TSTP Solution File: ALG007-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Tue Sep 6 16:07:00 EDT 2022
% Result : Unsatisfiable 9.30s 6.23s
% Output : Proof 9.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 57
% Syntax : Number of formulae : 251 ( 198 unt; 4 typ; 0 def)
% Number of atoms : 302 ( 298 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 98 ( 46 ~; 42 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 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 : 174 ( 167 !; 0 ?; 174 :)
% 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/sandbox/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(Y,X)) = X )
<=> ( difference(X,difference(Y,X)) = X ) )),
inference(bind,[status(th)],]) ).
tff(12,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)],[11]) ).
tff(13,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(14,axiom,
! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_1) ).
tff(15,plain,
! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,difference(b,c)),c))) = difference(difference(a,difference(b,c)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,difference(b,c)),c))) = difference(difference(a,difference(b,c)),c),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(difference(a,c),difference(difference(a,c),b)),difference(c,difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(a,c),difference(difference(a,c),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
difference(difference(difference(a,c),difference(difference(a,c),b)),difference(c,difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(a,c),difference(difference(a,c),b)),
inference(unit_resolution,[status(thm)],[20,17]) ).
tff(22,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,c),difference(difference(a,c),b)) = difference(difference(a,difference(difference(a,c),b)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
difference(difference(a,c),difference(difference(a,c),b)) = difference(difference(a,difference(difference(a,c),b)),c),
inference(unit_resolution,[status(thm)],[22,7]) ).
tff(24,plain,
difference(c,difference(difference(a,c),difference(difference(a,c),b))) = difference(c,difference(difference(a,difference(difference(a,c),b)),c)),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
difference(c,difference(difference(a,difference(difference(a,c),b)),c)) = difference(c,difference(difference(a,c),difference(difference(a,c),b))),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(c,difference(difference(a,difference(difference(a,c),b)),c)) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
difference(c,difference(difference(a,difference(difference(a,c),b)),c)) = c,
inference(unit_resolution,[status(thm)],[26,17]) ).
tff(28,plain,
c = difference(c,difference(difference(a,difference(difference(a,c),b)),c)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
c = difference(c,difference(difference(a,c),difference(difference(a,c),b))),
inference(transitivity,[status(thm)],[28,25]) ).
tff(30,plain,
difference(difference(difference(a,c),difference(difference(a,c),b)),c) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(c,difference(difference(a,c),difference(difference(a,c),b)))),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
difference(difference(difference(a,c),difference(difference(a,c),b)),c) = difference(difference(a,c),difference(difference(a,c),b)),
inference(transitivity,[status(thm)],[30,21]) ).
tff(32,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))) = difference(a,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))) = difference(a,c),
inference(unit_resolution,[status(thm)],[35,17]) ).
tff(37,plain,
difference(a,c) = difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
difference(difference(a,c),b) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),b),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),b) = difference(difference(a,c),b),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),b),
inference(unit_resolution,[status(thm)],[40,7]) ).
tff(42,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(43,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)],[42]) ).
tff(44,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(45,axiom,
! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_2) ).
tff(46,plain,
! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(a,c),b),
inference(transitivity,[status(thm)],[51,41,39]) ).
tff(53,plain,
difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(a,c),difference(difference(a,c),b)),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,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,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
inference(unit_resolution,[status(thm)],[55,7]) ).
tff(57,plain,
difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),b) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
inference(symmetry,[status(thm)],[41]) ).
tff(59,plain,
difference(difference(a,c),b) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),
inference(transitivity,[status(thm)],[38,58,50]) ).
tff(60,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(a,c),b),difference(difference(a,c),b)) = difference(difference(difference(a,c),difference(difference(a,c),b)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
difference(difference(difference(a,c),b),difference(difference(a,c),b)) = difference(difference(difference(a,c),difference(difference(a,c),b)),b),
inference(unit_resolution,[status(thm)],[60,7]) ).
tff(62,plain,
difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
inference(monotonicity,[status(thm)],[62,59]) ).
tff(64,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(a,c),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(a,c),b),
inference(unit_resolution,[status(thm)],[64,17]) ).
tff(66,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b),
inference(unit_resolution,[status(thm)],[66,7]) ).
tff(68,plain,
difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(symmetry,[status(thm)],[62]) ).
tff(70,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,c),difference(difference(a,c),b)),b)) = difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),
inference(unit_resolution,[status(thm)],[70,7]) ).
tff(72,plain,
difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(transitivity,[status(thm)],[72,69]) ).
tff(74,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),b) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),b) = difference(difference(a,c),b),
inference(transitivity,[status(thm)],[74,68,65]) ).
tff(76,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)),
inference(monotonicity,[status(thm)],[73,75]) ).
tff(77,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),b)) = difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),b)) = difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),
inference(unit_resolution,[status(thm)],[77,48]) ).
tff(79,plain,
difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) = difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),b)),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(transitivity,[status(thm)],[79,76,63,57,54]) ).
tff(81,plain,
difference(difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),c) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,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,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),c) = difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
difference(difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),c) = difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),
inference(unit_resolution,[status(thm)],[82,7]) ).
tff(84,plain,
difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) = difference(difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),c),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(b,c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c))) = difference(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
difference(difference(b,c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c))) = difference(b,c),
inference(unit_resolution,[status(thm)],[85,17]) ).
tff(87,plain,
difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
inference(monotonicity,[status(thm)],[65]) ).
tff(88,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)) = difference(difference(difference(difference(a,c),b),difference(difference(a,c),b)),difference(difference(difference(a,c),b),difference(difference(a,c),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)) = difference(difference(difference(difference(a,c),b),difference(difference(a,c),b)),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(unit_resolution,[status(thm)],[88,7]) ).
tff(90,plain,
difference(difference(difference(difference(a,c),b),difference(difference(a,c),b)),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)),
inference(symmetry,[status(thm)],[89]) ).
tff(91,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(92,plain,
difference(difference(difference(a,c),b),difference(a,c)) = difference(difference(difference(a,c),difference(a,c)),b),
inference(unit_resolution,[status(thm)],[91,7]) ).
tff(93,plain,
difference(difference(difference(a,c),difference(a,c)),b) = difference(difference(difference(a,c),b),difference(a,c)),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
inference(monotonicity,[status(thm)],[52,93]) ).
tff(95,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(a,c),b),
inference(transitivity,[status(thm)],[94,41,39]) ).
tff(96,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
inference(monotonicity,[status(thm)],[95,52]) ).
tff(97,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(a,c)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(a,c)),b)),
inference(unit_resolution,[status(thm)],[97,7]) ).
tff(99,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
inference(monotonicity,[status(thm)],[52,52]) ).
tff(101,plain,
difference(difference(difference(a,c),b),difference(difference(a,c),b)) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
difference(difference(difference(a,c),difference(difference(a,c),b)),b) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
inference(symmetry,[status(thm)],[61]) ).
tff(103,plain,
difference(difference(difference(a,c),difference(difference(a,c),b)),b) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
inference(transitivity,[status(thm)],[102,101]) ).
tff(104,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(a,c)),b)),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
inference(transitivity,[status(thm)],[104,99,96]) ).
tff(106,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(a,c),difference(a,c)),b))) = difference(difference(difference(difference(a,c),b),difference(difference(a,c),b)),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(monotonicity,[status(thm)],[102,105]) ).
tff(107,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(a,c),difference(a,c)),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(a,c),difference(a,c)),b))),
inference(unit_resolution,[status(thm)],[107,48]) ).
tff(109,plain,
difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),b),difference(a,c)),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(monotonicity,[status(thm)],[93,102]) ).
tff(110,plain,
difference(difference(difference(difference(a,c),b),difference(a,c)),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(a,c)) = difference(difference(difference(difference(a,c),b),difference(a,c)),difference(difference(difference(a,c),b),difference(difference(a,c),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(a,c)) = difference(difference(difference(difference(a,c),b),difference(a,c)),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(unit_resolution,[status(thm)],[111,7]) ).
tff(113,plain,
difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(a,c)) = difference(difference(difference(a,c),b),difference(a,c)),
inference(monotonicity,[status(thm)],[65]) ).
tff(114,plain,
difference(difference(difference(a,c),b),difference(a,c)) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(a,c)),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
difference(difference(difference(a,c),difference(a,c)),b) = difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(transitivity,[status(thm)],[93,114,112,110]) ).
tff(116,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(a,c)) = difference(difference(difference(a,c),b),difference(a,c)),
inference(monotonicity,[status(thm)],[52]) ).
tff(117,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(a,c)) = difference(difference(difference(a,c),difference(a,c)),b),
inference(transitivity,[status(thm)],[116,92]) ).
tff(118,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(a,c)),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
inference(monotonicity,[status(thm)],[117,115]) ).
tff(119,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(a,c)) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(a,c)),difference(difference(difference(a,c),difference(a,c)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(a,c)) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(a,c)),difference(difference(difference(a,c),difference(a,c)),b)),
inference(unit_resolution,[status(thm)],[119,7]) ).
tff(121,plain,
difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),
inference(symmetry,[status(thm)],[94]) ).
tff(122,plain,
difference(difference(a,c),b) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),
inference(transitivity,[status(thm)],[38,58,121]) ).
tff(123,plain,
difference(difference(difference(a,c),b),difference(a,c)) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(a,c)),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
difference(difference(difference(a,c),b),difference(a,c)) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
inference(transitivity,[status(thm)],[123,120,118,108,106,90,87]) ).
tff(125,plain,
difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(a,c),
inference(transitivity,[status(thm)],[72,69,126,36]) ).
tff(128,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)) = difference(difference(a,c),difference(b,c)),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
difference(difference(a,c),difference(b,c)) = difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
difference(difference(a,difference(b,c)),c) = difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),
inference(transitivity,[status(thm)],[10,129]) ).
tff(131,plain,
difference(difference(b,c),difference(difference(a,difference(b,c)),c)) = difference(difference(b,c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c))),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
difference(difference(b,c),difference(difference(a,difference(b,c)),c)) = difference(b,c),
inference(transitivity,[status(thm)],[131,86]) ).
tff(133,plain,
difference(difference(difference(b,c),difference(difference(a,difference(b,c)),c)),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) = difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),difference(difference(a,difference(b,c)),c)) = difference(difference(difference(b,c),difference(difference(a,difference(b,c)),c)),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
difference(difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),difference(difference(a,difference(b,c)),c)) = difference(difference(difference(b,c),difference(difference(a,difference(b,c)),c)),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),
inference(unit_resolution,[status(thm)],[134,7]) ).
tff(136,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),c),
inference(symmetry,[status(thm)],[81]) ).
tff(137,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),
inference(symmetry,[status(thm)],[34]) ).
tff(138,plain,
difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(symmetry,[status(thm)],[32]) ).
tff(139,plain,
difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),
inference(transitivity,[status(thm)],[138,137,136,83]) ).
tff(140,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,difference(b,c)),c)) = difference(difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),difference(difference(a,difference(b,c)),c)),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,difference(b,c)),c)) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(transitivity,[status(thm)],[140,135,133,84,81,34,32]) ).
tff(142,plain,
difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,difference(b,c)),c))) = difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,difference(b,c)),c))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
inference(monotonicity,[status(thm)],[130]) ).
tff(145,plain,
difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)),
inference(unit_resolution,[status(thm)],[146,7]) ).
tff(148,plain,
difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
| ( difference(b,difference(b,difference(a,c))) = difference(difference(a,c),difference(difference(a,c),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
difference(b,difference(b,difference(a,c))) = difference(difference(a,c),difference(difference(a,c),b)),
inference(unit_resolution,[status(thm)],[149,48]) ).
tff(151,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = b,
inference(unit_resolution,[status(thm)],[151,17]) ).
tff(153,plain,
b = difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
difference(b,difference(b,difference(a,c))) = difference(difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(b,difference(a,c))),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
difference(difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(b,difference(a,c))) = difference(b,difference(b,difference(a,c))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,difference(b,difference(a,c))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(b,difference(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,plain,
difference(difference(b,difference(b,difference(a,c))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(b,difference(a,c))),
inference(unit_resolution,[status(thm)],[156,7]) ).
tff(158,plain,
difference(difference(b,difference(b,difference(a,c))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(monotonicity,[status(thm)],[150]) ).
tff(159,plain,
difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(b,difference(b,difference(a,c))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(a,c),difference(difference(a,c),b)),
inference(transitivity,[status(thm)],[159,157,155,150]) ).
tff(161,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),c),
inference(monotonicity,[status(thm)],[73]) ).
tff(162,plain,
difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),c) = difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),c),
inference(monotonicity,[status(thm)],[69]) ).
tff(164,plain,
difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),
inference(transitivity,[status(thm)],[163,162]) ).
tff(165,plain,
difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),difference(difference(a,c),difference(difference(a,c),b))),
inference(monotonicity,[status(thm)],[164,160]) ).
tff(166,plain,
difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))),c) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),difference(difference(a,c),difference(difference(a,c),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))),c) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),difference(difference(a,c),difference(difference(a,c),b))),
inference(unit_resolution,[status(thm)],[167,7]) ).
tff(169,plain,
difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
inference(monotonicity,[status(thm)],[65]) ).
tff(170,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(unit_resolution,[status(thm)],[170,7]) ).
tff(172,plain,
difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),b),difference(a,c))),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(monotonicity,[status(thm)],[51,102]) ).
tff(174,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,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),b))),
inference(unit_resolution,[status(thm)],[174,7]) ).
tff(176,plain,
difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),b))),
inference(monotonicity,[status(thm)],[72]) ).
tff(178,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(a,c),b),
inference(transitivity,[status(thm)],[177,176,173,172,169,41,39]) ).
tff(179,plain,
difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))),c) = difference(difference(difference(a,c),b),c),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
difference(difference(difference(a,c),b),c) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))),c),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c),
inference(unit_resolution,[status(thm)],[181,7]) ).
tff(183,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(184,plain,
difference(difference(a,b),c) = difference(difference(a,c),b),
inference(unit_resolution,[status(thm)],[183,7]) ).
tff(185,plain,
difference(difference(difference(a,b),c),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(a,b),c),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(187,plain,
difference(difference(difference(a,b),c),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),c),
inference(unit_resolution,[status(thm)],[186,7]) ).
tff(188,plain,
difference(difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),c) = difference(difference(difference(a,b),c),difference(difference(difference(a,c),b),difference(a,c))),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
difference(difference(a,b),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),
inference(monotonicity,[status(thm)],[93]) ).
tff(190,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(a,b),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
difference(difference(a,b),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),
inference(unit_resolution,[status(thm)],[190,7]) ).
tff(192,plain,
difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b) = difference(difference(a,b),difference(difference(difference(a,c),difference(a,c)),b)),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b) = difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),
inference(transitivity,[status(thm)],[192,189]) ).
tff(194,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c) = difference(difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),c),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c) = difference(difference(a,c),b),
inference(transitivity,[status(thm)],[194,188,185,41,39]) ).
tff(196,plain,
difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
inference(monotonicity,[status(thm)],[195,93]) ).
tff(197,plain,
difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c),difference(difference(difference(a,c),difference(a,c)),b)),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c),
inference(transitivity,[status(thm)],[51,197,182]) ).
tff(199,plain,
difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(c,difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c)),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
difference(c,difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c)) = difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(c,difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c)) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(202,plain,
difference(c,difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c)) = c,
inference(unit_resolution,[status(thm)],[201,17]) ).
tff(203,plain,
c = difference(c,difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c)),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
c = difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
inference(transitivity,[status(thm)],[203,200]) ).
tff(205,plain,
difference(difference(difference(a,c),b),c) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))),
inference(monotonicity,[status(thm)],[59,204]) ).
tff(206,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(difference(a,c),b),c),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(208,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),
inference(unit_resolution,[status(thm)],[207,17]) ).
tff(209,plain,
difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),b))),
inference(monotonicity,[status(thm)],[72,160]) ).
tff(211,plain,
difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
inference(transitivity,[status(thm)],[210,176,173,172,169,50,209,206,180,168,166]) ).
tff(212,plain,
difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)) = difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(215,plain,
difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),c),
inference(unit_resolution,[status(thm)],[214,7]) ).
tff(216,plain,
difference(difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),c) = difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(b,difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(218,plain,
difference(b,difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b)) = b,
inference(unit_resolution,[status(thm)],[217,17]) ).
tff(219,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(220,plain,
difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),
inference(unit_resolution,[status(thm)],[219,7]) ).
tff(221,plain,
difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b) = difference(difference(a,c),b),
inference(transitivity,[status(thm)],[68,65]) ).
tff(222,plain,
difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(monotonicity,[status(thm)],[221,102]) ).
tff(223,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
| ( difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(224,plain,
difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),
inference(unit_resolution,[status(thm)],[223,7]) ).
tff(225,plain,
difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b) = difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
inference(transitivity,[status(thm)],[225,222,65,38,58]) ).
tff(227,plain,
difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
inference(monotonicity,[status(thm)],[226,102]) ).
tff(228,plain,
difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),b),difference(a,c))),
inference(symmetry,[status(thm)],[169]) ).
tff(230,plain,
difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),
inference(transitivity,[status(thm)],[51,229,171,228,220]) ).
tff(231,plain,
difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(b,difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b)),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = b,
inference(transitivity,[status(thm)],[231,218]) ).
tff(233,plain,
difference(difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),c) = difference(b,c),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
difference(b,c) = difference(difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),c),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
difference(b,c) = difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
inference(transitivity,[status(thm)],[234,216]) ).
tff(236,plain,
difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))),c),
inference(symmetry,[status(thm)],[168]) ).
tff(237,plain,
difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),
inference(transitivity,[status(thm)],[165,236,179,205,208]) ).
tff(238,plain,
difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))),
inference(monotonicity,[status(thm)],[237,235]) ).
tff(239,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
| ( difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(241,plain,
difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),
inference(unit_resolution,[status(thm)],[240,17]) ).
tff(242,plain,
difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
difference(difference(a,b),c) = difference(difference(a,c),difference(b,c)),
inference(transitivity,[status(thm)],[184,38,58,50,242,239,213,148,145,143,19,10]) ).
tff(244,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(245,axiom,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_difference_3) ).
tff(246,plain,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
$false,
inference(unit_resolution,[status(thm)],[246,243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 13:08:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 9.30/6.23 % SZS status Unsatisfiable
% 9.30/6.23 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------