]) ).
tff(50,plain,
difference(difference(a,b),difference(difference(a,b),a)) = difference(a,b),
inference(transitivity,[status(thm)],[49,47]) ).
tff(51,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),a) = difference(difference(a,b),a),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(a,difference(a,difference(a,b))) = difference(difference(a,b),difference(difference(a,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
difference(a,difference(a,difference(a,b))) = difference(difference(a,b),difference(difference(a,b),a)),
inference(unit_resolution,[status(thm)],[52,17]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(a,difference(a,b)) = difference(b,difference(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
difference(a,difference(a,b)) = difference(b,difference(b,a)),
inference(unit_resolution,[status(thm)],[54,17]) ).
tff(56,plain,
difference(b,difference(b,a)) = difference(a,difference(a,b)),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
difference(a,difference(b,difference(b,a))) = difference(a,difference(a,difference(a,b))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
difference(a,difference(b,difference(b,a))) = difference(difference(a,b),difference(difference(a,b),a)),
inference(transitivity,[status(thm)],[57,53]) ).
tff(59,plain,
difference(difference(a,difference(b,difference(b,a))),a) = difference(difference(difference(a,b),difference(difference(a,b),a)),a),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,difference(b,difference(b,a))),a) = difference(difference(a,a),difference(b,difference(b,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
difference(difference(a,difference(b,difference(b,a))),a) = difference(difference(a,a),difference(b,difference(b,a))),
inference(unit_resolution,[status(thm)],[60,7]) ).
tff(62,plain,
difference(difference(a,a),difference(b,difference(b,a))) = difference(difference(a,difference(b,difference(b,a))),a),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
difference(difference(a,a),b) = difference(difference(a,b),a),
inference(symmetry,[status(thm)],[42]) ).
tff(64,plain,
difference(a,difference(difference(a,a),b)) = difference(a,difference(difference(a,b),a)),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
difference(a,difference(difference(a,b),a)) = difference(a,difference(difference(a,a),b)),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
a = difference(a,difference(difference(a,a),b)),
inference(transitivity,[status(thm)],[45,65]) ).
tff(67,plain,
difference(a,a) = difference(a,difference(a,difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
difference(a,difference(a,difference(difference(a,a),b))) = difference(a,a),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(a,difference(a,difference(difference(a,a),b))) = difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
difference(a,difference(a,difference(difference(a,a),b))) = difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),a)),
inference(unit_resolution,[status(thm)],[69,17]) ).
tff(71,plain,
difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),a)) = difference(a,difference(a,difference(difference(a,a),b))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),a)) = difference(a,a),
inference(transitivity,[status(thm)],[71,68]) ).
tff(73,plain,
difference(difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),a)),difference(b,difference(b,a))) = difference(difference(a,a),difference(b,difference(b,a))),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,a),b),difference(b,difference(b,a))),difference(difference(difference(a,a),b),a)) = difference(difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),a)),difference(b,difference(b,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
difference(difference(difference(difference(a,a),b),difference(b,difference(b,a))),difference(difference(difference(a,a),b),a)) = difference(difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),a)),difference(b,difference(b,a))),
inference(unit_resolution,[status(thm)],[74,7]) ).
tff(76,plain,
difference(difference(difference(a,a),b),difference(b,difference(b,a))) = difference(difference(difference(a,b),a),difference(b,difference(b,a))),
inference(monotonicity,[status(thm)],[63]) ).
tff(77,plain,
difference(difference(difference(a,b),a),difference(b,difference(b,a))) = difference(difference(difference(a,a),b),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(a,b),difference(b,difference(b,a))),a) = difference(difference(difference(a,b),a),difference(b,difference(b,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
difference(difference(difference(a,b),difference(b,difference(b,a))),a) = difference(difference(difference(a,b),a),difference(b,difference(b,a))),
inference(unit_resolution,[status(thm)],[78,7]) ).
tff(80,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(a,b),difference(a,difference(a,b))) = difference(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
difference(difference(a,b),difference(a,difference(a,b))) = difference(a,b),
inference(unit_resolution,[status(thm)],[80,26]) ).
tff(82,plain,
difference(difference(a,b),difference(b,difference(b,a))) = difference(difference(a,b),difference(a,difference(a,b))),
inference(monotonicity,[status(thm)],[56]) ).
tff(83,plain,
difference(difference(a,b),difference(b,difference(b,a))) = difference(a,b),
inference(transitivity,[status(thm)],[82,81]) ).
tff(84,plain,
difference(difference(difference(a,b),difference(b,difference(b,a))),a) = difference(difference(a,b),a),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
difference(difference(a,b),a) = difference(difference(difference(a,b),difference(b,difference(b,a))),a),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
difference(difference(a,a),b) = difference(difference(difference(a,a),b),difference(b,difference(b,a))),
inference(transitivity,[status(thm)],[63,85,79,77]) ).
tff(87,plain,
difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),a)) = difference(difference(difference(difference(a,a),b),difference(b,difference(b,a))),difference(difference(difference(a,a),b),a)),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
difference(a,a) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[67,70,87,75,73,62,59,51,42]) ).
tff(89,plain,
difference(difference(a,a),difference(difference(b,c),difference(difference(a,a),b))) = difference(difference(difference(a,a),b),difference(difference(b,c),difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,a),difference(difference(b,c),difference(difference(a,a),b))) = difference(difference(a,difference(difference(b,c),difference(difference(a,a),b))),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
difference(difference(a,a),difference(difference(b,c),difference(difference(a,a),b))) = difference(difference(a,difference(difference(b,c),difference(difference(a,a),b))),a),
inference(unit_resolution,[status(thm)],[90,7]) ).
tff(92,plain,
difference(difference(a,difference(difference(b,c),difference(difference(a,a),b))),a) = difference(difference(a,a),difference(difference(b,c),difference(difference(a,a),b))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
difference(a,difference(difference(b,c),difference(difference(a,a),b))) = difference(a,difference(b,c)),
inference(monotonicity,[status(thm)],[37]) ).
tff(94,plain,
difference(a,difference(b,c)) = difference(a,difference(difference(b,c),difference(difference(a,a),b))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
difference(a,difference(b,c)) = difference(difference(a,difference(difference(a,a),b)),difference(b,c)),
inference(monotonicity,[status(thm)],[66]) ).
tff(96,plain,
difference(difference(a,difference(difference(a,a),b)),difference(b,c)) = difference(a,difference(b,c)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,difference(difference(a,a),b)),difference(b,c)) = difference(difference(a,difference(b,c)),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
difference(difference(a,difference(difference(a,a),b)),difference(b,c)) = difference(difference(a,difference(b,c)),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[97,7]) ).
tff(99,plain,
difference(difference(a,difference(b,c)),difference(difference(a,a),b)) = difference(difference(a,difference(difference(a,a),b)),difference(b,c)),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
difference(difference(a,difference(b,c)),difference(difference(a,a),b)) = difference(a,difference(difference(b,c),difference(difference(a,a),b))),
inference(transitivity,[status(thm)],[99,96,94]) ).
tff(101,plain,
difference(difference(difference(a,difference(b,c)),difference(difference(a,a),b)),a) = difference(difference(a,difference(difference(b,c),difference(difference(a,a),b))),a),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
difference(difference(difference(a,difference(b,c)),difference(difference(a,a),b)),a) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[101,92,89,40,28]) ).
tff(103,plain,
difference(difference(a,difference(b,c)),difference(difference(a,a),b)) = difference(a,difference(b,c)),
inference(transitivity,[status(thm)],[99,96]) ).
tff(104,plain,
difference(difference(difference(a,difference(b,c)),difference(difference(a,a),b)),difference(difference(difference(a,difference(b,c)),difference(difference(a,a),b)),a)) = difference(difference(a,difference(b,c)),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[103,102]) ).
tff(105,plain,
difference(difference(a,difference(b,c)),difference(difference(a,a),b)) = difference(difference(difference(a,difference(b,c)),difference(difference(a,a),b)),difference(difference(difference(a,difference(b,c)),difference(difference(a,a),b)),a)),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
difference(a,difference(b,c)) = difference(a,difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))),
inference(transitivity,[status(thm)],[95,98,105,19]) ).
tff(107,plain,
difference(difference(a,difference(b,c)),c) = difference(difference(a,difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))),c),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
difference(difference(a,difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))),c) = difference(difference(a,difference(b,c)),c),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))),c) = difference(difference(a,c),difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
difference(difference(a,difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))),c) = difference(difference(a,c),difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))),
inference(unit_resolution,[status(thm)],[109,7]) ).
tff(111,plain,
difference(difference(a,c),difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))) = difference(difference(a,difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))),c),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
difference(a,difference(difference(a,a),b)) = a,
inference(transitivity,[status(thm)],[64,44]) ).
tff(113,plain,
difference(difference(a,difference(difference(a,a),b)),c) = difference(a,c),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,c),difference(difference(a,a),b)) = difference(difference(a,difference(difference(a,a),b)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
difference(difference(a,c),difference(difference(a,a),b)) = difference(difference(a,difference(difference(a,a),b)),c),
inference(unit_resolution,[status(thm)],[114,7]) ).
tff(116,plain,
difference(difference(a,c),difference(difference(a,a),b)) = difference(a,c),
inference(transitivity,[status(thm)],[115,113]) ).
tff(117,plain,
difference(difference(difference(a,c),difference(difference(a,a),b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(a,c),difference(difference(a,a),b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
difference(difference(difference(a,c),difference(difference(a,a),b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[118,7]) ).
tff(120,plain,
difference(difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(a,a),b)) = difference(difference(difference(a,c),difference(difference(a,a),b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
difference(difference(a,b),difference(difference(a,a),b)) = difference(difference(a,b),difference(difference(a,b),a)),
inference(monotonicity,[status(thm)],[63]) ).
tff(122,plain,
difference(difference(difference(a,b),difference(difference(a,a),b)),a) = difference(difference(difference(a,b),difference(difference(a,b),a)),a),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(a,b),difference(difference(a,a),b)),a) = difference(difference(difference(a,b),a),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
difference(difference(difference(a,b),difference(difference(a,a),b)),a) = difference(difference(difference(a,b),a),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[123,7]) ).
tff(125,plain,
difference(difference(difference(a,b),a),difference(difference(a,a),b)) = difference(difference(difference(a,b),difference(difference(a,a),b)),a),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
difference(difference(difference(a,b),a),difference(b,difference(b,a))) = difference(difference(difference(a,b),difference(b,difference(b,a))),a),
inference(symmetry,[status(thm)],[79]) ).
tff(127,plain,
difference(difference(difference(a,a),b),difference(b,difference(b,a))) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[76,126,84,42]) ).
tff(128,plain,
difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),difference(b,difference(b,a)))) = difference(difference(difference(a,b),a),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[63,127]) ).
tff(129,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),difference(b,difference(b,a)))) = difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),difference(difference(a,a),b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),difference(b,difference(b,a)))) = difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),difference(difference(a,a),b))),
inference(unit_resolution,[status(thm)],[129,17]) ).
tff(131,plain,
difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),difference(difference(a,a),b))) = difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),difference(b,difference(b,a)))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
difference(a,difference(difference(a,b),difference(difference(a,b),a))) = difference(a,difference(a,b)),
inference(monotonicity,[status(thm)],[50]) ).
tff(133,plain,
difference(a,difference(a,b)) = difference(a,difference(difference(a,b),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
difference(b,difference(b,a)) = difference(a,difference(difference(a,b),difference(difference(a,b),a))),
inference(transitivity,[status(thm)],[56,133]) ).
tff(135,plain,
difference(difference(b,difference(b,a)),difference(difference(a,a),b)) = difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(difference(a,a),b)) = difference(difference(b,difference(b,a)),difference(difference(a,a),b)),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
difference(difference(a,difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[137,7]) ).
tff(139,plain,
difference(difference(a,difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a))) = difference(a,difference(a,b)),
inference(monotonicity,[status(thm)],[112,50]) ).
tff(140,plain,
difference(a,difference(a,b)) = difference(difference(a,difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
difference(b,difference(b,a)) = difference(difference(b,difference(b,a)),difference(difference(a,a),b)),
inference(transitivity,[status(thm)],[56,140,138,136]) ).
tff(142,plain,
difference(a,difference(difference(a,b),difference(difference(a,b),a))) = difference(b,difference(b,a)),
inference(transitivity,[status(thm)],[132,55]) ).
tff(143,plain,
difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(b,difference(b,a))) = difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[142,141]) ).
tff(144,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(b,difference(b,a))) = difference(difference(a,difference(b,difference(b,a))),difference(difference(a,b),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(b,difference(b,a))) = difference(difference(a,difference(b,difference(b,a))),difference(difference(a,b),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[144,7]) ).
tff(146,plain,
difference(difference(a,difference(b,difference(b,a))),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
difference(a,difference(a,difference(a,b))) = difference(a,difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[57]) ).
tff(148,plain,
difference(difference(a,b),difference(difference(a,b),a)) = difference(a,difference(a,difference(a,b))),
inference(symmetry,[status(thm)],[53]) ).
tff(149,plain,
difference(difference(a,difference(difference(a,b),a)),b) = difference(difference(a,b),difference(difference(a,b),a)),
inference(symmetry,[status(thm)],[49]) ).
tff(150,plain,
difference(a,b) = difference(a,difference(b,difference(b,a))),
inference(transitivity,[status(thm)],[46,149,148,147]) ).
tff(151,plain,
difference(difference(a,b),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(a,difference(b,difference(b,a))),difference(difference(a,b),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,b),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
difference(difference(a,b),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),b),
inference(unit_resolution,[status(thm)],[152,7]) ).
tff(154,plain,
difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),b) = difference(difference(a,b),difference(difference(a,b),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
difference(difference(b,difference(b,a)),b) = difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),b),
inference(monotonicity,[status(thm)],[134]) ).
tff(156,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(b,a)),b) = difference(difference(b,b),difference(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
difference(difference(b,difference(b,a)),b) = difference(difference(b,b),difference(b,a)),
inference(unit_resolution,[status(thm)],[156,7]) ).
tff(158,plain,
difference(difference(b,b),difference(b,a)) = difference(difference(b,difference(b,a)),b),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
difference(b,a) = difference(difference(b,difference(difference(a,a),b)),a),
inference(monotonicity,[status(thm)],[31]) ).
tff(160,plain,
difference(difference(b,difference(difference(a,a),b)),a) = difference(b,a),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(difference(a,a),b)),a) = difference(difference(b,a),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
difference(difference(b,difference(difference(a,a),b)),a) = difference(difference(b,a),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[161,7]) ).
tff(163,plain,
difference(difference(b,a),difference(difference(a,a),b)) = difference(difference(b,difference(difference(a,a),b)),a),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
difference(difference(b,a),b) = difference(difference(b,a),difference(b,difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[31]) ).
tff(165,plain,
difference(difference(b,a),difference(b,difference(difference(a,a),b))) = difference(difference(b,a),b),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(b,difference(difference(a,a),b))),a) = difference(difference(b,a),difference(b,difference(difference(a,a),b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
difference(difference(b,difference(b,difference(difference(a,a),b))),a) = difference(difference(b,a),difference(b,difference(difference(a,a),b))),
inference(unit_resolution,[status(thm)],[166,7]) ).
tff(168,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,b),difference(a,difference(a,b))) = difference(difference(a,difference(a,difference(a,b))),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
difference(difference(a,b),difference(a,difference(a,b))) = difference(difference(a,difference(a,difference(a,b))),b),
inference(unit_resolution,[status(thm)],[168,7]) ).
tff(170,plain,
difference(difference(a,difference(a,difference(a,b))),b) = difference(difference(a,b),difference(a,difference(a,b))),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),b) = difference(difference(a,difference(a,difference(a,b))),b),
inference(monotonicity,[status(thm)],[148]) ).
tff(172,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),b) = difference(a,b),
inference(transitivity,[status(thm)],[171,170,81]) ).
tff(173,plain,
difference(difference(difference(difference(a,b),difference(difference(a,b),a)),b),a) = difference(difference(a,b),a),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,b),difference(difference(a,b),a)),b),a) = difference(difference(difference(difference(a,b),difference(difference(a,b),a)),a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
difference(difference(difference(difference(a,b),difference(difference(a,b),a)),b),a) = difference(difference(difference(difference(a,b),difference(difference(a,b),a)),a),b),
inference(unit_resolution,[status(thm)],[174,7]) ).
tff(176,plain,
difference(difference(difference(difference(a,b),difference(difference(a,b),a)),a),b) = difference(difference(difference(difference(a,b),difference(difference(a,b),a)),b),a),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
difference(difference(a,b),a) = difference(difference(difference(a,b),difference(difference(a,b),a)),a),
inference(symmetry,[status(thm)],[51]) ).
tff(178,plain,
difference(difference(a,a),b) = difference(difference(difference(a,b),difference(difference(a,b),a)),a),
inference(transitivity,[status(thm)],[63,177]) ).
tff(179,plain,
difference(difference(difference(a,a),b),b) = difference(difference(difference(difference(a,b),difference(difference(a,b),a)),a),b),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
difference(difference(difference(a,a),b),b) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[179,176,173,42]) ).
tff(181,plain,
difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),b)) = difference(difference(difference(a,b),a),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[63,180]) ).
tff(182,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),b)) = difference(b,difference(b,difference(difference(a,a),b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(183,plain,
difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),b)) = difference(b,difference(b,difference(difference(a,a),b))),
inference(unit_resolution,[status(thm)],[182,17]) ).
tff(184,plain,
difference(b,difference(b,difference(difference(a,a),b))) = difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),b)),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
difference(b,difference(b,difference(difference(a,a),b))) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[184,181,125,122,51,42]) ).
tff(186,plain,
difference(difference(b,difference(b,difference(difference(a,a),b))),a) = difference(difference(difference(a,a),b),a),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
difference(difference(difference(a,a),b),a) = difference(difference(b,difference(b,difference(difference(a,a),b))),a),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
difference(difference(difference(a,a),b),a) = difference(difference(difference(a,a),b),difference(a,difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[66]) ).
tff(189,plain,
difference(difference(difference(a,a),b),difference(a,difference(difference(a,a),b))) = difference(difference(difference(a,a),b),a),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(difference(a,a),b),difference(a,difference(difference(a,a),b))) = difference(difference(a,a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(191,plain,
difference(difference(difference(a,a),b),difference(a,difference(difference(a,a),b))) = difference(difference(a,a),b),
inference(unit_resolution,[status(thm)],[190,26]) ).
tff(192,plain,
difference(difference(a,a),b) = difference(difference(difference(a,a),b),difference(a,difference(difference(a,a),b))),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
difference(difference(a,a),b) = difference(difference(b,a),b),
inference(transitivity,[status(thm)],[192,189,187,167,165]) ).
tff(194,plain,
difference(difference(b,a),difference(difference(a,a),b)) = difference(difference(b,a),difference(difference(b,a),b)),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
difference(difference(b,a),difference(difference(b,a),b)) = difference(difference(b,a),difference(difference(a,a),b)),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
difference(difference(b,a),difference(difference(b,a),b)) = difference(b,a),
inference(transitivity,[status(thm)],[195,163,160]) ).
tff(197,plain,
difference(b,b) = difference(b,difference(b,difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[31]) ).
tff(198,plain,
difference(b,difference(b,difference(difference(a,a),b))) = difference(b,b),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
difference(difference(difference(a,b),a),difference(difference(a,a),b)) = difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),b)),
inference(symmetry,[status(thm)],[181]) ).
tff(200,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a)))) = difference(difference(a,b),difference(difference(a,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a)))) = difference(difference(a,b),difference(difference(a,b),a)),
inference(unit_resolution,[status(thm)],[200,26]) ).
tff(202,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(b,c),difference(difference(a,b),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[37]) ).
tff(203,plain,
difference(difference(b,c),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(difference(a,b),difference(difference(a,b),a))),c) = difference(difference(b,c),difference(difference(a,b),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(205,plain,
difference(difference(b,difference(difference(a,b),difference(difference(a,b),a))),c) = difference(difference(b,c),difference(difference(a,b),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[204,7]) ).
tff(206,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(b,difference(difference(difference(a,b),difference(difference(a,b),a)),b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(207,plain,
difference(b,difference(difference(difference(a,b),difference(difference(a,b),a)),b)) = b,
inference(unit_resolution,[status(thm)],[206,26]) ).
tff(208,plain,
difference(difference(a,difference(a,difference(a,b))),b) = difference(difference(difference(a,b),difference(difference(a,b),a)),b),
inference(symmetry,[status(thm)],[171]) ).
tff(209,plain,
difference(a,b) = difference(difference(a,b),difference(a,difference(a,b))),
inference(symmetry,[status(thm)],[81]) ).
tff(210,plain,
difference(difference(a,b),difference(difference(a,b),a)) = difference(difference(difference(a,b),difference(difference(a,b),a)),b),
inference(transitivity,[status(thm)],[49,47,209,169,208]) ).
tff(211,plain,
difference(b,difference(difference(a,b),difference(difference(a,b),a))) = difference(b,difference(difference(difference(a,b),difference(difference(a,b),a)),b)),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
difference(b,difference(difference(a,b),difference(difference(a,b),a))) = b,
inference(transitivity,[status(thm)],[211,207]) ).
tff(213,plain,
difference(difference(b,difference(difference(a,b),difference(difference(a,b),a))),c) = difference(b,c),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
difference(b,c) = difference(difference(b,difference(difference(a,b),difference(difference(a,b),a))),c),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
difference(difference(b,c),difference(difference(a,a),b)) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a))),
inference(transitivity,[status(thm)],[36,33,214,205,203]) ).
tff(216,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(b,c),difference(difference(a,a),b))) = difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a)))),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(b,c),difference(difference(a,a),b))) = difference(difference(a,b),difference(difference(a,b),a)),
inference(transitivity,[status(thm)],[216,201]) ).
tff(218,plain,
difference(difference(a,b),difference(difference(a,b),a)) = difference(a,difference(b,difference(b,a))),
inference(transitivity,[status(thm)],[148,147]) ).
tff(219,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(b,c),difference(difference(a,a),b)))) = difference(difference(a,difference(b,difference(b,a))),difference(difference(a,b),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[218,217]) ).
tff(220,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(b,c),difference(difference(a,a),b)))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(221,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(b,c),difference(difference(a,a),b)))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a)))),
inference(unit_resolution,[status(thm)],[220,17]) ).
tff(222,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a)))) = difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(difference(a,b),difference(difference(a,b),a)),difference(difference(b,c),difference(difference(a,a),b)))),
inference(symmetry,[status(thm)],[221]) ).
tff(223,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,b),difference(difference(a,b),a)))),
inference(monotonicity,[status(thm)],[215]) ).
tff(224,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b))) = difference(b,b),
inference(transitivity,[status(thm)],[223,222,219,146,143,131,128,199,183,198]) ).
tff(225,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b))),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(b,b),difference(b,a)),
inference(monotonicity,[status(thm)],[224,196]) ).
tff(226,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b))),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(b,c),difference(difference(a,a),b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(227,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b))),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(b,c),difference(difference(a,a),b))),
inference(unit_resolution,[status(thm)],[226,7]) ).
tff(228,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(b,c),difference(difference(a,a),b))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b))),difference(difference(b,a),difference(difference(b,a),b))),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(b,c),difference(difference(a,a),b))) = difference(difference(a,b),a),
inference(transitivity,[status(thm)],[228,225,158,155,154,151,146,143,131,128,125,122,51]) ).
tff(230,plain,
difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(b,c),difference(difference(a,a),b))),difference(difference(a,a),b)) = difference(difference(difference(a,b),a),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(b,c),difference(difference(a,a),b))),difference(difference(a,a),b)) = difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(232,plain,
difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(b,c),difference(difference(a,a),b))),difference(difference(a,a),b)) = difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b))),
inference(unit_resolution,[status(thm)],[231,7]) ).
tff(233,plain,
difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b))) = difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(b,c),difference(difference(a,a),b))),difference(difference(a,a),b)),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b))) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[233,230,125,122,51,42]) ).
tff(235,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(a,b),difference(difference(a,b),a)),c) = difference(difference(difference(a,b),c),difference(difference(a,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(236,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),c) = difference(difference(difference(a,b),c),difference(difference(a,b),a)),
inference(unit_resolution,[status(thm)],[235,7]) ).
tff(237,plain,
difference(difference(a,difference(a,difference(a,b))),c) = difference(difference(difference(a,b),difference(difference(a,b),a)),c),
inference(monotonicity,[status(thm)],[53]) ).
tff(238,plain,
difference(a,b) = difference(a,difference(a,difference(a,b))),
inference(transitivity,[status(thm)],[46,149,148]) ).
tff(239,plain,
difference(difference(a,b),c) = difference(difference(a,difference(a,difference(a,b))),c),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,b),c) = difference(difference(a,c),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,plain,
difference(difference(a,b),c) = difference(difference(a,c),b),
inference(unit_resolution,[status(thm)],[240,7]) ).
tff(242,plain,
difference(difference(a,c),b) = difference(difference(a,b),c),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
difference(difference(a,c),b) = difference(difference(difference(a,b),c),difference(difference(a,b),a)),
inference(transitivity,[status(thm)],[242,239,237,236]) ).
tff(244,plain,
difference(difference(a,c),difference(difference(a,c),b)) = difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[243]) ).
tff(245,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(a,c),difference(difference(a,c),b)) = difference(b,difference(b,difference(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(246,plain,
difference(difference(a,c),difference(difference(a,c),b)) = difference(b,difference(b,difference(a,c))),
inference(unit_resolution,[status(thm)],[245,17]) ).
tff(247,plain,
difference(b,difference(b,difference(a,c))) = difference(difference(a,c),difference(difference(a,c),b)),
inference(symmetry,[status(thm)],[246]) ).
tff(248,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),c) = difference(difference(a,difference(a,difference(a,b))),c),
inference(symmetry,[status(thm)],[237]) ).
tff(249,plain,
difference(difference(difference(a,b),c),difference(difference(a,b),a)) = difference(difference(difference(a,b),difference(difference(a,b),a)),c),
inference(symmetry,[status(thm)],[236]) ).
tff(250,plain,
difference(difference(difference(a,b),c),difference(difference(a,b),a)) = difference(difference(a,difference(a,difference(a,b))),c),
inference(transitivity,[status(thm)],[249,248]) ).
tff(251,plain,
difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),b) = difference(difference(difference(a,difference(a,difference(a,b))),c),b),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
difference(difference(difference(a,difference(a,difference(a,b))),c),b) = difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),b),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(a,difference(a,difference(a,b))),b),c) = difference(difference(difference(a,difference(a,difference(a,b))),c),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
difference(difference(difference(a,difference(a,difference(a,b))),b),c) = difference(difference(difference(a,difference(a,difference(a,b))),c),b),
inference(unit_resolution,[status(thm)],[253,7]) ).
tff(255,plain,
difference(difference(a,difference(a,difference(a,b))),b) = difference(a,b),
inference(transitivity,[status(thm)],[170,81]) ).
tff(256,plain,
difference(difference(difference(a,difference(a,difference(a,b))),b),c) = difference(difference(a,b),c),
inference(monotonicity,[status(thm)],[255]) ).
tff(257,plain,
difference(difference(a,b),c) = difference(difference(difference(a,difference(a,difference(a,b))),b),c),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
difference(difference(a,difference(a,difference(a,b))),c) = difference(difference(a,b),c),
inference(symmetry,[status(thm)],[239]) ).
tff(259,plain,
difference(difference(difference(a,b),c),difference(difference(a,b),a)) = difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),b),
inference(transitivity,[status(thm)],[249,248,258,257,254,252]) ).
tff(260,plain,
difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(b,difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),b)),
inference(monotonicity,[status(thm)],[259]) ).
tff(261,plain,
difference(b,difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),b)) = difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(b,difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(263,plain,
difference(b,difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),b)) = b,
inference(unit_resolution,[status(thm)],[262,26]) ).
tff(264,plain,
b = difference(b,difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),b)),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
b = difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(transitivity,[status(thm)],[264,261]) ).
tff(266,plain,
difference(b,difference(a,c)) = difference(difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(a,c)),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
difference(difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(a,c)) = difference(b,difference(a,c)),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(a,c)) = difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(269,plain,
difference(difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(a,c)) = difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[268,7]) ).
tff(270,plain,
difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(a,c)),
inference(symmetry,[status(thm)],[269]) ).
tff(271,plain,
difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(b,difference(a,c)),
inference(transitivity,[status(thm)],[270,267]) ).
tff(272,plain,
difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))) = difference(b,difference(b,difference(a,c))),
inference(monotonicity,[status(thm)],[271]) ).
tff(273,plain,
difference(difference(b,difference(difference(a,b),difference(difference(a,b),a))),difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))) = difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))),
inference(monotonicity,[status(thm)],[212]) ).
tff(274,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(difference(a,b),difference(difference(a,b),a))),difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))) = difference(difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))),difference(difference(a,b),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(275,plain,
difference(difference(b,difference(difference(a,b),difference(difference(a,b),a))),difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))) = difference(difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))),difference(difference(a,b),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[274,7]) ).
tff(276,plain,
difference(difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(b,difference(difference(a,b),difference(difference(a,b),a))),difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
difference(b,difference(b,difference(a,c))) = difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))),
inference(symmetry,[status(thm)],[272]) ).
tff(278,plain,
difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(a,c),difference(difference(a,c),b)),
inference(symmetry,[status(thm)],[244]) ).
tff(279,plain,
difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))),
inference(transitivity,[status(thm)],[278,246,277]) ).
tff(280,plain,
difference(difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))),difference(difference(a,b),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(a,c),difference(difference(c,b),difference(a,c))) = difference(a,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(282,plain,
difference(difference(a,c),difference(difference(c,b),difference(a,c))) = difference(a,c),
inference(unit_resolution,[status(thm)],[281,26]) ).
tff(283,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(c,difference(a,c)),b) = difference(difference(c,b),difference(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(284,plain,
difference(difference(c,difference(a,c)),b) = difference(difference(c,b),difference(a,c)),
inference(unit_resolution,[status(thm)],[283,7]) ).
tff(285,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(c,difference(a,c)) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(286,plain,
difference(c,difference(a,c)) = c,
inference(unit_resolution,[status(thm)],[285,26]) ).
tff(287,plain,
difference(difference(c,difference(a,c)),b) = difference(c,b),
inference(monotonicity,[status(thm)],[286]) ).
tff(288,plain,
difference(c,b) = difference(difference(c,difference(a,c)),b),
inference(symmetry,[status(thm)],[287]) ).
tff(289,plain,
difference(c,b) = difference(difference(c,b),difference(a,c)),
inference(transitivity,[status(thm)],[288,284]) ).
tff(290,plain,
difference(difference(a,c),difference(c,b)) = difference(difference(a,c),difference(difference(c,b),difference(a,c))),
inference(monotonicity,[status(thm)],[289]) ).
tff(291,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,c),difference(c,b)) = difference(difference(a,difference(c,b)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(292,plain,
difference(difference(a,c),difference(c,b)) = difference(difference(a,difference(c,b)),c),
inference(unit_resolution,[status(thm)],[291,7]) ).
tff(293,plain,
difference(difference(a,difference(c,b)),c) = difference(difference(a,c),difference(c,b)),
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(a,difference(difference(difference(b,a),difference(difference(b,a),b)),a)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
difference(a,difference(difference(difference(b,a),difference(difference(b,a),b)),a)) = a,
inference(unit_resolution,[status(thm)],[294,26]) ).
tff(296,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(b,difference(b,difference(b,a))) = difference(difference(b,a),difference(difference(b,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(297,plain,
difference(b,difference(b,difference(b,a))) = difference(difference(b,a),difference(difference(b,a),b)),
inference(unit_resolution,[status(thm)],[296,17]) ).
tff(298,plain,
difference(difference(b,a),difference(difference(b,a),b)) = difference(b,difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[297]) ).
tff(299,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),a) = difference(difference(b,difference(b,difference(b,a))),a),
inference(monotonicity,[status(thm)],[298]) ).
tff(300,plain,
difference(difference(b,difference(b,difference(b,a))),a) = difference(difference(difference(b,a),difference(difference(b,a),b)),a),
inference(symmetry,[status(thm)],[299]) ).
tff(301,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,a),difference(b,difference(b,a))) = difference(difference(b,difference(b,difference(b,a))),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(302,plain,
difference(difference(b,a),difference(b,difference(b,a))) = difference(difference(b,difference(b,difference(b,a))),a),
inference(unit_resolution,[status(thm)],[301,7]) ).
tff(303,plain,
difference(b,a) = difference(b,difference(b,difference(b,a))),
inference(transitivity,[status(thm)],[159,162,194,298]) ).
tff(304,plain,
difference(difference(b,a),difference(b,difference(b,a))) = difference(difference(b,difference(b,difference(b,a))),difference(b,difference(b,a))),
inference(monotonicity,[status(thm)],[303]) ).
tff(305,plain,
difference(difference(b,difference(b,difference(b,a))),difference(b,difference(b,a))) = difference(difference(b,a),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
difference(b,difference(difference(b,a),difference(difference(b,a),b))) = difference(b,difference(b,a)),
inference(monotonicity,[status(thm)],[196]) ).
tff(307,plain,
difference(b,difference(b,a)) = difference(b,difference(difference(b,a),difference(difference(b,a),b))),
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
difference(difference(b,difference(b,difference(b,a))),difference(b,difference(b,a))) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(difference(b,a),difference(difference(b,a),b)))),
inference(monotonicity,[status(thm)],[297,307]) ).
tff(309,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(difference(b,a),difference(difference(b,a),b)))) = difference(difference(b,difference(b,difference(b,a))),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[308]) ).
tff(310,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(difference(b,a),difference(difference(b,a),b)))) = difference(difference(b,a),difference(difference(b,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(311,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(difference(b,a),difference(difference(b,a),b)))) = difference(difference(b,a),difference(difference(b,a),b)),
inference(unit_resolution,[status(thm)],[310,26]) ).
tff(312,plain,
difference(difference(b,a),difference(difference(b,a),b)) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(difference(b,a),difference(difference(b,a),b)))),
inference(symmetry,[status(thm)],[311]) ).
tff(313,plain,
difference(difference(b,a),difference(difference(b,a),b)) = difference(difference(difference(b,a),difference(difference(b,a),b)),a),
inference(transitivity,[status(thm)],[312,309,305,302,300]) ).
tff(314,plain,
difference(a,difference(difference(b,a),difference(difference(b,a),b))) = difference(a,difference(difference(difference(b,a),difference(difference(b,a),b)),a)),
inference(monotonicity,[status(thm)],[313]) ).
tff(315,plain,
difference(a,difference(difference(b,a),difference(difference(b,a),b))) = a,
inference(transitivity,[status(thm)],[314,295]) ).
tff(316,plain,
difference(difference(a,difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)) = difference(a,difference(c,b)),
inference(monotonicity,[status(thm)],[315]) ).
tff(317,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)) = difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(318,plain,
difference(difference(a,difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)) = difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),
inference(unit_resolution,[status(thm)],[317,7]) ).
tff(319,plain,
difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(a,difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),
inference(symmetry,[status(thm)],[318]) ).
tff(320,plain,
difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))) = difference(a,difference(c,b)),
inference(transitivity,[status(thm)],[319,316]) ).
tff(321,plain,
difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),c) = difference(difference(a,difference(c,b)),c),
inference(monotonicity,[status(thm)],[320]) ).
tff(322,plain,
difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),c) = difference(a,c),
inference(transitivity,[status(thm)],[321,293,290,282]) ).
tff(323,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),c),difference(c,b)) = difference(difference(a,c),difference(c,b)),
inference(monotonicity,[status(thm)],[322]) ).
tff(324,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),c),difference(c,b)) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(325,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),c),difference(c,b)) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),c),
inference(unit_resolution,[status(thm)],[324,7]) ).
tff(326,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),c) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),c),difference(c,b)),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)) = difference(difference(a,difference(c,b)),difference(c,b)),
inference(monotonicity,[status(thm)],[320]) ).
tff(328,plain,
difference(difference(a,difference(c,b)),difference(c,b)) = difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),
inference(symmetry,[status(thm)],[327]) ).
tff(329,plain,
difference(difference(difference(a,difference(c,b)),difference(c,b)),c) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),c),
inference(monotonicity,[status(thm)],[328]) ).
tff(330,plain,
difference(difference(difference(a,difference(c,b)),difference(c,b)),c) = difference(a,c),
inference(transitivity,[status(thm)],[329,326,323,290,282]) ).
tff(331,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),c),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[330]) ).
tff(332,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),c),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),c),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),c),
inference(unit_resolution,[status(thm)],[332,7]) ).
tff(334,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),c) = difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[333]) ).
tff(335,plain,
difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[328]) ).
tff(336,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[335]) ).
tff(337,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(338,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),
inference(unit_resolution,[status(thm)],[337,7]) ).
tff(339,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[338]) ).
tff(340,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)) = difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(transitivity,[status(thm)],[339,336]) ).
tff(341,plain,
difference(difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),c) = difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),c),
inference(monotonicity,[status(thm)],[340]) ).
tff(342,plain,
difference(difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),c) = difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(transitivity,[status(thm)],[341,334,331]) ).
tff(343,plain,
difference(difference(difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),c),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(a,b),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[342]) ).
tff(344,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),c) = difference(difference(difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),c),difference(difference(a,b),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(345,plain,
difference(difference(difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),c) = difference(difference(difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),c),difference(difference(a,b),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[344,7]) ).
tff(346,plain,
difference(difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(a,b),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[340]) ).
tff(347,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(a,b),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(349,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(a,b),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[348,7]) ).
tff(350,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(b,difference(c,b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(351,plain,
difference(b,difference(c,b)) = b,
inference(unit_resolution,[status(thm)],[350,26]) ).
tff(352,plain,
difference(difference(b,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))) = difference(b,difference(b,a)),
inference(monotonicity,[status(thm)],[351,196]) ).
tff(353,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)) = difference(difference(b,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(354,plain,
difference(difference(b,difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)) = difference(difference(b,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),
inference(unit_resolution,[status(thm)],[353,7]) ).
tff(355,plain,
difference(difference(b,difference(b,a)),difference(c,b)) = difference(difference(b,difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),
inference(monotonicity,[status(thm)],[307]) ).
tff(356,plain,
difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(c,b)) = difference(difference(b,difference(b,a)),difference(c,b)),
inference(monotonicity,[status(thm)],[142]) ).
tff(357,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(c,b)) = difference(difference(a,difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(358,plain,
difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(c,b)) = difference(difference(a,difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[357,7]) ).
tff(359,plain,
difference(difference(a,difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(c,b)),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(a,difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[320]) ).
tff(361,plain,
difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,b),difference(difference(a,b),a))) = difference(b,difference(b,a)),
inference(transitivity,[status(thm)],[360,359,356,355,354,352]) ).
tff(362,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,b),difference(difference(a,b),a))),difference(c,b)) = difference(difference(b,difference(b,a)),difference(c,b)),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,b),difference(difference(a,b),a))),difference(c,b)) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(364,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,b),difference(difference(a,b),a))),difference(c,b)) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[363,7]) ).
tff(365,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,b),difference(difference(a,b),a))),difference(c,b)),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[328]) ).
tff(367,plain,
difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))) = difference(b,difference(difference(b,a),difference(difference(b,a),b))),
inference(transitivity,[status(thm)],[366,365,362,355,354,352,307]) ).
tff(368,plain,
difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(b,difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[367]) ).
tff(369,plain,
difference(difference(b,difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(difference(difference(a,difference(c,b)),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[368]) ).
tff(370,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(b,difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(371,plain,
difference(difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(b,difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[370,7]) ).
tff(372,plain,
difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))) = b,
inference(transitivity,[status(thm)],[260,263]) ).
tff(373,plain,
difference(difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(b,a),difference(difference(b,a),b))) = difference(b,difference(b,a)),
inference(monotonicity,[status(thm)],[372,196]) ).
tff(374,plain,
difference(b,difference(b,a)) = difference(difference(b,difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(b,a),difference(difference(b,a),b))),
inference(symmetry,[status(thm)],[373]) ).
tff(375,plain,
difference(b,difference(b,a)) = difference(difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),
inference(transitivity,[status(thm)],[374,371,369,349,347]) ).
tff(376,plain,
difference(difference(b,difference(b,a)),c) = difference(difference(difference(difference(difference(difference(a,difference(c,b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(c,b)),difference(difference(a,b),difference(difference(a,b),a))),c),
inference(monotonicity,[status(thm)],[375]) ).
tff(377,plain,
difference(difference(b,difference(difference(b,a),difference(difference(b,a),b))),c) = difference(difference(b,difference(b,a)),c),
inference(monotonicity,[status(thm)],[306]) ).
tff(378,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,c),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(b,difference(difference(b,a),difference(difference(b,a),b))),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(379,plain,
difference(difference(b,c),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(b,difference(difference(b,a),difference(difference(b,a),b))),c),
inference(unit_resolution,[status(thm)],[378,7]) ).
tff(380,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(b,c),difference(difference(b,a),difference(difference(b,a),b))),
inference(monotonicity,[status(thm)],[37]) ).
tff(381,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),
inference(monotonicity,[status(thm)],[38]) ).
tff(382,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(383,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[382,7]) ).
tff(384,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),
inference(symmetry,[status(thm)],[383]) ).
tff(385,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)) = difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(transitivity,[status(thm)],[384,381,380,379,377,376,345,343,280,276,273,272,247,244]) ).
tff(386,plain,
difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b)))) = difference(difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[385,234]) ).
tff(387,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b)))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(388,plain,
difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b)))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)))),
inference(unit_resolution,[status(thm)],[387,17]) ).
tff(389,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)))) = difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)),difference(difference(b,c),difference(difference(a,a),b)))),
inference(symmetry,[status(thm)],[388]) ).
tff(390,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(391,plain,
difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))) = difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c),
inference(unit_resolution,[status(thm)],[390,7]) ).
tff(392,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)) = difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c),
inference(transitivity,[status(thm)],[384,381,380,379,377,376,345,343,280,276,273,272,247,244,391]) ).
tff(393,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b))) = difference(difference(b,c),difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c)),
inference(monotonicity,[status(thm)],[37,392]) ).
tff(394,plain,
difference(difference(b,c),difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c)) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b))),
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c)),c) = difference(difference(b,c),difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(396,plain,
difference(difference(b,difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c)),c) = difference(difference(b,c),difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c)),
inference(unit_resolution,[status(thm)],[395,7]) ).
tff(397,plain,
difference(difference(b,difference(difference(a,a),b)),difference(a,c)) = difference(b,difference(a,c)),
inference(monotonicity,[status(thm)],[30]) ).
tff(398,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(difference(a,a),b)),difference(a,c)) = difference(difference(b,difference(a,c)),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(399,plain,
difference(difference(b,difference(difference(a,a),b)),difference(a,c)) = difference(difference(b,difference(a,c)),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[398,7]) ).
tff(400,plain,
difference(difference(b,difference(a,c)),difference(difference(a,a),b)) = difference(difference(b,difference(difference(a,a),b)),difference(a,c)),
inference(symmetry,[status(thm)],[399]) ).
tff(401,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(difference(a,a),b),difference(difference(a,c),difference(difference(a,a),b))) = difference(difference(a,a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(402,plain,
difference(difference(difference(a,a),b),difference(difference(a,c),difference(difference(a,a),b))) = difference(difference(a,a),b),
inference(unit_resolution,[status(thm)],[401,26]) ).
tff(403,plain,
difference(difference(a,difference(difference(a,a),b)),c) = difference(difference(a,c),difference(difference(a,a),b)),
inference(symmetry,[status(thm)],[115]) ).
tff(404,plain,
difference(a,c) = difference(difference(a,difference(difference(a,a),b)),c),
inference(symmetry,[status(thm)],[113]) ).
tff(405,plain,
difference(a,c) = difference(difference(a,c),difference(difference(a,a),b)),
inference(transitivity,[status(thm)],[404,403]) ).
tff(406,plain,
difference(difference(difference(a,a),b),difference(a,c)) = difference(difference(difference(a,a),b),difference(difference(a,c),difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[405]) ).
tff(407,plain,
difference(b,b) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[197,184,181,125,122,51,42]) ).
tff(408,plain,
difference(difference(b,b),difference(a,c)) = difference(difference(difference(a,a),b),difference(a,c)),
inference(monotonicity,[status(thm)],[407]) ).
tff(409,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,b),difference(a,c)) = difference(difference(b,difference(a,c)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(410,plain,
difference(difference(b,b),difference(a,c)) = difference(difference(b,difference(a,c)),b),
inference(unit_resolution,[status(thm)],[409,7]) ).
tff(411,plain,
difference(difference(b,difference(a,c)),b) = difference(difference(b,b),difference(a,c)),
inference(symmetry,[status(thm)],[410]) ).
tff(412,plain,
difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),b) = difference(difference(b,difference(a,c)),b),
inference(monotonicity,[status(thm)],[271]) ).
tff(413,plain,
difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),b) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[412,411,408,406,402]) ).
tff(414,plain,
difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),b)) = difference(difference(b,difference(a,c)),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[271,413]) ).
tff(415,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),b)) = difference(b,difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(416,plain,
difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),b)) = difference(b,difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))))),
inference(unit_resolution,[status(thm)],[415,17]) ).
tff(417,plain,
difference(b,difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))))) = difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),b)),
inference(symmetry,[status(thm)],[416]) ).
tff(418,plain,
difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c) = difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[391]) ).
tff(419,plain,
difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c) = difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a)))),
inference(transitivity,[status(thm)],[418,278,246,277]) ).
tff(420,plain,
difference(b,difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c)) = difference(b,difference(b,difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))))),
inference(monotonicity,[status(thm)],[419]) ).
tff(421,plain,
difference(b,difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c)) = difference(b,difference(a,c)),
inference(transitivity,[status(thm)],[420,417,414,400,397]) ).
tff(422,plain,
difference(difference(b,difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c)),c) = difference(difference(b,difference(a,c)),c),
inference(monotonicity,[status(thm)],[421]) ).
tff(423,plain,
difference(difference(b,difference(a,c)),c) = difference(difference(b,difference(difference(a,difference(difference(difference(a,b),c),difference(difference(a,b),a))),c)),c),
inference(symmetry,[status(thm)],[422]) ).
tff(424,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,c),difference(a,c)) = difference(difference(b,difference(a,c)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(425,plain,
difference(difference(b,c),difference(a,c)) = difference(difference(b,difference(a,c)),c),
inference(unit_resolution,[status(thm)],[424,7]) ).
tff(426,plain,
difference(b,c) = difference(difference(b,c),difference(difference(a,a),b)),
inference(transitivity,[status(thm)],[32,35]) ).
tff(427,plain,
difference(difference(b,c),difference(a,c)) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),
inference(monotonicity,[status(thm)],[426]) ).
tff(428,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)) = difference(difference(b,c),difference(a,c)),
inference(symmetry,[status(thm)],[427]) ).
tff(429,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(a,c)),
inference(monotonicity,[status(thm)],[39]) ).
tff(430,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(a,c)) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),
inference(symmetry,[status(thm)],[429]) ).
tff(431,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(a,c)) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(432,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(a,c)) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[431,7]) ).
tff(433,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(a,c)),
inference(symmetry,[status(thm)],[432]) ).
tff(434,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b))),
inference(transitivity,[status(thm)],[433,430,428,425,423,396,394]) ).
tff(435,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(difference(a,a),b)))),
inference(monotonicity,[status(thm)],[434]) ).
tff(436,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),
inference(transitivity,[status(thm)],[433,430]) ).
tff(437,plain,
difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(b,a),difference(difference(b,a),b))),
inference(monotonicity,[status(thm)],[436]) ).
tff(438,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),
inference(symmetry,[status(thm)],[437]) ).
tff(439,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(440,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(a,c)),
inference(unit_resolution,[status(thm)],[439,7]) ).
tff(441,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(a,c)) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(b,a),difference(difference(b,a),b))),
inference(symmetry,[status(thm)],[440]) ).
tff(442,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(b,difference(b,a)),c),
inference(transitivity,[status(thm)],[380,379,377]) ).
tff(443,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(a,c)) = difference(difference(difference(b,difference(b,a)),c),difference(a,c)),
inference(monotonicity,[status(thm)],[442]) ).
tff(444,plain,
difference(difference(difference(b,difference(b,a)),c),difference(a,c)) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(a,c)),
inference(symmetry,[status(thm)],[443]) ).
tff(445,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(b,difference(b,a)),difference(a,c)),c) = difference(difference(difference(b,difference(b,a)),c),difference(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(446,plain,
difference(difference(difference(b,difference(b,a)),difference(a,c)),c) = difference(difference(difference(b,difference(b,a)),c),difference(a,c)),
inference(unit_resolution,[status(thm)],[445,7]) ).
tff(447,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(a,difference(a,c)) = difference(c,difference(c,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(448,plain,
difference(a,difference(a,c)) = difference(c,difference(c,a)),
inference(unit_resolution,[status(thm)],[447,17]) ).
tff(449,plain,
difference(c,difference(c,a)) = difference(a,difference(a,c)),
inference(symmetry,[status(thm)],[448]) ).
tff(450,plain,
difference(difference(c,difference(c,a)),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(a,difference(a,c)),difference(difference(a,b),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[449]) ).
tff(451,plain,
difference(difference(a,difference(a,c)),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(c,difference(c,a)),difference(difference(a,b),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[450]) ).
tff(452,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(a,c)) = difference(difference(a,difference(a,c)),difference(difference(a,b),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(453,plain,
difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(a,c)) = difference(difference(a,difference(a,c)),difference(difference(a,b),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[452,7]) ).
tff(454,plain,
difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(a,c)) = difference(difference(b,difference(b,a)),difference(a,c)),
inference(monotonicity,[status(thm)],[142]) ).
tff(455,plain,
difference(difference(b,difference(b,a)),difference(a,c)) = difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),difference(a,c)),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
difference(difference(b,difference(b,a)),difference(a,c)) = difference(difference(c,difference(c,a)),difference(difference(a,b),difference(difference(a,b),a))),
inference(transitivity,[status(thm)],[455,453,451]) ).
tff(457,plain,
difference(difference(difference(b,difference(b,a)),difference(a,c)),c) = difference(difference(difference(c,difference(c,a)),difference(difference(a,b),difference(difference(a,b),a))),c),
inference(monotonicity,[status(thm)],[456]) ).
tff(458,plain,
difference(difference(difference(c,difference(c,a)),difference(difference(a,b),difference(difference(a,b),a))),c) = difference(difference(difference(b,difference(b,a)),difference(a,c)),c),
inference(symmetry,[status(thm)],[457]) ).
tff(459,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(c,difference(c,a)),difference(difference(a,b),difference(difference(a,b),a))),c) = difference(difference(difference(c,difference(c,a)),c),difference(difference(a,b),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(460,plain,
difference(difference(difference(c,difference(c,a)),difference(difference(a,b),difference(difference(a,b),a))),c) = difference(difference(difference(c,difference(c,a)),c),difference(difference(a,b),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[459,7]) ).
tff(461,plain,
difference(difference(difference(c,difference(c,a)),c),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(difference(c,difference(c,a)),difference(difference(a,b),difference(difference(a,b),a))),c),
inference(symmetry,[status(thm)],[460]) ).
tff(462,plain,
difference(difference(difference(difference(a,a),b),difference(b,difference(b,a))),difference(difference(difference(a,a),b),a)) = difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),a)),
inference(symmetry,[status(thm)],[87]) ).
tff(463,plain,
difference(difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),a)),difference(b,difference(b,a))) = difference(difference(difference(difference(a,a),b),difference(b,difference(b,a))),difference(difference(difference(a,a),b),a)),
inference(symmetry,[status(thm)],[75]) ).
tff(464,plain,
difference(difference(a,a),difference(b,difference(b,a))) = difference(difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),a)),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[73]) ).
tff(465,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),a) = difference(difference(a,difference(b,difference(b,a))),a),
inference(symmetry,[status(thm)],[59]) ).
tff(466,plain,
difference(difference(difference(a,a),b),difference(a,c)) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[406,402]) ).
tff(467,plain,
difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),difference(a,c))) = difference(difference(difference(a,b),a),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[63,466]) ).
tff(468,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(a,c),difference(difference(a,c),difference(difference(a,a),b))) = difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),difference(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(469,plain,
difference(difference(a,c),difference(difference(a,c),difference(difference(a,a),b))) = difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),difference(a,c))),
inference(unit_resolution,[status(thm)],[468,17]) ).
tff(470,plain,
difference(difference(a,difference(difference(b,a),difference(difference(b,a),b))),c) = difference(a,c),
inference(monotonicity,[status(thm)],[315]) ).
tff(471,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,difference(difference(b,a),difference(difference(b,a),b))),c) = difference(difference(a,c),difference(difference(b,a),difference(difference(b,a),b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(472,plain,
difference(difference(a,difference(difference(b,a),difference(difference(b,a),b))),c) = difference(difference(a,c),difference(difference(b,a),difference(difference(b,a),b))),
inference(unit_resolution,[status(thm)],[471,7]) ).
tff(473,plain,
difference(difference(a,c),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(a,difference(difference(b,a),difference(difference(b,a),b))),c),
inference(symmetry,[status(thm)],[472]) ).
tff(474,plain,
difference(difference(a,c),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(a,c),difference(difference(a,a),b)),
inference(transitivity,[status(thm)],[473,470,404,403]) ).
tff(475,plain,
difference(difference(a,c),difference(difference(a,c),difference(difference(b,a),difference(difference(b,a),b)))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[474]) ).
tff(476,plain,
difference(a,c) = difference(difference(a,difference(difference(b,a),difference(difference(b,a),b))),c),
inference(symmetry,[status(thm)],[470]) ).
tff(477,plain,
difference(a,c) = difference(difference(a,c),difference(difference(b,a),difference(difference(b,a),b))),
inference(transitivity,[status(thm)],[476,472]) ).
tff(478,plain,
difference(difference(a,c),difference(a,c)) = difference(difference(a,c),difference(difference(a,c),difference(difference(b,a),difference(difference(b,a),b)))),
inference(monotonicity,[status(thm)],[477]) ).
tff(479,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,difference(a,c)),c) = difference(difference(a,c),difference(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(480,plain,
difference(difference(a,difference(a,c)),c) = difference(difference(a,c),difference(a,c)),
inference(unit_resolution,[status(thm)],[479,7]) ).
tff(481,plain,
difference(difference(c,difference(c,a)),c) = difference(difference(a,difference(a,c)),c),
inference(monotonicity,[status(thm)],[449]) ).
tff(482,plain,
difference(difference(c,difference(c,a)),c) = difference(a,a),
inference(transitivity,[status(thm)],[481,480,478,475,469,467,125,122,465,61,464,463,462,71,68]) ).
tff(483,plain,
difference(difference(difference(c,difference(c,a)),c),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(a,a),difference(difference(a,b),difference(difference(a,b),a))),
inference(monotonicity,[status(thm)],[482]) ).
tff(484,plain,
difference(difference(a,a),difference(difference(a,b),difference(difference(a,b),a))) = difference(difference(difference(c,difference(c,a)),c),difference(difference(a,b),difference(difference(a,b),a))),
inference(symmetry,[status(thm)],[483]) ).
tff(485,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),a) = difference(difference(a,a),difference(difference(a,b),difference(difference(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(486,plain,
difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),a) = difference(difference(a,a),difference(difference(a,b),difference(difference(a,b),a))),
inference(unit_resolution,[status(thm)],[485,7]) ).
tff(487,plain,
difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),a) = difference(difference(b,difference(b,a)),a),
inference(monotonicity,[status(thm)],[142]) ).
tff(488,plain,
difference(difference(b,difference(b,a)),a) = difference(difference(a,difference(difference(a,b),difference(difference(a,b),a))),a),
inference(symmetry,[status(thm)],[487]) ).
tff(489,plain,
difference(difference(b,difference(b,a)),a) = difference(difference(difference(b,difference(b,a)),difference(difference(a,a),b)),a),
inference(monotonicity,[status(thm)],[141]) ).
tff(490,plain,
difference(difference(difference(b,difference(b,a)),difference(difference(a,a),b)),a) = difference(difference(b,difference(b,a)),a),
inference(symmetry,[status(thm)],[489]) ).
tff(491,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(b,difference(b,a)),difference(difference(a,a),b)),a) = difference(difference(difference(b,difference(b,a)),a),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(492,plain,
difference(difference(difference(b,difference(b,a)),difference(difference(a,a),b)),a) = difference(difference(difference(b,difference(b,a)),a),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[491,7]) ).
tff(493,plain,
difference(difference(difference(b,difference(b,a)),a),difference(difference(a,a),b)) = difference(difference(difference(b,difference(b,a)),difference(difference(a,a),b)),a),
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(b,difference(b,a)),difference(b,difference(b,a))),a) = difference(difference(difference(b,difference(b,a)),a),difference(b,difference(b,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(495,plain,
difference(difference(difference(b,difference(b,a)),difference(b,difference(b,a))),a) = difference(difference(difference(b,difference(b,a)),a),difference(b,difference(b,a))),
inference(unit_resolution,[status(thm)],[494,7]) ).
tff(496,plain,
difference(difference(b,difference(b,a)),difference(b,difference(b,a))) = difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[141]) ).
tff(497,plain,
difference(difference(b,difference(b,a)),difference(b,difference(b,a))) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[496,131,128,125,122,51,42]) ).
tff(498,plain,
difference(difference(difference(b,difference(b,a)),difference(b,difference(b,a))),a) = difference(difference(difference(a,a),b),a),
inference(monotonicity,[status(thm)],[497]) ).
tff(499,plain,
difference(difference(difference(a,a),b),a) = difference(difference(difference(b,difference(b,a)),difference(b,difference(b,a))),a),
inference(symmetry,[status(thm)],[498]) ).
tff(500,plain,
difference(difference(a,a),b) = difference(difference(difference(b,difference(b,a)),a),difference(b,difference(b,a))),
inference(transitivity,[status(thm)],[192,189,499,495]) ).
tff(501,plain,
difference(difference(difference(b,difference(b,a)),a),difference(difference(a,a),b)) = difference(difference(difference(b,difference(b,a)),a),difference(difference(difference(b,difference(b,a)),a),difference(b,difference(b,a)))),
inference(monotonicity,[status(thm)],[500]) ).
tff(502,plain,
difference(difference(difference(b,difference(b,a)),a),difference(difference(difference(b,difference(b,a)),a),difference(b,difference(b,a)))) = difference(difference(difference(b,difference(b,a)),a),difference(difference(a,a),b)),
inference(symmetry,[status(thm)],[501]) ).
tff(503,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),a))) = difference(difference(difference(b,difference(b,a)),a),difference(difference(difference(b,difference(b,a)),a),difference(b,difference(b,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(504,plain,
difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),a))) = difference(difference(difference(b,difference(b,a)),a),difference(difference(difference(b,difference(b,a)),a),difference(b,difference(b,a)))),
inference(unit_resolution,[status(thm)],[503,17]) ).
tff(505,plain,
difference(a,difference(b,difference(b,a))) = difference(a,b),
inference(transitivity,[status(thm)],[57,53,49,47]) ).
tff(506,plain,
difference(a,difference(a,difference(b,difference(b,a)))) = difference(a,difference(a,b)),
inference(monotonicity,[status(thm)],[505]) ).
tff(507,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(a,difference(a,difference(b,difference(b,a)))) = difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(508,plain,
difference(a,difference(a,difference(b,difference(b,a)))) = difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),a)),
inference(unit_resolution,[status(thm)],[507,17]) ).
tff(509,plain,
difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),a)) = difference(a,difference(a,difference(b,difference(b,a)))),
inference(symmetry,[status(thm)],[508]) ).
tff(510,plain,
difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),a)) = difference(difference(b,difference(b,a)),difference(difference(a,a),b)),
inference(transitivity,[status(thm)],[509,506,140,138,136]) ).
tff(511,plain,
difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),a))) = difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[510]) ).
tff(512,plain,
difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),difference(difference(a,a),b))) = difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),difference(difference(b,difference(b,a)),a))),
inference(symmetry,[status(thm)],[511]) ).
tff(513,plain,
difference(difference(difference(a,b),a),difference(difference(a,a),b)) = difference(difference(difference(a,a),b),difference(difference(difference(a,a),b),difference(b,difference(b,a)))),
inference(symmetry,[status(thm)],[128]) ).
tff(514,plain,
difference(difference(difference(a,b),difference(difference(a,b),a)),a) = difference(difference(difference(a,b),difference(difference(a,a),b)),a),
inference(symmetry,[status(thm)],[122]) ).
tff(515,plain,
difference(difference(a,a),b) = difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b))),
inference(transitivity,[status(thm)],[63,177,514,124,513,130,512,504,502,493,490,488,486,484,461,458,446,444,441,438]) ).
tff(516,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),
inference(transitivity,[status(thm)],[429,432]) ).
tff(517,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)) = difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b)))),
inference(monotonicity,[status(thm)],[516,515]) ).
tff(518,plain,
difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b)))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),
inference(symmetry,[status(thm)],[517]) ).
tff(519,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b)))) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(520,plain,
difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b)))) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))),
inference(unit_resolution,[status(thm)],[519,17]) ).
tff(521,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))) = difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),difference(difference(b,a),difference(difference(b,a),b)))),
inference(symmetry,[status(thm)],[520]) ).
tff(522,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))) = difference(difference(b,difference(b,difference(b,a))),difference(b,difference(b,a))),
inference(monotonicity,[status(thm)],[298]) ).
tff(523,plain,
difference(difference(b,difference(b,difference(b,a))),difference(b,difference(b,a))) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[522]) ).
tff(524,plain,
difference(difference(b,a),difference(difference(b,a),b)) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),
inference(transitivity,[status(thm)],[312,309,523]) ).
tff(525,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))),
inference(monotonicity,[status(thm)],[524]) ).
tff(526,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))),
inference(symmetry,[status(thm)],[525]) ).
tff(527,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))),difference(b,difference(b,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(528,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))),difference(b,difference(b,a))),
inference(unit_resolution,[status(thm)],[527,7]) ).
tff(529,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))),difference(b,difference(b,a))) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))),
inference(symmetry,[status(thm)],[528]) ).
tff(530,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),
inference(transitivity,[status(thm)],[521,518,433,430]) ).
tff(531,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))),difference(b,difference(b,a))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(b,difference(b,a))),
inference(monotonicity,[status(thm)],[530]) ).
tff(532,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(b,difference(b,a))) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)))),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[531]) ).
tff(533,plain,
difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),c) = difference(difference(b,difference(a,c)),c),
inference(monotonicity,[status(thm)],[271]) ).
tff(534,plain,
difference(difference(b,difference(a,c)),c) = difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),c),
inference(symmetry,[status(thm)],[533]) ).
tff(535,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)) = difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),c),
inference(transitivity,[status(thm)],[428,425,534]) ).
tff(536,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(b,difference(b,a))) = difference(difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),c),difference(b,difference(b,a))),
inference(monotonicity,[status(thm)],[535]) ).
tff(537,plain,
difference(difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),c),difference(b,difference(b,a))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[536]) ).
tff(538,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(b,difference(b,a))),c) = difference(difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),c),difference(b,difference(b,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(539,plain,
difference(difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(b,difference(b,a))),c) = difference(difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),c),difference(b,difference(b,a))),
inference(unit_resolution,[status(thm)],[538,7]) ).
tff(540,plain,
difference(difference(b,difference(difference(a,a),b)),difference(b,difference(b,a))) = difference(b,difference(b,difference(b,a))),
inference(monotonicity,[status(thm)],[30]) ).
tff(541,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(difference(a,a),b)),difference(b,difference(b,a))) = difference(difference(b,difference(b,difference(b,a))),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(542,plain,
difference(difference(b,difference(difference(a,a),b)),difference(b,difference(b,a))) = difference(difference(b,difference(b,difference(b,a))),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[541,7]) ).
tff(543,plain,
difference(difference(b,difference(b,difference(b,a))),difference(difference(a,a),b)) = difference(difference(b,difference(difference(a,a),b)),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[542]) ).
tff(544,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c))) = difference(difference(a,c),difference(difference(a,c),difference(difference(b,a),difference(difference(b,a),b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(545,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c))) = difference(difference(a,c),difference(difference(a,c),difference(difference(b,a),difference(difference(b,a),b)))),
inference(unit_resolution,[status(thm)],[544,17]) ).
tff(546,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))) = difference(difference(b,a),difference(difference(b,a),b)),
inference(transitivity,[status(thm)],[522,308,311]) ).
tff(547,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),difference(a,c)) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),
inference(monotonicity,[status(thm)],[546]) ).
tff(548,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),difference(a,c)) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(549,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),difference(a,c)) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),
inference(unit_resolution,[status(thm)],[548,7]) ).
tff(550,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),difference(a,c)),
inference(symmetry,[status(thm)],[549]) ).
tff(551,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),
inference(transitivity,[status(thm)],[550,547]) ).
tff(552,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a)))) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c))),
inference(monotonicity,[status(thm)],[551]) ).
tff(553,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a)))) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[552,545,475,469,467,125,122,51,42]) ).
tff(554,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))))) = difference(difference(b,difference(b,difference(b,a))),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[298,553]) ).
tff(555,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))))) = difference(difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),difference(difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),difference(difference(b,a),difference(difference(b,a),b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(556,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))))) = difference(difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),difference(difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),difference(difference(b,a),difference(difference(b,a),b)))),
inference(unit_resolution,[status(thm)],[555,17]) ).
tff(557,plain,
difference(difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),difference(difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),difference(difference(b,a),difference(difference(b,a),b)))) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))))),
inference(symmetry,[status(thm)],[556]) ).
tff(558,plain,
difference(difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(difference(b,a),difference(difference(b,a),b))),
inference(monotonicity,[status(thm)],[551]) ).
tff(559,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),difference(difference(b,a),difference(difference(b,a),b))),
inference(symmetry,[status(thm)],[558]) ).
tff(560,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(a,c)) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(difference(b,a),difference(difference(b,a),b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(561,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(a,c)) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(difference(b,a),difference(difference(b,a),b))),
inference(unit_resolution,[status(thm)],[560,7]) ).
tff(562,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(b,a)),difference(b,difference(b,a))) = difference(difference(b,difference(b,difference(b,a))),difference(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(563,plain,
difference(difference(b,difference(b,a)),difference(b,difference(b,a))) = difference(difference(b,difference(b,difference(b,a))),difference(b,a)),
inference(unit_resolution,[status(thm)],[562,7]) ).
tff(564,plain,
difference(difference(b,difference(b,difference(b,a))),difference(b,a)) = difference(difference(b,difference(b,a)),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[563]) ).
tff(565,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(b,difference(b,difference(b,a))),difference(b,a)),
inference(monotonicity,[status(thm)],[298,196]) ).
tff(566,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(b,a),difference(difference(b,a),b))) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[565,564,496,131,128,125,122,51,42]) ).
tff(567,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(a,c)) = difference(difference(difference(a,a),b),difference(a,c)),
inference(monotonicity,[status(thm)],[566]) ).
tff(568,plain,
difference(difference(difference(a,a),b),difference(a,c)) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(b,a),difference(difference(b,a),b))),difference(a,c)),
inference(symmetry,[status(thm)],[567]) ).
tff(569,plain,
difference(difference(difference(a,a),b),difference(difference(a,c),difference(difference(a,a),b))) = difference(difference(difference(a,a),b),difference(a,c)),
inference(symmetry,[status(thm)],[406]) ).
tff(570,plain,
difference(difference(a,a),b) = difference(difference(difference(a,a),b),difference(difference(a,c),difference(difference(a,a),b))),
inference(symmetry,[status(thm)],[402]) ).
tff(571,plain,
difference(difference(a,a),b) = difference(difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),difference(difference(b,a),difference(difference(b,a),b))),
inference(transitivity,[status(thm)],[570,569,568,561,559]) ).
tff(572,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(b,difference(b,a))),difference(a,c)),
inference(symmetry,[status(thm)],[547]) ).
tff(573,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),
inference(transitivity,[status(thm)],[572,549]) ).
tff(574,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(difference(a,a),b)) = difference(difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),difference(difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(b,difference(b,a))),difference(difference(b,a),difference(difference(b,a),b)))),
inference(monotonicity,[status(thm)],[573,571]) ).
tff(575,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(a,a),b)),difference(a,c)) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(576,plain,
difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(a,a),b)),difference(a,c)) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[575,7]) ).
tff(577,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(a,a),b)) = difference(difference(b,difference(b,difference(b,a))),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[298]) ).
tff(578,plain,
difference(difference(b,difference(b,difference(b,a))),difference(difference(a,a),b)) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(a,a),b)),
inference(symmetry,[status(thm)],[577]) ).
tff(579,plain,
difference(b,difference(b,difference(b,a))) = difference(difference(b,difference(difference(a,a),b)),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[540]) ).
tff(580,plain,
difference(difference(b,a),difference(difference(b,a),b)) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(a,a),b)),
inference(transitivity,[status(thm)],[298,579,542,578]) ).
tff(581,plain,
difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)) = difference(difference(difference(difference(b,a),difference(difference(b,a),b)),difference(difference(a,a),b)),difference(a,c)),
inference(monotonicity,[status(thm)],[580]) ).
tff(582,plain,
difference(difference(b,difference(b,difference(b,a))),difference(a,c)) = difference(difference(difference(b,a),difference(difference(b,a),b)),difference(a,c)),
inference(monotonicity,[status(thm)],[297]) ).
tff(583,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(b,difference(b,a))),difference(a,c)) = difference(difference(b,difference(a,c)),difference(b,difference(b,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(584,plain,
difference(difference(b,difference(b,difference(b,a))),difference(a,c)) = difference(difference(b,difference(a,c)),difference(b,difference(b,a))),
inference(unit_resolution,[status(thm)],[583,7]) ).
tff(585,plain,
difference(difference(b,difference(a,c)),difference(b,difference(b,a))) = difference(difference(b,difference(b,difference(b,a))),difference(a,c)),
inference(symmetry,[status(thm)],[584]) ).
tff(586,plain,
difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(b,difference(b,a))) = difference(difference(b,difference(a,c)),difference(b,difference(b,a))),
inference(monotonicity,[status(thm)],[271]) ).
tff(587,plain,
difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(b,difference(b,a))) = difference(b,difference(b,difference(b,a))),
inference(transitivity,[status(thm)],[586,585,582,581,576,574,557,554,543,540]) ).
tff(588,plain,
difference(difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(b,difference(b,a))),c) = difference(difference(b,difference(b,difference(b,a))),c),
inference(monotonicity,[status(thm)],[587]) ).
tff(589,plain,
difference(difference(b,difference(b,difference(b,a))),c) = difference(difference(difference(difference(b,difference(a,c)),difference(difference(difference(a,b),c),difference(difference(a,b),a))),difference(b,difference(b,a))),c),
inference(symmetry,[status(thm)],[588]) ).
tff(590,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,c),difference(b,difference(b,a))) = difference(difference(b,difference(b,difference(b,a))),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(591,plain,
difference(difference(b,c),difference(b,difference(b,a))) = difference(difference(b,difference(b,difference(b,a))),c),
inference(unit_resolution,[status(thm)],[590,7]) ).
tff(592,plain,
difference(difference(b,c),difference(b,difference(b,a))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(b,difference(b,a))),
inference(monotonicity,[status(thm)],[426]) ).
tff(593,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(b,difference(b,a))) = difference(difference(b,c),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[592]) ).
tff(594,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(b,difference(b,a))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(b,difference(b,a))),
inference(monotonicity,[status(thm)],[39]) ).
tff(595,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(b,difference(b,a))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[594]) ).
tff(596,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(b,difference(b,a))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(b,difference(b,a))),difference(difference(a,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(597,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(b,difference(b,a))) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(b,difference(b,a))),difference(difference(a,a),b)),
inference(unit_resolution,[status(thm)],[596,7]) ).
tff(598,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(b,difference(b,a))),difference(difference(a,a),b)) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(a,a),b)),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[597]) ).
tff(599,plain,
difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(b,difference(b,a))),difference(difference(a,a),b)) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b)),
inference(transitivity,[status(thm)],[598,595,593,591,589,539,537,532,529,526,521,518]) ).
tff(600,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(b,difference(b,a))),difference(difference(a,a),b))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(a,c)),difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[599]) ).
tff(601,plain,
difference(difference(b,difference(b,difference(b,a))),c) = difference(difference(b,c),difference(b,difference(b,a))),
inference(symmetry,[status(thm)],[591]) ).
tff(602,plain,
difference(difference(b,a),c) = difference(difference(b,difference(b,difference(b,a))),c),
inference(monotonicity,[status(thm)],[303]) ).
tff(603,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,c),a) = difference(difference(b,a),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(604,plain,
difference(difference(b,c),a) = difference(difference(b,a),c),
inference(unit_resolution,[status(thm)],[603,7]) ).
tff(605,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),a) = difference(difference(b,c),a),
inference(monotonicity,[status(thm)],[37]) ).
tff(606,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),a) = difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(b,difference(b,a))),difference(difference(a,a),b)),
inference(transitivity,[status(thm)],[605,604,602,601,592,594,597]) ).
tff(607,plain,
difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(b,c),difference(difference(a,a),b)),a)) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(difference(b,c),difference(difference(a,a),b)),difference(b,difference(b,a))),difference(difference(a,a),b))),
inference(monotonicity,[status(thm)],[606]) ).
tff(608,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(a,difference(a,difference(difference(b,c),difference(difference(a,a),b)))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(b,c),difference(difference(a,a),b)),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(609,plain,
difference(a,difference(a,difference(difference(b,c),difference(difference(a,a),b)))) = difference(difference(difference(b,c),difference(difference(a,a),b)),difference(difference(difference(b,c),difference(difference(a,a),b)),a)),
inference(unit_resolution,[status(thm)],[608,17]) ).
tff(610,plain,
difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b))) = difference(a,difference(a,difference(difference(b,c),difference(difference(a,a),b)))),
inference(monotonicity,[status(thm)],[100]) ).
tff(611,plain,
difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b))) = difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a))),
inference(transitivity,[status(thm)],[610,609,607,600,435,389,386,120,117]) ).
tff(612,plain,
difference(difference(a,c),difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))) = difference(difference(a,c),difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a)))),
inference(monotonicity,[status(thm)],[611]) ).
tff(613,plain,
difference(difference(a,c),difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a)))) = difference(difference(a,c),difference(a,difference(difference(a,difference(b,c)),difference(difference(a,a),b)))),
inference(symmetry,[status(thm)],[612]) ).
tff(614,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(a,c))) = difference(difference(a,c),difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(615,plain,
difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(a,c))) = difference(difference(a,c),difference(difference(a,c),difference(difference(difference(a,b),c),difference(difference(a,b),a)))),
inference(unit_resolution,[status(thm)],[614,17]) ).
tff(616,plain,
difference(difference(a,c),difference(a,c)) = difference(difference(difference(a,b),difference(difference(a,b),a)),a),
inference(transitivity,[status(thm)],[478,475,469,467,125,122]) ).
tff(617,plain,
difference(difference(difference(a,c),difference(a,c)),b) = difference(difference(difference(difference(a,b),difference(difference(a,b),a)),a),b),
inference(monotonicity,[status(thm)],[616]) ).
tff(618,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(a,c),b),difference(a,c)) = difference(difference(difference(a,c),difference(a,c)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(619,plain,
difference(difference(difference(a,c),b),difference(a,c)) = difference(difference(difference(a,c),difference(a,c)),b),
inference(unit_resolution,[status(thm)],[618,7]) ).
tff(620,plain,
difference(difference(difference(a,b),c),difference(difference(a,b),a)) = difference(difference(a,c),b),
inference(transitivity,[status(thm)],[249,248,258,241]) ).
tff(621,plain,
difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(a,c)) = difference(difference(difference(a,c),b),difference(a,c)),
inference(monotonicity,[status(thm)],[620]) ).
tff(622,plain,
difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(a,c)) = difference(difference(a,a),b),
inference(transitivity,[status(thm)],[621,619,617,176,173,42]) ).
tff(623,plain,
difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(a,c))) = difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(difference(a,a),b)),
inference(monotonicity,[status(thm)],[622]) ).
tff(624,plain,
difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(difference(a,a),b)) = difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(a,c))),
inference(symmetry,[status(thm)],[623]) ).
tff(625,plain,
difference(difference(difference(a,b),c),difference(difference(a,b),a)) = difference(difference(a,b),c),
inference(transitivity,[status(thm)],[249,248,258]) ).
tff(626,plain,
difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(difference(a,a),b)) = difference(difference(difference(a,b),c),difference(difference(a,b),a)),
inference(monotonicity,[status(thm)],[625,63]) ).
tff(627,plain,
difference(difference(difference(a,b),c),difference(difference(a,b),a)) = difference(difference(difference(difference(a,b),c),difference(difference(a,b),a)),difference(difference(a,a),b)),
inference(symmetry,[status(thm)],[626]) ).
tff(628,plain,
difference(difference(a,b),c) = difference(difference(a,c),difference(b,c)),
inference(transitivity,[status(thm)],[239,237,236,627,624,615,613,111,108,10]) ).
tff(629,plain,
( ( difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)) )
<=> ( difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(630,axiom,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_difference_3) ).
tff(631,plain,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
inference(modus_ponens,[status(thm)],[630,629]) ).
tff(632,plain,
$false,
inference(unit_resolution,[status(thm)],[631,628]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG007-1 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n009.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Jun 19 10:41:33 EDT 2025
% 0.10/0.32 % CPUTime :
% 7.58/7.75 % SZS status Unsatisfiable
% 7.58/7.75 % SZS output start Proof
% See solution above
% 7.67/7.83 % E exiting
%------------------------------------------------------------------------------