TSTP Solution File: LAT013-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT013-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 Sep 17 18:31:43 EDT 2022
% Result : Unsatisfiable 0.94s 0.85s
% Output : Proof 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 108
% Number of leaves : 159
% Syntax : Number of formulae : 943 ( 789 unt; 5 typ; 0 def)
% Number of atoms : 1095 (1090 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 297 ( 144 ~; 140 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 528 ( 516 !; 0 ?; 528 :)
% Comments :
%------------------------------------------------------------------------------
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(X,join(Y,join(X,Z))) = X )
<=> ( meet(X,join(Y,join(X,Z))) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie2) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,meet(b,c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
meet(meet(a,meet(b,c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(X,meet(Y,meet(X,Z))) = X )
<=> ( join(X,meet(Y,meet(X,Z))) = X ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie1) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
<=> ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie4) ).
tff(23,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c)))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c)))),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
meet(a,meet(b,c)) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))),
inference(symmetry,[status(thm)],[27]) ).
tff(31,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(a,meet(b,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a)))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
join(meet(a,meet(b,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a)))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[31,16]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,meet(b,c)),join(meet(a,b),join(meet(a,meet(b,c)),a))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
meet(meet(a,meet(b,c)),join(meet(a,b),join(meet(a,meet(b,c)),a))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,b),join(meet(a,meet(b,c)),join(meet(a,b),a))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
meet(meet(a,b),join(meet(a,meet(b,c)),join(meet(a,b),a))) = meet(a,b),
inference(unit_resolution,[status(thm)],[35,7]) ).
tff(37,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
<=> ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie3) ).
tff(41,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(a,b),a),meet(a,b)),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
join(join(meet(meet(a,b),a),meet(a,b)),a) = a,
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,b),join(a,join(meet(a,b),b))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
meet(meet(a,b),join(a,join(meet(a,b),b))) = meet(a,b),
inference(unit_resolution,[status(thm)],[46,7]) ).
tff(48,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(a,b),meet(b,meet(meet(a,b),c))),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
join(join(meet(a,b),meet(b,meet(meet(a,b),c))),b) = b,
inference(unit_resolution,[status(thm)],[48,43]) ).
tff(50,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(a,b),meet(b,meet(meet(a,b),c))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
join(meet(a,b),meet(b,meet(meet(a,b),c))) = meet(a,b),
inference(unit_resolution,[status(thm)],[50,16]) ).
tff(52,plain,
meet(a,b) = join(meet(a,b),meet(b,meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
join(meet(a,b),b) = join(join(meet(a,b),meet(b,meet(meet(a,b),c))),b),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
join(meet(a,b),b) = b,
inference(transitivity,[status(thm)],[53,49]) ).
tff(55,plain,
join(a,join(meet(a,b),b)) = join(a,b),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
join(a,b) = join(a,join(meet(a,b),b)),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
meet(meet(a,b),join(a,b)) = meet(meet(a,b),join(a,join(meet(a,b),b))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
meet(meet(a,b),join(a,b)) = meet(a,b),
inference(transitivity,[status(thm)],[57,47]) ).
tff(59,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(join(a,b),join(b,meet(a,b))),meet(a,meet(meet(join(a,b),join(b,meet(a,b))),b))) = meet(join(a,b),join(b,meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
join(meet(join(a,b),join(b,meet(a,b))),meet(a,meet(meet(join(a,b),join(b,meet(a,b))),b))) = meet(join(a,b),join(b,meet(a,b))),
inference(unit_resolution,[status(thm)],[59,16]) ).
tff(61,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(a,b),join(b,meet(a,b))),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
meet(meet(join(a,b),join(b,meet(a,b))),b) = b,
inference(unit_resolution,[status(thm)],[61,25]) ).
tff(63,plain,
meet(a,meet(meet(join(a,b),join(b,meet(a,b))),b)) = meet(a,b),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
meet(a,b) = meet(a,meet(meet(join(a,b),join(b,meet(a,b))),b)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)) = join(meet(join(a,b),join(b,meet(a,b))),meet(a,meet(meet(join(a,b),join(b,meet(a,b))),b))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)) = meet(join(a,b),join(b,meet(a,b))),
inference(transitivity,[status(thm)],[65,60]) ).
tff(67,plain,
meet(join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)),join(meet(a,b),b)) = meet(meet(join(a,b),join(b,meet(a,b))),b),
inference(monotonicity,[status(thm)],[66,54]) ).
tff(68,plain,
meet(meet(join(a,b),join(b,meet(a,b))),b) = meet(join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)),join(meet(a,b),b)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
b = meet(meet(join(a,b),join(b,meet(a,b))),b),
inference(symmetry,[status(thm)],[62]) ).
tff(70,plain,
b = meet(join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)),join(meet(a,b),b)),
inference(transitivity,[status(thm)],[69,68]) ).
tff(71,plain,
meet(b,meet(meet(a,b),join(a,b))) = meet(meet(join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)),join(meet(a,b),b)),meet(a,b)),
inference(monotonicity,[status(thm)],[70,58]) ).
tff(72,plain,
meet(meet(join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)),join(meet(a,b),b)),meet(a,b)) = meet(b,meet(meet(a,b),join(a,b))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)),join(meet(a,b),b)),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
meet(meet(join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)),join(meet(a,b),b)),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[73,25]) ).
tff(75,plain,
meet(a,b) = meet(meet(join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)),join(meet(a,b),b)),meet(a,b)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
meet(a,b) = meet(b,meet(meet(a,b),join(a,b))),
inference(transitivity,[status(thm)],[75,72]) ).
tff(77,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,b),join(a,join(meet(a,b),meet(b,meet(meet(a,b),c))))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
meet(meet(a,b),join(a,join(meet(a,b),meet(b,meet(meet(a,b),c))))) = meet(a,b),
inference(unit_resolution,[status(thm)],[77,7]) ).
tff(79,plain,
meet(b,meet(a,b)) = meet(meet(join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)),join(meet(a,b),b)),meet(a,b)),
inference(monotonicity,[status(thm)],[70]) ).
tff(80,plain,
meet(meet(join(meet(join(a,b),join(b,meet(a,b))),meet(a,b)),join(meet(a,b),b)),meet(a,b)) = meet(b,meet(a,b)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
join(meet(a,b),meet(b,meet(meet(a,b),c))) = meet(b,meet(a,b)),
inference(transitivity,[status(thm)],[51,75,80]) ).
tff(82,plain,
join(a,join(meet(a,b),meet(b,meet(meet(a,b),c)))) = join(a,meet(b,meet(a,b))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
join(a,meet(b,meet(a,b))) = join(a,join(meet(a,b),meet(b,meet(meet(a,b),c)))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(a,meet(b,meet(a,b))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
join(a,meet(b,meet(a,b))) = a,
inference(unit_resolution,[status(thm)],[84,16]) ).
tff(86,plain,
a = join(a,meet(b,meet(a,b))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
a = join(a,join(meet(a,b),meet(b,meet(meet(a,b),c)))),
inference(transitivity,[status(thm)],[86,83]) ).
tff(88,plain,
meet(meet(a,b),a) = meet(meet(a,b),join(a,join(meet(a,b),meet(b,meet(meet(a,b),c))))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
meet(meet(a,b),a) = meet(a,b),
inference(transitivity,[status(thm)],[88,78]) ).
tff(90,plain,
join(meet(meet(a,b),a),meet(a,b)) = join(meet(a,b),meet(b,meet(meet(a,b),join(a,b)))),
inference(monotonicity,[status(thm)],[89,76]) ).
tff(91,plain,
join(meet(a,b),meet(b,meet(meet(a,b),join(a,b)))) = join(meet(meet(a,b),a),meet(a,b)),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(a,b),meet(b,meet(meet(a,b),join(a,b)))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
join(meet(a,b),meet(b,meet(meet(a,b),join(a,b)))) = meet(a,b),
inference(unit_resolution,[status(thm)],[92,16]) ).
tff(94,plain,
meet(a,b) = join(meet(a,b),meet(b,meet(meet(a,b),join(a,b)))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
meet(a,b) = join(meet(meet(a,b),a),meet(a,b)),
inference(transitivity,[status(thm)],[94,91]) ).
tff(96,plain,
join(meet(a,b),a) = join(join(meet(meet(a,b),a),meet(a,b)),a),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
join(meet(a,b),a) = a,
inference(transitivity,[status(thm)],[96,45]) ).
tff(98,plain,
join(meet(a,meet(b,c)),join(meet(a,b),a)) = join(meet(a,meet(b,c)),a),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
join(meet(a,meet(b,c)),a) = join(meet(a,meet(b,c)),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
meet(meet(a,b),join(meet(a,meet(b,c)),a)) = meet(meet(a,b),join(meet(a,meet(b,c)),join(meet(a,b),a))),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
meet(meet(a,b),join(meet(a,meet(b,c)),a)) = meet(a,b),
inference(transitivity,[status(thm)],[100,36]) ).
tff(102,plain,
join(meet(meet(a,b),join(meet(a,meet(b,c)),a)),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))) = join(meet(a,b),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
join(meet(a,b),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))) = join(meet(meet(a,b),join(meet(a,meet(b,c)),a)),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(a,b),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
join(meet(a,b),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))) = meet(a,b),
inference(unit_resolution,[status(thm)],[104,16]) ).
tff(106,plain,
meet(a,b) = join(meet(a,b),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
meet(a,b) = join(meet(meet(a,b),join(meet(a,meet(b,c)),a)),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))),
inference(transitivity,[status(thm)],[106,103]) ).
tff(108,plain,
join(meet(a,b),join(meet(a,meet(b,c)),a)) = join(join(meet(meet(a,b),join(meet(a,meet(b,c)),a)),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))),join(meet(a,meet(b,c)),a)),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
join(join(meet(meet(a,b),join(meet(a,meet(b,c)),a)),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))),join(meet(a,meet(b,c)),a)) = join(meet(a,b),join(meet(a,meet(b,c)),a)),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(a,b),join(meet(a,meet(b,c)),a)),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))),join(meet(a,meet(b,c)),a)) = join(meet(a,meet(b,c)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
join(join(meet(meet(a,b),join(meet(a,meet(b,c)),a)),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))),join(meet(a,meet(b,c)),a)) = join(meet(a,meet(b,c)),a),
inference(unit_resolution,[status(thm)],[110,43]) ).
tff(112,plain,
join(meet(a,meet(b,c)),a) = join(join(meet(meet(a,b),join(meet(a,meet(b,c)),a)),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))),join(meet(a,meet(b,c)),a)),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
join(meet(a,meet(b,c)),a) = join(meet(a,b),join(meet(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[112,109]) ).
tff(114,plain,
meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a)) = meet(meet(a,meet(b,c)),join(meet(a,b),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a)) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[114,34]) ).
tff(116,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
meet(a,meet(b,c)) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a))),
inference(transitivity,[status(thm)],[30,117]) ).
tff(119,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = join(meet(a,meet(b,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a)))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[119,32,30,29]) ).
tff(121,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))))),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[121,18]) ).
tff(123,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)) = meet(b,c),
inference(unit_resolution,[status(thm)],[123,43]) ).
tff(125,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,c)),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
join(join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,c)),b) = b,
inference(unit_resolution,[status(thm)],[125,43]) ).
tff(127,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
meet(meet(join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(unit_resolution,[status(thm)],[127,25]) ).
tff(129,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(meet(b,meet(b,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(meet(b,meet(b,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(unit_resolution,[status(thm)],[129,16]) ).
tff(131,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(unit_resolution,[status(thm)],[131,7]) ).
tff(133,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),
inference(monotonicity,[status(thm)],[124]) ).
tff(134,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
meet(b,c) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),
inference(symmetry,[status(thm)],[124]) ).
tff(136,plain,
meet(b,c) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),
inference(transitivity,[status(thm)],[135,134]) ).
tff(137,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)) = meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(transitivity,[status(thm)],[137,132]) ).
tff(139,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
join(b,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))) = b,
inference(unit_resolution,[status(thm)],[139,16]) ).
tff(141,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))) = meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),
inference(symmetry,[status(thm)],[137]) ).
tff(142,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))),
inference(symmetry,[status(thm)],[132]) ).
tff(143,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),
inference(transitivity,[status(thm)],[142,141]) ).
tff(144,plain,
join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(b,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = b,
inference(transitivity,[status(thm)],[144,140]) ).
tff(146,plain,
meet(join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))) = meet(b,meet(b,c)),
inference(monotonicity,[status(thm)],[145,124]) ).
tff(147,plain,
meet(b,meet(b,c)) = meet(join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
meet(meet(b,meet(b,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))) = meet(meet(join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(monotonicity,[status(thm)],[147,138]) ).
tff(149,plain,
meet(meet(join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(meet(b,meet(b,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(meet(join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(symmetry,[status(thm)],[128]) ).
tff(151,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(meet(b,meet(b,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),
inference(transitivity,[status(thm)],[150,149]) ).
tff(152,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(meet(b,meet(b,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(transitivity,[status(thm)],[152,130]) ).
tff(154,plain,
meet(meet(b,meet(b,c)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(meet(join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(monotonicity,[status(thm)],[147,153]) ).
tff(155,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,meet(b,c)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(b,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
meet(meet(b,meet(b,c)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(b,meet(b,c)),
inference(unit_resolution,[status(thm)],[155,7]) ).
tff(157,plain,
meet(b,meet(b,c)) = meet(meet(b,meet(b,c)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,meet(b,c)),join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(b,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
meet(meet(b,meet(b,c)),join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(b,meet(b,c)),
inference(unit_resolution,[status(thm)],[158,7]) ).
tff(160,plain,
join(b,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))) = join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(symmetry,[status(thm)],[144]) ).
tff(161,plain,
b = join(b,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[140]) ).
tff(162,plain,
b = join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(transitivity,[status(thm)],[161,160]) ).
tff(163,plain,
meet(meet(join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(meet(b,meet(b,c)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(symmetry,[status(thm)],[154]) ).
tff(164,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(b,meet(b,c)),
inference(transitivity,[status(thm)],[150,163,156]) ).
tff(165,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b) = meet(meet(b,meet(b,c)),join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(monotonicity,[status(thm)],[164,162]) ).
tff(166,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(transitivity,[status(thm)],[165,159,157,154,128]) ).
tff(167,plain,
join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,c)) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)) = join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,c)),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
meet(b,c) = join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,c)),
inference(transitivity,[status(thm)],[135,168]) ).
tff(170,plain,
join(meet(b,c),b) = join(join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,c)),b),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
join(meet(b,c),b) = b,
inference(transitivity,[status(thm)],[170,126]) ).
tff(172,plain,
join(meet(b,c),join(meet(b,c),b)) = join(join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,c)),b),
inference(monotonicity,[status(thm)],[169,171]) ).
tff(173,plain,
join(join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,c)),b) = join(meet(b,c),join(meet(b,c),b)),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
join(meet(b,c),b) = join(meet(b,c),join(meet(b,c),b)),
inference(transitivity,[status(thm)],[170,173]) ).
tff(175,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),join(meet(b,c),b)) = meet(meet(b,c),join(meet(b,c),join(meet(b,c),b))),
inference(monotonicity,[status(thm)],[124,174]) ).
tff(176,plain,
meet(meet(b,c),join(meet(b,c),join(meet(b,c),b))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),join(meet(b,c),b)),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,c),join(meet(b,c),join(meet(b,c),b))) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(178,plain,
meet(meet(b,c),join(meet(b,c),join(meet(b,c),b))) = meet(b,c),
inference(unit_resolution,[status(thm)],[177,7]) ).
tff(179,plain,
meet(b,c) = meet(meet(b,c),join(meet(b,c),join(meet(b,c),b))),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
meet(b,c) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),join(meet(b,c),b)),
inference(transitivity,[status(thm)],[179,176]) ).
tff(181,plain,
meet(meet(b,c),meet(b,c)) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),join(meet(b,c),b)),meet(b,c)),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),join(meet(b,c),b)),meet(b,c)) = meet(meet(b,c),meet(b,c)),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),join(meet(b,c),b)),meet(b,c)) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),join(meet(b,c),b)),meet(b,c)) = meet(b,c),
inference(unit_resolution,[status(thm)],[183,25]) ).
tff(185,plain,
meet(b,c) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),join(meet(b,c),b)),meet(b,c)),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
meet(b,c) = meet(meet(b,c),meet(b,c)),
inference(transitivity,[status(thm)],[185,182]) ).
tff(187,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(monotonicity,[status(thm)],[164,186]) ).
tff(188,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(190,plain,
join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(unit_resolution,[status(thm)],[189,43]) ).
tff(191,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,c),join(a,join(meet(b,c),b))) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(192,plain,
meet(meet(b,c),join(a,join(meet(b,c),b))) = meet(b,c),
inference(unit_resolution,[status(thm)],[191,7]) ).
tff(193,plain,
join(a,join(meet(b,c),b)) = join(a,b),
inference(monotonicity,[status(thm)],[171]) ).
tff(194,plain,
join(a,b) = join(a,join(meet(b,c),b)),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
meet(meet(b,c),join(a,b)) = meet(meet(b,c),join(a,join(meet(b,c),b))),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
meet(meet(b,c),join(a,b)) = meet(b,c),
inference(transitivity,[status(thm)],[195,192]) ).
tff(197,plain,
meet(a,meet(meet(b,c),join(a,b))) = meet(a,meet(b,c)),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
meet(a,meet(b,c)) = meet(a,meet(meet(b,c),join(a,b))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(b,c),
inference(transitivity,[status(thm)],[188,124]) ).
tff(200,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))) = join(meet(b,c),meet(a,meet(meet(b,c),join(a,b)))),
inference(monotonicity,[status(thm)],[199,198]) ).
tff(201,plain,
join(meet(b,c),meet(a,meet(meet(b,c),join(a,b)))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(b,c),meet(a,meet(meet(b,c),join(a,b)))) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(203,plain,
join(meet(b,c),meet(a,meet(meet(b,c),join(a,b)))) = meet(b,c),
inference(unit_resolution,[status(thm)],[202,16]) ).
tff(204,plain,
meet(b,c) = join(meet(b,c),meet(a,meet(meet(b,c),join(a,b)))),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),
inference(transitivity,[status(thm)],[188,124,204,201]) ).
tff(206,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(208,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[207,7]) ).
tff(209,plain,
meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[206]) ).
tff(210,plain,
meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(212,plain,
meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[211,25]) ).
tff(213,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(215,plain,
join(join(meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[214,43]) ).
tff(216,plain,
join(meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[212]) ).
tff(217,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(219,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[218,16]) ).
tff(220,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = join(meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(transitivity,[status(thm)],[220,217]) ).
tff(222,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(join(meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(transitivity,[status(thm)],[222,215,213,210]) ).
tff(224,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(227,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(unit_resolution,[status(thm)],[226,16]) ).
tff(228,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[228,225]) ).
tff(230,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[230,208]) ).
tff(232,plain,
join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a))) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[231,206]) ).
tff(233,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
join(join(meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[222]) ).
tff(235,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = join(join(meet(meet(join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[215]) ).
tff(236,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(transitivity,[status(thm)],[235,234,233]) ).
tff(237,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(b,c),
inference(transitivity,[status(thm)],[237,190,188,124]) ).
tff(239,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(a,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,join(join(c,join(c,c)),join(join(a,b),join(a,b)))))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(240,plain,
join(a,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,join(join(c,join(c,c)),join(join(a,b),join(a,b)))))) = a,
inference(unit_resolution,[status(thm)],[239,16]) ).
tff(241,plain,
meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(a,meet(b,c)),
inference(monotonicity,[status(thm)],[199]) ).
tff(242,plain,
meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a))),
inference(transitivity,[status(thm)],[241,30,117]) ).
tff(243,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,meet(b,c)),join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(244,plain,
meet(meet(a,meet(b,c)),join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[243,7]) ).
tff(245,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[241]) ).
tff(246,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(transitivity,[status(thm)],[119,32,30,246]) ).
tff(248,plain,
join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(a,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))),
inference(monotonicity,[status(thm)],[247]) ).
tff(249,plain,
join(a,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))) = join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(a,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(251,plain,
join(a,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))) = a,
inference(unit_resolution,[status(thm)],[250,16]) ).
tff(252,plain,
a = join(a,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
a = join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[252,249]) ).
tff(254,plain,
meet(meet(a,meet(b,c)),a) = meet(meet(a,meet(b,c)),join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(monotonicity,[status(thm)],[253]) ).
tff(255,plain,
meet(meet(a,meet(b,c)),a) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[254,244]) ).
tff(256,plain,
join(meet(meet(a,meet(b,c)),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = join(meet(a,meet(b,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a)))),
inference(monotonicity,[status(thm)],[255,242]) ).
tff(257,plain,
join(meet(a,meet(b,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a)))) = join(meet(meet(a,meet(b,c)),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
meet(a,meet(b,c)) = join(meet(a,meet(b,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[32]) ).
tff(259,plain,
meet(a,meet(b,c)) = join(meet(meet(a,meet(b,c)),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(transitivity,[status(thm)],[258,257]) ).
tff(260,plain,
join(meet(a,meet(b,c)),a) = join(join(meet(meet(a,meet(b,c)),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),a),
inference(monotonicity,[status(thm)],[259]) ).
tff(261,plain,
join(join(meet(meet(a,meet(b,c)),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),a) = join(meet(a,meet(b,c)),a),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(a,meet(b,c)),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
join(join(meet(meet(a,meet(b,c)),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),a) = a,
inference(unit_resolution,[status(thm)],[262,43]) ).
tff(264,plain,
a = join(join(meet(meet(a,meet(b,c)),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),a),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(join(c,join(c,c)),join(a,b))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(266,plain,
meet(a,join(join(c,join(c,c)),join(a,b))) = a,
inference(unit_resolution,[status(thm)],[265,7]) ).
tff(267,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(join(a,b),b),meet(b,join(a,b))),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(268,plain,
join(join(meet(join(a,b),b),meet(b,join(a,b))),b) = b,
inference(unit_resolution,[status(thm)],[267,43]) ).
tff(269,plain,
meet(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),b)) = meet(meet(join(a,b),join(b,meet(a,b))),b),
inference(monotonicity,[status(thm)],[62]) ).
tff(270,plain,
meet(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),b)) = b,
inference(transitivity,[status(thm)],[269,62]) ).
tff(271,plain,
meet(meet(join(a,b),join(b,meet(a,b))),b) = meet(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),b)),
inference(symmetry,[status(thm)],[269]) ).
tff(272,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(b,join(a,join(b,meet(a,meet(b,c))))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(273,plain,
meet(b,join(a,join(b,meet(a,meet(b,c))))) = b,
inference(unit_resolution,[status(thm)],[272,7]) ).
tff(274,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(a,meet(b,c))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(275,plain,
join(b,meet(a,meet(b,c))) = b,
inference(unit_resolution,[status(thm)],[274,16]) ).
tff(276,plain,
join(a,join(b,meet(a,meet(b,c)))) = join(a,b),
inference(monotonicity,[status(thm)],[275]) ).
tff(277,plain,
join(a,b) = join(a,join(b,meet(a,meet(b,c)))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
meet(b,join(a,b)) = meet(b,join(a,join(b,meet(a,meet(b,c))))),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
meet(b,join(a,b)) = meet(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),b)),
inference(transitivity,[status(thm)],[278,273,69,271]) ).
tff(280,plain,
meet(b,join(a,b)) = b,
inference(transitivity,[status(thm)],[278,273]) ).
tff(281,plain,
meet(a,meet(b,join(a,b))) = meet(a,b),
inference(monotonicity,[status(thm)],[280]) ).
tff(282,plain,
meet(a,b) = meet(a,meet(b,join(a,b))),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
join(b,meet(a,b)) = join(b,meet(a,meet(b,join(a,b)))),
inference(monotonicity,[status(thm)],[282]) ).
tff(284,plain,
join(b,meet(a,meet(b,join(a,b)))) = join(b,meet(a,b)),
inference(symmetry,[status(thm)],[283]) ).
tff(285,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(a,meet(b,join(a,b)))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(286,plain,
join(b,meet(a,meet(b,join(a,b)))) = b,
inference(unit_resolution,[status(thm)],[285,16]) ).
tff(287,plain,
b = join(b,meet(a,meet(b,join(a,b)))),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
b = join(b,meet(a,b)),
inference(transitivity,[status(thm)],[287,284]) ).
tff(289,plain,
meet(join(a,b),b) = meet(join(a,b),join(b,meet(a,b))),
inference(monotonicity,[status(thm)],[288]) ).
tff(290,plain,
join(meet(join(a,b),b),meet(b,join(a,b))) = join(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),b))),
inference(monotonicity,[status(thm)],[289,279]) ).
tff(291,plain,
join(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),b))) = join(meet(join(a,b),b),meet(b,join(a,b))),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),b))) = meet(join(a,b),join(b,meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(293,plain,
join(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),b))) = meet(join(a,b),join(b,meet(a,b))),
inference(unit_resolution,[status(thm)],[292,16]) ).
tff(294,plain,
meet(join(a,b),join(b,meet(a,b))) = join(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),b))),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
meet(join(a,b),join(b,meet(a,b))) = join(meet(join(a,b),b),meet(b,join(a,b))),
inference(transitivity,[status(thm)],[294,291]) ).
tff(296,plain,
join(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),b))) = join(join(meet(join(a,b),b),meet(b,join(a,b))),b),
inference(monotonicity,[status(thm)],[295,270]) ).
tff(297,plain,
meet(join(a,b),b) = b,
inference(transitivity,[status(thm)],[289,294,296,268]) ).
tff(298,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(b,join(a,b))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(299,plain,
meet(a,join(b,join(a,b))) = a,
inference(unit_resolution,[status(thm)],[298,7]) ).
tff(300,plain,
meet(meet(a,b),join(a,b)) = join(meet(a,b),meet(b,meet(meet(a,b),c))),
inference(transitivity,[status(thm)],[57,47,52]) ).
tff(301,plain,
join(meet(meet(a,b),join(a,b)),meet(join(a,b),b)) = join(join(meet(a,b),meet(b,meet(meet(a,b),c))),b),
inference(monotonicity,[status(thm)],[300,297]) ).
tff(302,plain,
join(join(meet(a,b),meet(b,meet(meet(a,b),c))),b) = join(meet(meet(a,b),join(a,b)),meet(join(a,b),b)),
inference(symmetry,[status(thm)],[301]) ).
tff(303,plain,
b = join(join(meet(a,b),meet(b,meet(meet(a,b),c))),b),
inference(symmetry,[status(thm)],[49]) ).
tff(304,plain,
b = join(meet(meet(a,b),join(a,b)),meet(join(a,b),b)),
inference(transitivity,[status(thm)],[303,302]) ).
tff(305,plain,
join(b,join(a,b)) = join(join(meet(meet(a,b),join(a,b)),meet(join(a,b),b)),join(a,b)),
inference(monotonicity,[status(thm)],[304]) ).
tff(306,plain,
join(join(meet(meet(a,b),join(a,b)),meet(join(a,b),b)),join(a,b)) = join(b,join(a,b)),
inference(symmetry,[status(thm)],[305]) ).
tff(307,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(a,b),join(a,b)),meet(join(a,b),b)),join(a,b)) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(308,plain,
join(join(meet(meet(a,b),join(a,b)),meet(join(a,b),b)),join(a,b)) = join(a,b),
inference(unit_resolution,[status(thm)],[307,43]) ).
tff(309,plain,
join(a,b) = join(join(meet(meet(a,b),join(a,b)),meet(join(a,b),b)),join(a,b)),
inference(symmetry,[status(thm)],[308]) ).
tff(310,plain,
join(a,b) = join(b,join(a,b)),
inference(transitivity,[status(thm)],[309,306]) ).
tff(311,plain,
meet(a,join(a,b)) = meet(a,join(b,join(a,b))),
inference(monotonicity,[status(thm)],[310]) ).
tff(312,plain,
meet(a,join(a,b)) = a,
inference(transitivity,[status(thm)],[311,299]) ).
tff(313,plain,
join(meet(a,join(a,b)),meet(join(a,b),b)) = join(a,b),
inference(monotonicity,[status(thm)],[312,297]) ).
tff(314,plain,
join(a,b) = join(meet(a,join(a,b)),meet(join(a,b),b)),
inference(symmetry,[status(thm)],[313]) ).
tff(315,plain,
join(join(a,b),join(a,b)) = join(join(meet(a,join(a,b)),meet(join(a,b),b)),join(a,b)),
inference(monotonicity,[status(thm)],[314]) ).
tff(316,plain,
join(join(meet(a,join(a,b)),meet(join(a,b),b)),join(a,b)) = join(join(a,b),join(a,b)),
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(a,join(a,b)),meet(join(a,b),b)),join(a,b)) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(318,plain,
join(join(meet(a,join(a,b)),meet(join(a,b),b)),join(a,b)) = join(a,b),
inference(unit_resolution,[status(thm)],[317,43]) ).
tff(319,plain,
join(a,b) = join(join(meet(a,join(a,b)),meet(join(a,b),b)),join(a,b)),
inference(symmetry,[status(thm)],[318]) ).
tff(320,plain,
join(a,b) = join(join(a,b),join(a,b)),
inference(transitivity,[status(thm)],[319,316]) ).
tff(321,plain,
join(join(c,join(c,c)),join(a,b)) = join(join(c,join(c,c)),join(join(a,b),join(a,b))),
inference(monotonicity,[status(thm)],[320]) ).
tff(322,plain,
join(join(c,join(c,c)),join(join(a,b),join(a,b))) = join(join(c,join(c,c)),join(a,b)),
inference(symmetry,[status(thm)],[321]) ).
tff(323,plain,
meet(a,join(join(c,join(c,c)),join(join(a,b),join(a,b)))) = meet(a,join(join(c,join(c,c)),join(a,b))),
inference(monotonicity,[status(thm)],[322]) ).
tff(324,plain,
meet(a,join(join(c,join(c,c)),join(join(a,b),join(a,b)))) = join(meet(a,meet(b,c)),a),
inference(transitivity,[status(thm)],[323,266,264,261]) ).
tff(325,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,join(join(c,join(c,c)),join(join(a,b),join(a,b))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(monotonicity,[status(thm)],[205,324]) ).
tff(326,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,join(join(c,join(c,c)),join(join(a,b),join(a,b))))),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(a,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,join(join(c,join(c,c)),join(join(a,b),join(a,b)))))),
inference(monotonicity,[status(thm)],[326]) ).
tff(328,plain,
join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = a,
inference(transitivity,[status(thm)],[327,240]) ).
tff(329,plain,
meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(a,meet(b,c)),
inference(monotonicity,[status(thm)],[328,238]) ).
tff(330,plain,
meet(a,meet(b,c)) = meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(symmetry,[status(thm)],[329]) ).
tff(331,plain,
meet(meet(a,meet(b,c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[330,122]) ).
tff(332,plain,
meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(a,meet(b,c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(symmetry,[status(thm)],[331]) ).
tff(333,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(334,plain,
meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[333,25]) ).
tff(335,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(meet(a,b),c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(337,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(meet(a,b),c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[336,7]) ).
tff(338,plain,
meet(a,b) = meet(b,meet(a,b)),
inference(transitivity,[status(thm)],[75,80]) ).
tff(339,plain,
join(a,meet(a,b)) = join(a,meet(b,meet(a,b))),
inference(monotonicity,[status(thm)],[338]) ).
tff(340,plain,
join(a,meet(a,b)) = a,
inference(transitivity,[status(thm)],[339,85]) ).
tff(341,plain,
join(meet(a,b),join(a,meet(a,b))) = join(join(meet(meet(a,b),a),meet(a,b)),a),
inference(monotonicity,[status(thm)],[95,340]) ).
tff(342,plain,
join(join(meet(meet(a,b),a),meet(a,b)),a) = join(meet(a,b),join(a,meet(a,b))),
inference(symmetry,[status(thm)],[341]) ).
tff(343,plain,
a = join(join(meet(meet(a,b),a),meet(a,b)),a),
inference(symmetry,[status(thm)],[45]) ).
tff(344,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(345,plain,
join(join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),a) = a,
inference(unit_resolution,[status(thm)],[344,43]) ).
tff(346,plain,
meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[241,30,29]) ).
tff(347,plain,
a = join(meet(a,meet(b,c)),a),
inference(transitivity,[status(thm)],[264,261]) ).
tff(348,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),a) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(monotonicity,[status(thm)],[205,347]) ).
tff(349,plain,
join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))))),
inference(monotonicity,[status(thm)],[348,346]) ).
tff(350,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))))) = join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(symmetry,[status(thm)],[349]) ).
tff(351,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))))),
inference(symmetry,[status(thm)],[18]) ).
tff(352,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(transitivity,[status(thm)],[351,350]) ).
tff(353,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a) = join(join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),a),meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),a),
inference(monotonicity,[status(thm)],[352]) ).
tff(354,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a) = join(meet(a,b),join(a,meet(a,b))),
inference(transitivity,[status(thm)],[353,345,343,342]) ).
tff(355,plain,
meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)) = meet(a,join(meet(a,b),join(a,meet(a,b)))),
inference(monotonicity,[status(thm)],[328,354]) ).
tff(356,plain,
meet(a,join(meet(a,b),join(a,meet(a,b)))) = meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),
inference(symmetry,[status(thm)],[355]) ).
tff(357,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(meet(a,b),join(a,meet(a,b)))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(358,plain,
meet(a,join(meet(a,b),join(a,meet(a,b)))) = a,
inference(unit_resolution,[status(thm)],[357,7]) ).
tff(359,plain,
a = meet(a,join(meet(a,b),join(a,meet(a,b)))),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
a = meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),
inference(transitivity,[status(thm)],[359,356]) ).
tff(361,plain,
meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[360]) ).
tff(362,plain,
meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[361]) ).
tff(363,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(364,plain,
meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[363,25]) ).
tff(365,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(transitivity,[status(thm)],[222,215,365,362]) ).
tff(367,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(b,meet(meet(a,b),c)),join(meet(b,meet(meet(a,b),c)),b)))) = meet(b,meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(368,plain,
join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(b,meet(meet(a,b),c)),join(meet(b,meet(meet(a,b),c)),b)))) = meet(b,meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[367,16]) ).
tff(369,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,meet(meet(a,b),c)),join(b,join(meet(b,meet(meet(a,b),c)),b))) = meet(b,meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(370,plain,
meet(meet(b,meet(meet(a,b),c)),join(b,join(meet(b,meet(meet(a,b),c)),b))) = meet(b,meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[369,7]) ).
tff(371,plain,
b = join(b,meet(a,meet(b,c))),
inference(symmetry,[status(thm)],[275]) ).
tff(372,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(b,join(meet(a,b),join(b,meet(b,meet(b,c))))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(373,plain,
meet(b,join(meet(a,b),join(b,meet(b,meet(b,c))))) = b,
inference(unit_resolution,[status(thm)],[372,7]) ).
tff(374,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(b,meet(b,c))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(375,plain,
join(b,meet(b,meet(b,c))) = b,
inference(unit_resolution,[status(thm)],[374,16]) ).
tff(376,plain,
join(meet(a,b),join(b,meet(b,meet(b,c)))) = join(join(meet(a,b),meet(b,meet(meet(a,b),c))),b),
inference(monotonicity,[status(thm)],[52,375]) ).
tff(377,plain,
join(join(meet(a,b),meet(b,meet(meet(a,b),c))),b) = join(meet(a,b),join(b,meet(b,meet(b,c)))),
inference(symmetry,[status(thm)],[376]) ).
tff(378,plain,
b = join(meet(a,b),join(b,meet(b,meet(b,c)))),
inference(transitivity,[status(thm)],[303,377]) ).
tff(379,plain,
meet(b,b) = meet(b,join(meet(a,b),join(b,meet(b,meet(b,c))))),
inference(monotonicity,[status(thm)],[378]) ).
tff(380,plain,
meet(b,b) = join(b,meet(a,meet(b,c))),
inference(transitivity,[status(thm)],[379,373,371]) ).
tff(381,plain,
meet(join(meet(b,meet(meet(a,b),c)),b),meet(b,b)) = meet(join(meet(b,meet(meet(a,b),c)),b),join(b,meet(a,meet(b,c)))),
inference(monotonicity,[status(thm)],[380]) ).
tff(382,plain,
meet(join(meet(b,meet(meet(a,b),c)),b),join(b,meet(a,meet(b,c)))) = meet(join(meet(b,meet(meet(a,b),c)),b),meet(b,b)),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
meet(join(meet(b,meet(meet(a,b),c)),b),b) = meet(join(meet(b,meet(meet(a,b),c)),b),join(b,meet(a,meet(b,c)))),
inference(monotonicity,[status(thm)],[371]) ).
tff(384,plain,
meet(join(meet(b,meet(meet(a,b),c)),b),b) = meet(join(meet(b,meet(meet(a,b),c)),b),meet(b,b)),
inference(transitivity,[status(thm)],[383,382]) ).
tff(385,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(b,join(meet(b,meet(meet(a,b),c)),join(b,meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(386,plain,
meet(b,join(meet(b,meet(meet(a,b),c)),join(b,meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))))) = b,
inference(unit_resolution,[status(thm)],[385,7]) ).
tff(387,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(388,plain,
join(b,meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))) = b,
inference(unit_resolution,[status(thm)],[387,16]) ).
tff(389,plain,
join(meet(b,meet(meet(a,b),c)),join(b,meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))))) = join(meet(b,meet(meet(a,b),c)),b),
inference(monotonicity,[status(thm)],[388]) ).
tff(390,plain,
join(meet(b,meet(meet(a,b),c)),b) = join(meet(b,meet(meet(a,b),c)),join(b,meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))))),
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
meet(b,join(meet(b,meet(meet(a,b),c)),b)) = meet(b,join(meet(b,meet(meet(a,b),c)),join(b,meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))))),
inference(monotonicity,[status(thm)],[390]) ).
tff(392,plain,
meet(b,join(meet(b,meet(meet(a,b),c)),b)) = b,
inference(transitivity,[status(thm)],[391,386]) ).
tff(393,plain,
join(meet(b,join(meet(b,meet(meet(a,b),c)),b)),meet(join(meet(b,meet(meet(a,b),c)),b),b)) = join(b,meet(join(meet(b,meet(meet(a,b),c)),b),meet(b,b))),
inference(monotonicity,[status(thm)],[392,384]) ).
tff(394,plain,
join(b,meet(join(meet(b,meet(meet(a,b),c)),b),meet(b,b))) = join(meet(b,join(meet(b,meet(meet(a,b),c)),b)),meet(join(meet(b,meet(meet(a,b),c)),b),b)),
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(join(meet(b,meet(meet(a,b),c)),b),meet(b,b))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(396,plain,
join(b,meet(join(meet(b,meet(meet(a,b),c)),b),meet(b,b))) = b,
inference(unit_resolution,[status(thm)],[395,16]) ).
tff(397,plain,
b = join(b,meet(join(meet(b,meet(meet(a,b),c)),b),meet(b,b))),
inference(symmetry,[status(thm)],[396]) ).
tff(398,plain,
b = join(meet(b,join(meet(b,meet(meet(a,b),c)),b)),meet(join(meet(b,meet(meet(a,b),c)),b),b)),
inference(transitivity,[status(thm)],[397,394]) ).
tff(399,plain,
join(b,join(meet(b,meet(meet(a,b),c)),b)) = join(join(meet(b,join(meet(b,meet(meet(a,b),c)),b)),meet(join(meet(b,meet(meet(a,b),c)),b),b)),join(meet(b,meet(meet(a,b),c)),b)),
inference(monotonicity,[status(thm)],[398]) ).
tff(400,plain,
join(join(meet(b,join(meet(b,meet(meet(a,b),c)),b)),meet(join(meet(b,meet(meet(a,b),c)),b),b)),join(meet(b,meet(meet(a,b),c)),b)) = join(b,join(meet(b,meet(meet(a,b),c)),b)),
inference(symmetry,[status(thm)],[399]) ).
tff(401,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(b,join(meet(b,meet(meet(a,b),c)),b)),meet(join(meet(b,meet(meet(a,b),c)),b),b)),join(meet(b,meet(meet(a,b),c)),b)) = join(meet(b,meet(meet(a,b),c)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(402,plain,
join(join(meet(b,join(meet(b,meet(meet(a,b),c)),b)),meet(join(meet(b,meet(meet(a,b),c)),b),b)),join(meet(b,meet(meet(a,b),c)),b)) = join(meet(b,meet(meet(a,b),c)),b),
inference(unit_resolution,[status(thm)],[401,43]) ).
tff(403,plain,
join(meet(b,meet(meet(a,b),c)),b) = join(join(meet(b,join(meet(b,meet(meet(a,b),c)),b)),meet(join(meet(b,meet(meet(a,b),c)),b),b)),join(meet(b,meet(meet(a,b),c)),b)),
inference(symmetry,[status(thm)],[402]) ).
tff(404,plain,
join(meet(b,meet(meet(a,b),c)),b) = join(b,join(meet(b,meet(meet(a,b),c)),b)),
inference(transitivity,[status(thm)],[403,400]) ).
tff(405,plain,
meet(meet(b,meet(meet(a,b),c)),join(meet(b,meet(meet(a,b),c)),b)) = meet(meet(b,meet(meet(a,b),c)),join(b,join(meet(b,meet(meet(a,b),c)),b))),
inference(monotonicity,[status(thm)],[404]) ).
tff(406,plain,
meet(meet(b,meet(meet(a,b),c)),join(meet(b,meet(meet(a,b),c)),b)) = meet(b,meet(meet(a,b),c)),
inference(transitivity,[status(thm)],[405,370]) ).
tff(407,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(meet(a,b),meet(b,meet(meet(a,b),c)))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(408,plain,
join(b,meet(meet(a,b),meet(b,meet(meet(a,b),c)))) = b,
inference(unit_resolution,[status(thm)],[407,16]) ).
tff(409,plain,
join(meet(b,meet(meet(a,b),c)),join(meet(a,b),b)) = join(meet(b,meet(meet(a,b),c)),b),
inference(monotonicity,[status(thm)],[54]) ).
tff(410,plain,
join(meet(b,meet(meet(a,b),c)),b) = join(meet(b,meet(meet(a,b),c)),join(meet(a,b),b)),
inference(symmetry,[status(thm)],[409]) ).
tff(411,plain,
meet(join(meet(a,b),meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)) = meet(meet(a,b),join(meet(b,meet(meet(a,b),c)),join(meet(a,b),b))),
inference(monotonicity,[status(thm)],[51,410]) ).
tff(412,plain,
meet(meet(a,b),join(meet(b,meet(meet(a,b),c)),join(meet(a,b),b))) = meet(join(meet(a,b),meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),
inference(symmetry,[status(thm)],[411]) ).
tff(413,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,b),join(meet(b,meet(meet(a,b),c)),join(meet(a,b),b))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(414,plain,
meet(meet(a,b),join(meet(b,meet(meet(a,b),c)),join(meet(a,b),b))) = meet(a,b),
inference(unit_resolution,[status(thm)],[413,7]) ).
tff(415,plain,
meet(a,b) = meet(meet(a,b),join(meet(b,meet(meet(a,b),c)),join(meet(a,b),b))),
inference(symmetry,[status(thm)],[414]) ).
tff(416,plain,
meet(a,b) = meet(join(meet(a,b),meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),
inference(transitivity,[status(thm)],[415,412]) ).
tff(417,plain,
meet(meet(a,b),meet(b,meet(meet(a,b),c))) = meet(meet(join(meet(a,b),meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),meet(b,meet(meet(a,b),c))),
inference(monotonicity,[status(thm)],[416]) ).
tff(418,plain,
meet(meet(join(meet(a,b),meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),meet(b,meet(meet(a,b),c))) = meet(meet(a,b),meet(b,meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[417]) ).
tff(419,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(meet(a,b),meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),meet(b,meet(meet(a,b),c))) = meet(b,meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(420,plain,
meet(meet(join(meet(a,b),meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),meet(b,meet(meet(a,b),c))) = meet(b,meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[419,25]) ).
tff(421,plain,
meet(b,meet(meet(a,b),c)) = meet(meet(join(meet(a,b),meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),meet(b,meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
meet(b,meet(meet(a,b),c)) = meet(meet(a,b),meet(b,meet(meet(a,b),c))),
inference(transitivity,[status(thm)],[421,418]) ).
tff(423,plain,
join(b,meet(b,meet(meet(a,b),c))) = join(b,meet(meet(a,b),meet(b,meet(meet(a,b),c)))),
inference(monotonicity,[status(thm)],[422]) ).
tff(424,plain,
join(b,meet(b,meet(meet(a,b),c))) = b,
inference(transitivity,[status(thm)],[423,408]) ).
tff(425,plain,
meet(join(b,meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)) = meet(b,join(meet(b,meet(meet(a,b),c)),join(b,meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))))),
inference(monotonicity,[status(thm)],[424,390]) ).
tff(426,plain,
meet(b,join(meet(b,meet(meet(a,b),c)),join(b,meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))))) = meet(join(b,meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),
inference(symmetry,[status(thm)],[425]) ).
tff(427,plain,
b = meet(b,join(meet(b,meet(meet(a,b),c)),join(b,meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))))),
inference(symmetry,[status(thm)],[386]) ).
tff(428,plain,
b = meet(join(b,meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),
inference(transitivity,[status(thm)],[427,426]) ).
tff(429,plain,
meet(b,meet(meet(b,meet(meet(a,b),c)),join(meet(b,meet(meet(a,b),c)),b))) = meet(meet(join(b,meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),meet(b,meet(meet(a,b),c))),
inference(monotonicity,[status(thm)],[428,406]) ).
tff(430,plain,
meet(meet(join(b,meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),meet(b,meet(meet(a,b),c))) = meet(b,meet(meet(b,meet(meet(a,b),c)),join(meet(b,meet(meet(a,b),c)),b))),
inference(symmetry,[status(thm)],[429]) ).
tff(431,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(b,meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),meet(b,meet(meet(a,b),c))) = meet(b,meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(432,plain,
meet(meet(join(b,meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),meet(b,meet(meet(a,b),c))) = meet(b,meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[431,25]) ).
tff(433,plain,
meet(b,meet(meet(a,b),c)) = meet(meet(join(b,meet(b,meet(meet(a,b),c))),join(meet(b,meet(meet(a,b),c)),b)),meet(b,meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[432]) ).
tff(434,plain,
meet(b,meet(meet(a,b),c)) = meet(b,meet(meet(b,meet(meet(a,b),c)),join(meet(b,meet(meet(a,b),c)),b))),
inference(transitivity,[status(thm)],[433,430]) ).
tff(435,plain,
join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))) = join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(b,meet(meet(a,b),c)),join(meet(b,meet(meet(a,b),c)),b)))),
inference(monotonicity,[status(thm)],[434]) ).
tff(436,plain,
join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))) = meet(b,meet(meet(a,b),c)),
inference(transitivity,[status(thm)],[435,368]) ).
tff(437,plain,
join(meet(a,b),join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c)))) = join(meet(a,b),meet(b,meet(meet(a,b),c))),
inference(monotonicity,[status(thm)],[436]) ).
tff(438,plain,
join(meet(a,b),meet(b,meet(meet(a,b),c))) = join(meet(a,b),join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c)))),
inference(symmetry,[status(thm)],[437]) ).
tff(439,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(a,meet(a,b)),join(meet(a,b),a)),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(440,plain,
meet(meet(join(a,meet(a,b)),join(meet(a,b),a)),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[439,25]) ).
tff(441,plain,
join(meet(a,b),a) = join(meet(a,b),join(a,meet(a,b))),
inference(transitivity,[status(thm)],[96,342]) ).
tff(442,plain,
meet(join(a,meet(a,b)),join(meet(a,b),a)) = meet(a,join(meet(a,b),join(a,meet(a,b)))),
inference(monotonicity,[status(thm)],[340,441]) ).
tff(443,plain,
meet(a,join(meet(a,b),join(a,meet(a,b)))) = meet(join(a,meet(a,b)),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[442]) ).
tff(444,plain,
a = meet(join(a,meet(a,b)),join(meet(a,b),a)),
inference(transitivity,[status(thm)],[359,443]) ).
tff(445,plain,
meet(a,meet(a,b)) = meet(meet(join(a,meet(a,b)),join(meet(a,b),a)),meet(a,b)),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
meet(a,meet(a,b)) = join(meet(a,b),join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c)))),
inference(transitivity,[status(thm)],[445,440,52,438]) ).
tff(447,plain,
meet(meet(b,meet(meet(a,b),c)),meet(a,meet(a,b))) = meet(meet(b,meet(meet(a,b),c)),join(meet(a,b),join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))),
inference(monotonicity,[status(thm)],[446]) ).
tff(448,plain,
meet(meet(b,meet(meet(a,b),c)),join(meet(a,b),join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))) = meet(meet(b,meet(meet(a,b),c)),meet(a,meet(a,b))),
inference(symmetry,[status(thm)],[447]) ).
tff(449,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,meet(meet(a,b),c)),join(meet(a,b),join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))) = meet(b,meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(450,plain,
meet(meet(b,meet(meet(a,b),c)),join(meet(a,b),join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))) = meet(b,meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[449,7]) ).
tff(451,plain,
meet(b,meet(meet(a,b),c)) = meet(meet(b,meet(meet(a,b),c)),join(meet(a,b),join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))),
inference(symmetry,[status(thm)],[450]) ).
tff(452,plain,
join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))) = meet(meet(b,meet(meet(a,b),c)),meet(a,meet(a,b))),
inference(transitivity,[status(thm)],[435,368,451,448]) ).
tff(453,plain,
join(a,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c)))) = join(a,meet(meet(b,meet(meet(a,b),c)),meet(a,meet(a,b)))),
inference(monotonicity,[status(thm)],[452]) ).
tff(454,plain,
join(a,meet(meet(b,meet(meet(a,b),c)),meet(a,meet(a,b)))) = join(a,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c)))),
inference(symmetry,[status(thm)],[453]) ).
tff(455,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(a,meet(meet(b,meet(meet(a,b),c)),meet(a,meet(a,b)))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(456,plain,
join(a,meet(meet(b,meet(meet(a,b),c)),meet(a,meet(a,b)))) = a,
inference(unit_resolution,[status(thm)],[455,16]) ).
tff(457,plain,
a = join(a,meet(meet(b,meet(meet(a,b),c)),meet(a,meet(a,b)))),
inference(symmetry,[status(thm)],[456]) ).
tff(458,plain,
a = join(a,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c)))),
inference(transitivity,[status(thm)],[457,454]) ).
tff(459,plain,
meet(meet(b,meet(meet(a,b),c)),a) = meet(meet(b,meet(meet(a,b),c)),join(a,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))),
inference(monotonicity,[status(thm)],[458]) ).
tff(460,plain,
meet(meet(b,meet(meet(a,b),c)),join(a,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))) = meet(meet(b,meet(meet(a,b),c)),a),
inference(symmetry,[status(thm)],[459]) ).
tff(461,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,meet(meet(a,b),c)),join(a,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))) = meet(b,meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(462,plain,
meet(meet(b,meet(meet(a,b),c)),join(a,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))) = meet(b,meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[461,7]) ).
tff(463,plain,
meet(b,meet(meet(a,b),c)) = meet(meet(b,meet(meet(a,b),c)),join(a,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))),
inference(symmetry,[status(thm)],[462]) ).
tff(464,plain,
meet(b,meet(meet(a,b),c)) = meet(meet(b,meet(meet(a,b),c)),a),
inference(transitivity,[status(thm)],[463,460]) ).
tff(465,plain,
join(meet(b,meet(meet(a,b),c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(monotonicity,[status(thm)],[464,366]) ).
tff(466,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(b,meet(meet(a,b),c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[465]) ).
tff(467,plain,
meet(a,meet(b,c)) = meet(meet(a,meet(b,c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(symmetry,[status(thm)],[9]) ).
tff(468,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(469,plain,
join(join(meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(unit_resolution,[status(thm)],[468,43]) ).
tff(470,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(471,plain,
meet(meet(join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[470,25]) ).
tff(472,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c),meet(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(473,plain,
join(join(meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c),meet(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c) = c,
inference(unit_resolution,[status(thm)],[472,43]) ).
tff(474,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(a,b),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(475,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(a,b),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[474,7]) ).
tff(476,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(a,b),join(b,join(join(a,b),meet(b,meet(b,c))))) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(477,plain,
meet(join(a,b),join(b,join(join(a,b),meet(b,meet(b,c))))) = join(a,b),
inference(unit_resolution,[status(thm)],[476,7]) ).
tff(478,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(join(a,b),meet(meet(b,meet(b,c)),meet(join(a,b),b))) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(479,plain,
join(join(a,b),meet(meet(b,meet(b,c)),meet(join(a,b),b))) = join(a,b),
inference(unit_resolution,[status(thm)],[478,16]) ).
tff(480,plain,
meet(join(a,b),b) = join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(transitivity,[status(thm)],[289,294,296,268,161,160]) ).
tff(481,plain,
meet(meet(b,meet(b,c)),meet(join(a,b),b)) = meet(meet(b,meet(b,c)),join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(monotonicity,[status(thm)],[480]) ).
tff(482,plain,
meet(meet(b,meet(b,c)),join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(meet(b,meet(b,c)),meet(join(a,b),b)),
inference(symmetry,[status(thm)],[481]) ).
tff(483,plain,
meet(b,meet(b,c)) = meet(meet(b,meet(b,c)),join(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(symmetry,[status(thm)],[159]) ).
tff(484,plain,
meet(b,meet(b,c)) = meet(meet(b,meet(b,c)),meet(join(a,b),b)),
inference(transitivity,[status(thm)],[483,482]) ).
tff(485,plain,
join(join(a,b),meet(b,meet(b,c))) = join(join(a,b),meet(meet(b,meet(b,c)),meet(join(a,b),b))),
inference(monotonicity,[status(thm)],[484]) ).
tff(486,plain,
join(join(a,b),meet(b,meet(b,c))) = join(a,b),
inference(transitivity,[status(thm)],[485,479]) ).
tff(487,plain,
join(b,join(join(a,b),meet(b,meet(b,c)))) = join(join(meet(meet(a,b),join(a,b)),meet(join(a,b),b)),join(a,b)),
inference(monotonicity,[status(thm)],[304,486]) ).
tff(488,plain,
join(join(meet(meet(a,b),join(a,b)),meet(join(a,b),b)),join(a,b)) = join(b,join(join(a,b),meet(b,meet(b,c)))),
inference(symmetry,[status(thm)],[487]) ).
tff(489,plain,
join(a,b) = join(b,join(join(a,b),meet(b,meet(b,c)))),
inference(transitivity,[status(thm)],[309,488]) ).
tff(490,plain,
meet(join(a,b),join(a,b)) = meet(join(a,b),join(b,join(join(a,b),meet(b,meet(b,c))))),
inference(monotonicity,[status(thm)],[489]) ).
tff(491,plain,
meet(join(a,b),join(a,b)) = join(b,join(a,b)),
inference(transitivity,[status(thm)],[490,477,309,306]) ).
tff(492,plain,
meet(a,meet(join(a,b),join(a,b))) = meet(a,join(b,join(a,b))),
inference(monotonicity,[status(thm)],[491]) ).
tff(493,plain,
meet(a,join(b,join(a,b))) = meet(a,meet(join(a,b),join(a,b))),
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
a = meet(a,join(b,join(a,b))),
inference(symmetry,[status(thm)],[299]) ).
tff(495,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(496,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a) = a,
inference(unit_resolution,[status(thm)],[495,43]) ).
tff(497,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a) = meet(a,meet(join(a,b),join(a,b))),
inference(transitivity,[status(thm)],[496,494,493]) ).
tff(498,plain,
join(join(a,b),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)) = join(join(a,b),meet(a,meet(join(a,b),join(a,b)))),
inference(monotonicity,[status(thm)],[497]) ).
tff(499,plain,
join(join(a,b),meet(a,meet(join(a,b),join(a,b)))) = join(join(a,b),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),
inference(symmetry,[status(thm)],[498]) ).
tff(500,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(join(a,b),meet(a,meet(join(a,b),join(a,b)))) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(501,plain,
join(join(a,b),meet(a,meet(join(a,b),join(a,b)))) = join(a,b),
inference(unit_resolution,[status(thm)],[500,16]) ).
tff(502,plain,
join(a,b) = join(join(a,b),meet(a,meet(join(a,b),join(a,b)))),
inference(symmetry,[status(thm)],[501]) ).
tff(503,plain,
join(a,b) = join(join(a,b),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),
inference(transitivity,[status(thm)],[502,499]) ).
tff(504,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(a,b)) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(a,b),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))),
inference(monotonicity,[status(thm)],[503]) ).
tff(505,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(a,b)) = join(meet(b,meet(meet(a,b),c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[504,475,466]) ).
tff(506,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(a,b))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(meet(a,b),c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[505]) ).
tff(507,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(meet(a,b),c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(a,b))),
inference(symmetry,[status(thm)],[506]) ).
tff(508,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(meet(a,b),c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(symmetry,[status(thm)],[337]) ).
tff(509,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(510,plain,
meet(meet(join(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[509,25]) ).
tff(511,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(c,meet(b,meet(c,join(c,join(c,c))))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(512,plain,
join(c,meet(b,meet(c,join(c,join(c,c))))) = c,
inference(unit_resolution,[status(thm)],[511,16]) ).
tff(513,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(c,join(c,join(c,c))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(514,plain,
meet(c,join(c,join(c,c))) = c,
inference(unit_resolution,[status(thm)],[513,7]) ).
tff(515,plain,
meet(b,meet(c,join(c,join(c,c)))) = meet(b,c),
inference(monotonicity,[status(thm)],[514]) ).
tff(516,plain,
meet(b,c) = meet(b,meet(c,join(c,join(c,c)))),
inference(symmetry,[status(thm)],[515]) ).
tff(517,plain,
join(c,meet(b,c)) = join(c,meet(b,meet(c,join(c,join(c,c))))),
inference(monotonicity,[status(thm)],[516]) ).
tff(518,plain,
join(c,meet(b,c)) = c,
inference(transitivity,[status(thm)],[517,512]) ).
tff(519,plain,
join(c,join(c,meet(b,c))) = join(c,c),
inference(monotonicity,[status(thm)],[518]) ).
tff(520,plain,
join(c,c) = join(c,join(c,meet(b,c))),
inference(symmetry,[status(thm)],[519]) ).
tff(521,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(c,join(meet(b,meet(meet(a,b),c)),join(c,join(c,c)))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(522,plain,
meet(c,join(meet(b,meet(meet(a,b),c)),join(c,join(c,c)))) = c,
inference(unit_resolution,[status(thm)],[521,7]) ).
tff(523,plain,
meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(c,join(meet(b,meet(meet(a,b),c)),join(c,join(c,c))))) = meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),c),
inference(monotonicity,[status(thm)],[522]) ).
tff(524,plain,
meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),c) = meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(c,join(meet(b,meet(meet(a,b),c)),join(c,join(c,c))))),
inference(symmetry,[status(thm)],[523]) ).
tff(525,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(526,plain,
meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),c) = c,
inference(unit_resolution,[status(thm)],[525,25]) ).
tff(527,plain,
c = meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),c),
inference(symmetry,[status(thm)],[526]) ).
tff(528,plain,
c = meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(c,join(meet(b,meet(meet(a,b),c)),join(c,join(c,c))))),
inference(transitivity,[status(thm)],[527,524]) ).
tff(529,plain,
join(c,c) = join(c,meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(c,join(meet(b,meet(meet(a,b),c)),join(c,join(c,c)))))),
inference(monotonicity,[status(thm)],[528]) ).
tff(530,plain,
join(c,meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(c,join(meet(b,meet(meet(a,b),c)),join(c,join(c,c)))))) = join(c,c),
inference(symmetry,[status(thm)],[529]) ).
tff(531,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(c,meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(c,join(meet(b,meet(meet(a,b),c)),join(c,join(c,c)))))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(532,plain,
join(c,meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(c,join(meet(b,meet(meet(a,b),c)),join(c,join(c,c)))))) = c,
inference(unit_resolution,[status(thm)],[531,16]) ).
tff(533,plain,
c = join(c,meet(meet(join(join(c,join(c,c)),c),join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(c,join(meet(b,meet(meet(a,b),c)),join(c,join(c,c)))))),
inference(symmetry,[status(thm)],[532]) ).
tff(534,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c),meet(c,meet(a,meet(b,c)))),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(535,plain,
join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c),meet(c,meet(a,meet(b,c)))),c) = c,
inference(unit_resolution,[status(thm)],[534,43]) ).
tff(536,plain,
meet(join(c,join(c,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c)))) = meet(join(c,join(c,c)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[27]) ).
tff(537,plain,
meet(join(c,join(c,c)),meet(a,meet(b,c))) = meet(join(c,join(c,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c)))),
inference(symmetry,[status(thm)],[536]) ).
tff(538,plain,
join(c,c) = c,
inference(transitivity,[status(thm)],[529,532]) ).
tff(539,plain,
join(c,join(c,c)) = join(c,c),
inference(monotonicity,[status(thm)],[538]) ).
tff(540,plain,
join(c,c) = join(c,join(c,c)),
inference(symmetry,[status(thm)],[539]) ).
tff(541,plain,
c = join(c,join(c,c)),
inference(transitivity,[status(thm)],[533,530,540]) ).
tff(542,plain,
meet(c,meet(a,meet(b,c))) = meet(join(c,join(c,c)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[541]) ).
tff(543,plain,
meet(c,meet(a,meet(b,c))) = meet(join(c,join(c,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[542,537]) ).
tff(544,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(c,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(545,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(c,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[544,7]) ).
tff(546,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)) = meet(b,meet(c,join(c,join(c,c)))),
inference(transitivity,[status(thm)],[124,516]) ).
tff(547,plain,
join(c,join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))) = join(c,meet(b,meet(c,join(c,join(c,c))))),
inference(monotonicity,[status(thm)],[546]) ).
tff(548,plain,
join(c,meet(b,meet(c,join(c,join(c,c))))) = join(c,join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[547]) ).
tff(549,plain,
c = join(c,meet(b,meet(c,join(c,join(c,c))))),
inference(symmetry,[status(thm)],[512]) ).
tff(550,plain,
meet(c,join(c,join(c,c))) = join(c,join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),
inference(transitivity,[status(thm)],[514,549,548]) ).
tff(551,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(c,join(c,join(c,c)))) = meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(c,join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))),
inference(monotonicity,[status(thm)],[550]) ).
tff(552,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(c,join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))) = meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(c,join(c,join(c,c)))),
inference(symmetry,[status(thm)],[551]) ).
tff(553,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(c,join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(554,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(c,join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(unit_resolution,[status(thm)],[553,7]) ).
tff(555,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(c,join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))),
inference(symmetry,[status(thm)],[554]) ).
tff(556,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(c,join(c,join(c,c)))),
inference(transitivity,[status(thm)],[237,190,555,552]) ).
tff(557,plain,
join(c,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = join(c,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(c,join(c,join(c,c))))),
inference(monotonicity,[status(thm)],[556]) ).
tff(558,plain,
join(c,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(c,join(c,join(c,c))))) = join(c,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(symmetry,[status(thm)],[557]) ).
tff(559,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(c,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(c,join(c,join(c,c))))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(560,plain,
join(c,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(c,join(c,join(c,c))))) = c,
inference(unit_resolution,[status(thm)],[559,16]) ).
tff(561,plain,
c = join(c,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(c,join(c,join(c,c))))),
inference(symmetry,[status(thm)],[560]) ).
tff(562,plain,
c = join(c,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(transitivity,[status(thm)],[561,558]) ).
tff(563,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(c,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))),
inference(monotonicity,[status(thm)],[562]) ).
tff(564,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[563,545]) ).
tff(565,plain,
join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c),meet(c,meet(a,meet(b,c)))) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))))),
inference(monotonicity,[status(thm)],[564,543]) ).
tff(566,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))))) = join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c),meet(c,meet(a,meet(b,c)))),
inference(symmetry,[status(thm)],[565]) ).
tff(567,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(568,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[567,16]) ).
tff(569,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(a,meet(b,c))))),
inference(symmetry,[status(thm)],[568]) ).
tff(570,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c),meet(c,meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[569,566]) ).
tff(571,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c) = join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c),meet(c,meet(a,meet(b,c)))),c),
inference(monotonicity,[status(thm)],[570]) ).
tff(572,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c) = join(c,join(c,meet(b,c))),
inference(transitivity,[status(thm)],[571,535,533,530,520]) ).
tff(573,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(c,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(574,plain,
join(c,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))) = c,
inference(unit_resolution,[status(thm)],[573,16]) ).
tff(575,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),c)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(576,plain,
meet(meet(join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),c)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(unit_resolution,[status(thm)],[575,25]) ).
tff(577,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(join(a,b),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(578,plain,
meet(meet(join(join(a,b),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(unit_resolution,[status(thm)],[577,25]) ).
tff(579,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,meet(b,c))),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(580,plain,
join(join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,meet(b,c))),b) = b,
inference(unit_resolution,[status(thm)],[579,43]) ).
tff(581,plain,
meet(b,meet(b,c)) = meet(meet(b,meet(b,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c))),
inference(transitivity,[status(thm)],[157,154,149]) ).
tff(582,plain,
join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,meet(b,c))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(meet(b,meet(b,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))),
inference(monotonicity,[status(thm)],[166,581]) ).
tff(583,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(meet(b,meet(b,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))) = join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,meet(b,c))),
inference(symmetry,[status(thm)],[582]) ).
tff(584,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(meet(b,meet(b,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(b,c)))),
inference(symmetry,[status(thm)],[130]) ).
tff(585,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,meet(b,c))),
inference(transitivity,[status(thm)],[584,583]) ).
tff(586,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b) = join(join(meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b),meet(b,meet(b,c))),b),
inference(monotonicity,[status(thm)],[585]) ).
tff(587,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b) = join(b,meet(a,b)),
inference(transitivity,[status(thm)],[586,580,287,284]) ).
tff(588,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(meet(b,meet(b,c)),meet(join(a,b),b)),
inference(transitivity,[status(thm)],[150,163,156,483,482]) ).
tff(589,plain,
join(join(a,b),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(join(a,b),meet(meet(b,meet(b,c)),meet(join(a,b),b))),
inference(monotonicity,[status(thm)],[588]) ).
tff(590,plain,
join(join(a,b),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(a,b),
inference(transitivity,[status(thm)],[589,479]) ).
tff(591,plain,
meet(join(join(a,b),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b)) = meet(join(a,b),join(b,meet(a,b))),
inference(monotonicity,[status(thm)],[590,587]) ).
tff(592,plain,
meet(join(a,b),join(b,meet(a,b))) = meet(join(join(a,b),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b)),
inference(symmetry,[status(thm)],[591]) ).
tff(593,plain,
join(join(meet(join(a,b),b),meet(b,join(a,b))),b) = join(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),meet(meet(join(a,b),join(b,meet(a,b))),b))),
inference(symmetry,[status(thm)],[296]) ).
tff(594,plain,
b = join(join(meet(join(a,b),b),meet(b,join(a,b))),b),
inference(symmetry,[status(thm)],[268]) ).
tff(595,plain,
b = meet(join(join(a,b),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b)),
inference(transitivity,[status(thm)],[594,593,293,592]) ).
tff(596,plain,
meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(meet(join(join(a,b),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(monotonicity,[status(thm)],[595]) ).
tff(597,plain,
meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(transitivity,[status(thm)],[596,578]) ).
tff(598,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(b,c),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(599,plain,
join(join(meet(b,c),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),c) = c,
inference(unit_resolution,[status(thm)],[598,43]) ).
tff(600,plain,
meet(meet(join(join(a,b),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(symmetry,[status(thm)],[596]) ).
tff(601,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(meet(join(join(a,b),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(symmetry,[status(thm)],[578]) ).
tff(602,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b) = meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(transitivity,[status(thm)],[165,159,157,154,128,601,600]) ).
tff(603,plain,
meet(join(c,join(c,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b)) = meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(monotonicity,[status(thm)],[602]) ).
tff(604,plain,
meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(join(c,join(c,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b)),
inference(symmetry,[status(thm)],[603]) ).
tff(605,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(transitivity,[status(thm)],[601,600]) ).
tff(606,plain,
meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(monotonicity,[status(thm)],[541,605]) ).
tff(607,plain,
meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(join(c,join(c,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b)),
inference(transitivity,[status(thm)],[606,604]) ).
tff(608,plain,
meet(b,c) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(transitivity,[status(thm)],[135,187]) ).
tff(609,plain,
join(meet(b,c),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(join(c,join(c,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b))),
inference(monotonicity,[status(thm)],[608,607]) ).
tff(610,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(join(c,join(c,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b))) = join(meet(b,c),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(symmetry,[status(thm)],[609]) ).
tff(611,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(join(c,join(c,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(612,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(join(c,join(c,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b))) = join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),
inference(unit_resolution,[status(thm)],[611,16]) ).
tff(613,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(join(c,join(c,c)),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),b))),
inference(symmetry,[status(thm)],[612]) ).
tff(614,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = join(meet(b,c),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(transitivity,[status(thm)],[613,610]) ).
tff(615,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),c) = join(join(meet(b,c),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),c),
inference(monotonicity,[status(thm)],[614]) ).
tff(616,plain,
join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),c) = join(c,join(c,meet(b,c))),
inference(transitivity,[status(thm)],[615,599,533,530,520]) ).
tff(617,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(c,join(c,join(c,c)))),
inference(transitivity,[status(thm)],[555,552]) ).
tff(618,plain,
join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(c,meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(c,join(c,join(c,c))))),
inference(monotonicity,[status(thm)],[617]) ).
tff(619,plain,
join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = c,
inference(transitivity,[status(thm)],[618,560]) ).
tff(620,plain,
meet(join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),c)) = meet(c,join(c,join(c,meet(b,c)))),
inference(monotonicity,[status(thm)],[619,616]) ).
tff(621,plain,
meet(c,join(c,join(c,meet(b,c)))) = meet(join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),c)),
inference(symmetry,[status(thm)],[620]) ).
tff(622,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(c,join(c,join(c,meet(b,c)))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(623,plain,
meet(c,join(c,join(c,meet(b,c)))) = c,
inference(unit_resolution,[status(thm)],[622,7]) ).
tff(624,plain,
c = meet(c,join(c,join(c,meet(b,c)))),
inference(symmetry,[status(thm)],[623]) ).
tff(625,plain,
join(c,join(c,c)) = meet(join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),c)),
inference(transitivity,[status(thm)],[539,529,532,624,621]) ).
tff(626,plain,
meet(join(c,join(c,c)),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(meet(join(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),c)),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(monotonicity,[status(thm)],[625,597]) ).
tff(627,plain,
meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[606,626,576,228,225]) ).
tff(628,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[627]) ).
tff(629,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(symmetry,[status(thm)],[628]) ).
tff(630,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(symmetry,[status(thm)],[208]) ).
tff(631,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(transitivity,[status(thm)],[630,629]) ).
tff(632,plain,
join(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(c,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(c,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))),
inference(monotonicity,[status(thm)],[631]) ).
tff(633,plain,
join(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = c,
inference(transitivity,[status(thm)],[632,574]) ).
tff(634,plain,
meet(join(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)) = meet(c,join(c,join(c,meet(b,c)))),
inference(monotonicity,[status(thm)],[633,572]) ).
tff(635,plain,
meet(c,join(c,join(c,meet(b,c)))) = meet(join(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),
inference(symmetry,[status(thm)],[634]) ).
tff(636,plain,
c = meet(join(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),
inference(transitivity,[status(thm)],[624,635]) ).
tff(637,plain,
meet(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(join(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[636]) ).
tff(638,plain,
meet(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(a,b))),
inference(transitivity,[status(thm)],[637,510,508,507]) ).
tff(639,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(c,join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(640,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(c,join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[639,7]) ).
tff(641,plain,
meet(meet(a,b),meet(c,join(c,join(c,c)))) = meet(meet(a,b),c),
inference(monotonicity,[status(thm)],[514]) ).
tff(642,plain,
meet(meet(a,b),c) = meet(meet(a,b),meet(c,join(c,join(c,c)))),
inference(symmetry,[status(thm)],[641]) ).
tff(643,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(b,meet(meet(a,b),c)),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(644,plain,
join(join(meet(b,meet(meet(a,b),c)),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[643,43]) ).
tff(645,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(646,plain,
meet(meet(join(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[645,25]) ).
tff(647,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c) = c,
inference(transitivity,[status(thm)],[571,535]) ).
tff(648,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(a,b),meet(meet(a,b),meet(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(649,plain,
join(meet(a,b),meet(meet(a,b),meet(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(a,b),
inference(unit_resolution,[status(thm)],[648,16]) ).
tff(650,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(651,plain,
meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[650,25]) ).
tff(652,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(653,plain,
join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b) = b,
inference(unit_resolution,[status(thm)],[652,43]) ).
tff(654,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(655,plain,
meet(meet(join(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[654,25]) ).
tff(656,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(b,b))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(657,plain,
join(b,meet(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(b,b))) = b,
inference(unit_resolution,[status(thm)],[656,16]) ).
tff(658,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(659,plain,
join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b) = b,
inference(unit_resolution,[status(thm)],[658,43]) ).
tff(660,plain,
join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b)) = join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b),
inference(monotonicity,[status(thm)],[659]) ).
tff(661,plain,
join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b) = join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b)),
inference(symmetry,[status(thm)],[660]) ).
tff(662,plain,
b = join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b),
inference(symmetry,[status(thm)],[659]) ).
tff(663,plain,
meet(b,b) = join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b)),
inference(transitivity,[status(thm)],[379,373,662,661]) ).
tff(664,plain,
meet(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(b,b)) = meet(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b))),
inference(monotonicity,[status(thm)],[663]) ).
tff(665,plain,
meet(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b))) = meet(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(b,b)),
inference(symmetry,[status(thm)],[664]) ).
tff(666,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b))) = join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(667,plain,
meet(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b))) = join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),
inference(unit_resolution,[status(thm)],[666,7]) ).
tff(668,plain,
join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),b))),
inference(symmetry,[status(thm)],[667]) ).
tff(669,plain,
join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(b,b)),
inference(transitivity,[status(thm)],[668,665]) ).
tff(670,plain,
join(b,join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))) = join(b,meet(join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),meet(b,b))),
inference(monotonicity,[status(thm)],[669]) ).
tff(671,plain,
join(b,join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))) = b,
inference(transitivity,[status(thm)],[670,657]) ).
tff(672,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(b,join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))))) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b),
inference(monotonicity,[status(thm)],[671]) ).
tff(673,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(b,join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))))),
inference(symmetry,[status(thm)],[672]) ).
tff(674,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(b,c))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(675,plain,
join(b,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(b,c))) = b,
inference(unit_resolution,[status(thm)],[674,16]) ).
tff(676,plain,
meet(b,c) = join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[135,187,228,225]) ).
tff(677,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(b,c)) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[676]) ).
tff(678,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(b,c)),
inference(symmetry,[status(thm)],[677]) ).
tff(679,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(b,c)),
inference(transitivity,[status(thm)],[630,678]) ).
tff(680,plain,
join(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(b,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(b,c))),
inference(monotonicity,[status(thm)],[679]) ).
tff(681,plain,
join(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = b,
inference(transitivity,[status(thm)],[680,675]) ).
tff(682,plain,
meet(join(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)) = meet(b,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(b,join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))))),
inference(monotonicity,[status(thm)],[681,673]) ).
tff(683,plain,
meet(b,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(b,join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))))) = meet(join(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),
inference(symmetry,[status(thm)],[682]) ).
tff(684,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(b,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(b,join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(685,plain,
meet(b,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(b,join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))))) = b,
inference(unit_resolution,[status(thm)],[684,7]) ).
tff(686,plain,
b = meet(b,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(b,join(meet(a,b),meet(b,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))))))),
inference(symmetry,[status(thm)],[685]) ).
tff(687,plain,
b = meet(join(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),
inference(transitivity,[status(thm)],[686,683]) ).
tff(688,plain,
meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(join(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[687]) ).
tff(689,plain,
meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[688,655]) ).
tff(690,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(b,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c))))))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(691,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(b,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c))))))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[690,7]) ).
tff(692,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(a,b),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(693,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(a,b),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[692,16]) ).
tff(694,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(695,plain,
join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[694,43]) ).
tff(696,plain,
join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[695]) ).
tff(697,plain,
join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[696]) ).
tff(698,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[695]) ).
tff(699,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(a,b),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(700,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(a,b),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[699,7]) ).
tff(701,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(a,b),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[700,698,697]) ).
tff(702,plain,
meet(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(a,b),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))) = meet(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[701]) ).
tff(703,plain,
meet(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(a,b),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))),
inference(symmetry,[status(thm)],[702]) ).
tff(704,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(705,plain,
meet(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),
inference(unit_resolution,[status(thm)],[704,7]) ).
tff(706,plain,
join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))) = meet(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(symmetry,[status(thm)],[705]) ).
tff(707,plain,
join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))) = meet(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(a,b),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))),
inference(transitivity,[status(thm)],[706,703]) ).
tff(708,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c))))))) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(join(a,b),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))))),
inference(monotonicity,[status(thm)],[707]) ).
tff(709,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c))))))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(b,c)),
inference(transitivity,[status(thm)],[708,693,630,678]) ).
tff(710,plain,
join(b,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))))) = join(b,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(b,c))),
inference(monotonicity,[status(thm)],[709]) ).
tff(711,plain,
join(b,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(b,c))) = join(b,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))))),
inference(symmetry,[status(thm)],[710]) ).
tff(712,plain,
b = join(b,meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(b,c))),
inference(symmetry,[status(thm)],[675]) ).
tff(713,plain,
b = join(b,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c)))))))),
inference(transitivity,[status(thm)],[712,711]) ).
tff(714,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(b,join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(c,join(c,c)),meet(join(c,join(c,c)),meet(a,meet(b,c))))))))),
inference(monotonicity,[status(thm)],[713]) ).
tff(715,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[714,691]) ).
tff(716,plain,
join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[715,689]) ).
tff(717,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[716]) ).
tff(718,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[235,234,717]) ).
tff(719,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b) = join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b),
inference(monotonicity,[status(thm)],[718]) ).
tff(720,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b) = b,
inference(transitivity,[status(thm)],[719,653]) ).
tff(721,plain,
meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)) = meet(a,b),
inference(monotonicity,[status(thm)],[328,720]) ).
tff(722,plain,
meet(a,b) = meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),
inference(symmetry,[status(thm)],[721]) ).
tff(723,plain,
meet(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[722]) ).
tff(724,plain,
meet(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[723,651]) ).
tff(725,plain,
meet(meet(a,b),meet(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[722,724]) ).
tff(726,plain,
meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(a,b),meet(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(meet(join(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),b)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[651]) ).
tff(728,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(meet(a,b),meet(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[727,726]) ).
tff(729,plain,
join(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(meet(a,b),meet(meet(a,b),meet(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[728]) ).
tff(730,plain,
join(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(a,b),
inference(transitivity,[status(thm)],[729,649]) ).
tff(731,plain,
meet(join(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)) = meet(meet(a,b),c),
inference(monotonicity,[status(thm)],[730,647]) ).
tff(732,plain,
meet(meet(a,b),c) = meet(join(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),
inference(symmetry,[status(thm)],[731]) ).
tff(733,plain,
meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(join(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[732]) ).
tff(734,plain,
meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(transitivity,[status(thm)],[733,646,365,362]) ).
tff(735,plain,
join(meet(b,meet(meet(a,b),c)),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(monotonicity,[status(thm)],[464,734]) ).
tff(736,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(b,meet(meet(a,b),c)),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[735]) ).
tff(737,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)) = join(join(meet(b,meet(meet(a,b),c)),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[736]) ).
tff(738,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)) = meet(meet(a,b),meet(c,join(c,join(c,c)))),
inference(transitivity,[status(thm)],[737,644,642]) ).
tff(739,plain,
join(c,join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c))) = join(c,meet(meet(a,b),meet(c,join(c,join(c,c))))),
inference(monotonicity,[status(thm)],[738]) ).
tff(740,plain,
join(c,meet(meet(a,b),meet(c,join(c,join(c,c))))) = join(c,join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[739]) ).
tff(741,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(c,meet(meet(a,b),meet(c,join(c,join(c,c))))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(742,plain,
join(c,meet(meet(a,b),meet(c,join(c,join(c,c))))) = c,
inference(unit_resolution,[status(thm)],[741,16]) ).
tff(743,plain,
c = join(c,meet(meet(a,b),meet(c,join(c,join(c,c))))),
inference(symmetry,[status(thm)],[742]) ).
tff(744,plain,
c = join(c,join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c))),
inference(transitivity,[status(thm)],[743,740]) ).
tff(745,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(c,join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)))),
inference(monotonicity,[status(thm)],[744]) ).
tff(746,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[745,640]) ).
tff(747,plain,
join(meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c),meet(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(a,b)))),
inference(monotonicity,[status(thm)],[746,638]) ).
tff(748,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(a,b)))) = join(meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c),meet(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[747]) ).
tff(749,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(a,b)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(750,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(a,b)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[749,16]) ).
tff(751,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(a,b)))),
inference(symmetry,[status(thm)],[750]) ).
tff(752,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c),meet(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[751,748]) ).
tff(753,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c) = join(join(meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c),meet(c,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c),
inference(monotonicity,[status(thm)],[752]) ).
tff(754,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c) = c,
inference(transitivity,[status(thm)],[753,473]) ).
tff(755,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(b,join(join(c,join(c,c)),join(join(a,b),join(a,b)))))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(756,plain,
join(b,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(b,join(join(c,join(c,c)),join(join(a,b),join(a,b)))))) = b,
inference(unit_resolution,[status(thm)],[755,16]) ).
tff(757,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(b,meet(meet(a,b),c)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(758,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b) = b,
inference(unit_resolution,[status(thm)],[757,43]) ).
tff(759,plain,
meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(transitivity,[status(thm)],[688,655,365,362]) ).
tff(760,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,meet(meet(a,b),c)),join(b,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))) = meet(b,meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(761,plain,
meet(meet(b,meet(meet(a,b),c)),join(b,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))) = meet(b,meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[760,7]) ).
tff(762,plain,
join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))) = meet(meet(a,b),meet(b,meet(meet(a,b),c))),
inference(transitivity,[status(thm)],[435,368,421,418]) ).
tff(763,plain,
join(b,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c)))) = join(b,meet(meet(a,b),meet(b,meet(meet(a,b),c)))),
inference(monotonicity,[status(thm)],[762]) ).
tff(764,plain,
join(b,meet(meet(a,b),meet(b,meet(meet(a,b),c)))) = join(b,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c)))),
inference(symmetry,[status(thm)],[763]) ).
tff(765,plain,
b = join(b,meet(meet(a,b),meet(b,meet(meet(a,b),c)))),
inference(symmetry,[status(thm)],[408]) ).
tff(766,plain,
b = join(b,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c)))),
inference(transitivity,[status(thm)],[765,764]) ).
tff(767,plain,
meet(meet(b,meet(meet(a,b),c)),b) = meet(meet(b,meet(meet(a,b),c)),join(b,join(meet(b,meet(meet(a,b),c)),meet(b,meet(meet(a,b),c))))),
inference(monotonicity,[status(thm)],[766]) ).
tff(768,plain,
meet(meet(b,meet(meet(a,b),c)),b) = meet(meet(b,meet(meet(a,b),c)),a),
inference(transitivity,[status(thm)],[767,761,463,460]) ).
tff(769,plain,
join(meet(meet(b,meet(meet(a,b),c)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(monotonicity,[status(thm)],[768,759]) ).
tff(770,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(meet(b,meet(meet(a,b),c)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[769]) ).
tff(771,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b) = join(join(meet(meet(b,meet(meet(a,b),c)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b),
inference(monotonicity,[status(thm)],[770]) ).
tff(772,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b) = b,
inference(transitivity,[status(thm)],[771,758]) ).
tff(773,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b)) = join(join(meet(meet(b,meet(meet(a,b),c)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b),
inference(monotonicity,[status(thm)],[770,772]) ).
tff(774,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b)),
inference(symmetry,[status(thm)],[773]) ).
tff(775,plain,
b = join(join(meet(meet(b,meet(meet(a,b),c)),b),meet(b,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b),
inference(symmetry,[status(thm)],[758]) ).
tff(776,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(b,join(join(c,join(c,c)),join(b,join(a,b)))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(777,plain,
meet(b,join(join(c,join(c,c)),join(b,join(a,b)))) = b,
inference(unit_resolution,[status(thm)],[776,7]) ).
tff(778,plain,
join(b,join(a,b)) = join(join(a,b),join(a,b)),
inference(transitivity,[status(thm)],[305,308,319,316]) ).
tff(779,plain,
join(join(c,join(c,c)),join(b,join(a,b))) = join(join(c,join(c,c)),join(join(a,b),join(a,b))),
inference(monotonicity,[status(thm)],[778]) ).
tff(780,plain,
join(join(c,join(c,c)),join(join(a,b),join(a,b))) = join(join(c,join(c,c)),join(b,join(a,b))),
inference(symmetry,[status(thm)],[779]) ).
tff(781,plain,
meet(b,join(join(c,join(c,c)),join(join(a,b),join(a,b)))) = meet(b,join(join(c,join(c,c)),join(b,join(a,b)))),
inference(monotonicity,[status(thm)],[780]) ).
tff(782,plain,
meet(b,join(join(c,join(c,c)),join(join(a,b),join(a,b)))) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b)),
inference(transitivity,[status(thm)],[781,777,775,774]) ).
tff(783,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(b,join(join(c,join(c,c)),join(join(a,b),join(a,b))))) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b))),
inference(monotonicity,[status(thm)],[782]) ).
tff(784,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b))) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(b,join(join(c,join(c,c)),join(join(a,b),join(a,b))))),
inference(symmetry,[status(thm)],[783]) ).
tff(785,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(786,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[785,7]) ).
tff(787,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),b))),
inference(symmetry,[status(thm)],[786]) ).
tff(788,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(b,join(join(c,join(c,c)),join(join(a,b),join(a,b))))),
inference(transitivity,[status(thm)],[787,784]) ).
tff(789,plain,
join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(b,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(b,join(join(c,join(c,c)),join(join(a,b),join(a,b)))))),
inference(monotonicity,[status(thm)],[788]) ).
tff(790,plain,
join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = b,
inference(transitivity,[status(thm)],[789,756]) ).
tff(791,plain,
meet(join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c)) = meet(b,c),
inference(monotonicity,[status(thm)],[790,754]) ).
tff(792,plain,
meet(b,c) = meet(join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c)),
inference(symmetry,[status(thm)],[791]) ).
tff(793,plain,
join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))) = meet(join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c)),
inference(transitivity,[status(thm)],[188,124,792]) ).
tff(794,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),c)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[793]) ).
tff(795,plain,
meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[794,471]) ).
tff(796,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(meet(b,meet(meet(a,b),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(797,plain,
meet(meet(join(meet(b,meet(meet(a,b),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[796,25]) ).
tff(798,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a),
inference(monotonicity,[status(thm)],[496]) ).
tff(799,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),
inference(symmetry,[status(thm)],[798]) ).
tff(800,plain,
a = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a),
inference(symmetry,[status(thm)],[496]) ).
tff(801,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),
inference(transitivity,[status(thm)],[353,345,800,799]) ).
tff(802,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(transitivity,[status(thm)],[365,362]) ).
tff(803,plain,
join(meet(b,meet(meet(a,b),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(monotonicity,[status(thm)],[464,802]) ).
tff(804,plain,
meet(join(meet(b,meet(meet(a,b),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))),
inference(monotonicity,[status(thm)],[803,801]) ).
tff(805,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))) = meet(join(meet(b,meet(meet(a,b),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),
inference(symmetry,[status(thm)],[804]) ).
tff(806,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(807,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[806,7]) ).
tff(808,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))),
inference(symmetry,[status(thm)],[807]) ).
tff(809,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = meet(join(meet(b,meet(meet(a,b),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),
inference(transitivity,[status(thm)],[808,805]) ).
tff(810,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(join(meet(b,meet(meet(a,b),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[809]) ).
tff(811,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[810,797]) ).
tff(812,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(meet(a,b),c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[466]) ).
tff(813,plain,
meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[812,337]) ).
tff(814,plain,
join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[813,811]) ).
tff(815,plain,
join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[814]) ).
tff(816,plain,
meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[241,467,331,334,235,234,815]) ).
tff(817,plain,
join(meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))) = join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[816,795]) ).
tff(818,plain,
join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))),
inference(symmetry,[status(thm)],[817]) ).
tff(819,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(820,plain,
join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[819,43]) ).
tff(821,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(join(meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(symmetry,[status(thm)],[820]) ).
tff(822,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))),
inference(transitivity,[status(thm)],[821,818]) ).
tff(823,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = join(join(meet(a,join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),meet(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))),
inference(monotonicity,[status(thm)],[822]) ).
tff(824,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c)))) = meet(b,c),
inference(transitivity,[status(thm)],[823,469,188,124]) ).
tff(825,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(a,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(a,join(meet(a,meet(b,c)),a)))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(826,plain,
join(a,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(a,join(meet(a,meet(b,c)),a)))) = a,
inference(unit_resolution,[status(thm)],[825,16]) ).
tff(827,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(meet(a,meet(b,c)),join(a,meet(a,b)))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(828,plain,
meet(a,join(meet(a,meet(b,c)),join(a,meet(a,b)))) = a,
inference(unit_resolution,[status(thm)],[827,7]) ).
tff(829,plain,
join(meet(a,meet(b,c)),join(a,meet(a,b))) = join(meet(a,meet(b,c)),a),
inference(monotonicity,[status(thm)],[340]) ).
tff(830,plain,
join(meet(a,meet(b,c)),a) = join(meet(a,meet(b,c)),join(a,meet(a,b))),
inference(symmetry,[status(thm)],[829]) ).
tff(831,plain,
meet(a,join(meet(a,meet(b,c)),a)) = meet(a,join(meet(a,meet(b,c)),join(a,meet(a,b)))),
inference(monotonicity,[status(thm)],[830]) ).
tff(832,plain,
meet(a,join(meet(a,meet(b,c)),a)) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),
inference(transitivity,[status(thm)],[831,828,800,799]) ).
tff(833,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(a,join(meet(a,meet(b,c)),a))) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))),
inference(monotonicity,[status(thm)],[832]) ).
tff(834,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(a,join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[833]) ).
tff(835,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(a,join(meet(a,meet(b,c)),a))),
inference(transitivity,[status(thm)],[808,834]) ).
tff(836,plain,
join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(a,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(a,join(meet(a,meet(b,c)),a)))),
inference(monotonicity,[status(thm)],[835]) ).
tff(837,plain,
join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = a,
inference(transitivity,[status(thm)],[836,826]) ).
tff(838,plain,
meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(a,meet(b,c)),
inference(monotonicity,[status(thm)],[837,824]) ).
tff(839,plain,
meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[838,467,331,334]) ).
tff(840,plain,
meet(meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),join(meet(b,meet(meet(a,b),c)),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[839,466]) ).
tff(841,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(842,plain,
meet(meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[841,25]) ).
tff(843,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = meet(meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(symmetry,[status(thm)],[842]) ).
tff(844,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(845,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[844,7]) ).
tff(846,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[737,644]) ).
tff(847,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c))) = join(join(meet(b,meet(meet(a,b),c)),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[736,846]) ).
tff(848,plain,
join(join(meet(b,meet(meet(a,b),c)),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[847]) ).
tff(849,plain,
meet(meet(a,b),c) = join(join(meet(b,meet(meet(a,b),c)),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[644]) ).
tff(850,plain,
meet(meet(a,b),c) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c))),
inference(transitivity,[status(thm)],[849,848]) ).
tff(851,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(852,plain,
meet(meet(join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[851,25]) ).
tff(853,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(a,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(a,meet(b,c)),a)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(854,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(a,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(a,meet(b,c)),a)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[853,16]) ).
tff(855,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(a,meet(b,c)),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(856,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(a,meet(b,c)),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[855,7]) ).
tff(857,plain,
join(meet(a,meet(b,c)),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)) = join(meet(a,meet(b,c)),a),
inference(monotonicity,[status(thm)],[496]) ).
tff(858,plain,
join(meet(a,meet(b,c)),a) = join(meet(a,meet(b,c)),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),
inference(symmetry,[status(thm)],[857]) ).
tff(859,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(a,meet(b,c)),a)) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(a,meet(b,c)),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a))),
inference(monotonicity,[status(thm)],[858]) ).
tff(860,plain,
meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(a,meet(b,c)),a)) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[859,856]) ).
tff(861,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a) = join(meet(a,b),join(a,meet(a,b))),
inference(transitivity,[status(thm)],[496,343,342]) ).
tff(862,plain,
meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)) = meet(a,join(meet(a,b),join(a,meet(a,b)))),
inference(monotonicity,[status(thm)],[837,861]) ).
tff(863,plain,
meet(a,join(meet(a,b),join(a,meet(a,b)))) = meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),
inference(symmetry,[status(thm)],[862]) ).
tff(864,plain,
a = meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),
inference(transitivity,[status(thm)],[359,863]) ).
tff(865,plain,
meet(a,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(a,meet(b,c)),a))) = meet(meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[864,860]) ).
tff(866,plain,
meet(meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(a,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[865]) ).
tff(867,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(868,plain,
meet(meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[867,25]) ).
tff(869,plain,
join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = meet(meet(join(a,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),a)),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(symmetry,[status(thm)],[868]) ).
tff(870,plain,
join(meet(b,meet(meet(a,b),c)),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(monotonicity,[status(thm)],[464]) ).
tff(871,plain,
join(meet(b,meet(meet(a,b),c)),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = meet(a,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(a,meet(b,c)),a))),
inference(transitivity,[status(thm)],[870,869,866]) ).
tff(872,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(meet(a,b),c)),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(a,meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(a,meet(b,c)),a)))),
inference(monotonicity,[status(thm)],[871]) ).
tff(873,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(meet(a,b),c)),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[872,854]) ).
tff(874,plain,
meet(join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c))) = meet(b,meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[790,846]) ).
tff(875,plain,
meet(b,meet(meet(a,b),c)) = meet(join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[874]) ).
tff(876,plain,
meet(meet(b,meet(meet(a,b),c)),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(meet(a,b),c)),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))) = meet(meet(join(b,join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c))),join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[875,873]) ).
tff(877,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,meet(meet(a,b),c)),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(meet(a,b),c)),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))) = meet(b,meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(878,plain,
meet(meet(b,meet(meet(a,b),c)),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(meet(a,b),c)),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))) = meet(b,meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[877,7]) ).
tff(879,plain,
meet(b,meet(meet(a,b),c)) = meet(meet(b,meet(meet(a,b),c)),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(b,meet(meet(a,b),c)),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))))),
inference(symmetry,[status(thm)],[878]) ).
tff(880,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(meet(a,b),c),meet(a,meet(meet(meet(a,b),c),c))) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(881,plain,
join(meet(meet(a,b),c),meet(a,meet(meet(meet(a,b),c),c))) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[880,16]) ).
tff(882,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(meet(a,b),c),join(c,join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(883,plain,
meet(meet(meet(a,b),c),join(c,join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[882,7]) ).
tff(884,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(meet(a,b),c),meet(meet(meet(a,b),c),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(885,plain,
join(meet(meet(a,b),c),meet(meet(meet(a,b),c),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[884,16]) ).
tff(886,plain,
meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[733,646]) ).
tff(887,plain,
meet(meet(meet(a,b),c),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = meet(meet(join(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[732,886]) ).
tff(888,plain,
meet(meet(join(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(meet(a,b),c),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[887]) ).
tff(889,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(meet(join(meet(a,b),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),join(meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)),c)),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))),
inference(symmetry,[status(thm)],[646]) ).
tff(890,plain,
meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)) = meet(meet(meet(a,b),c),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[889,888]) ).
tff(891,plain,
join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = join(meet(meet(a,b),c),meet(meet(meet(a,b),c),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[890]) ).
tff(892,plain,
join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(a,b),meet(c,join(c,join(c,c)))),
inference(transitivity,[status(thm)],[891,885,642]) ).
tff(893,plain,
join(c,join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(c,meet(meet(a,b),meet(c,join(c,join(c,c))))),
inference(monotonicity,[status(thm)],[892]) ).
tff(894,plain,
join(c,meet(meet(a,b),meet(c,join(c,join(c,c))))) = join(c,join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[893]) ).
tff(895,plain,
c = join(c,join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[743,894]) ).
tff(896,plain,
meet(meet(meet(a,b),c),c) = meet(meet(meet(a,b),c),join(c,join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[895]) ).
tff(897,plain,
meet(meet(meet(a,b),c),c) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[896,883]) ).
tff(898,plain,
meet(a,meet(meet(meet(a,b),c),c)) = meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[347,897]) ).
tff(899,plain,
meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c)) = meet(a,meet(meet(meet(a,b),c),c)),
inference(symmetry,[status(thm)],[898]) ).
tff(900,plain,
join(meet(meet(a,b),c),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))) = join(meet(meet(a,b),c),meet(a,meet(meet(meet(a,b),c),c))),
inference(monotonicity,[status(thm)],[899]) ).
tff(901,plain,
join(meet(meet(a,b),c),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c))) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[900,881]) ).
tff(902,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(meet(meet(a,b),c),meet(b,meet(a,b)))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(903,plain,
join(b,meet(meet(meet(a,b),c),meet(b,meet(a,b)))) = b,
inference(unit_resolution,[status(thm)],[902,16]) ).
tff(904,plain,
join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[891,885]) ).
tff(905,plain,
join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(join(meet(b,meet(meet(a,b),c)),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[736,904]) ).
tff(906,plain,
join(join(meet(b,meet(meet(a,b),c)),meet(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[905]) ).
tff(907,plain,
meet(meet(a,b),c) = join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[849,906]) ).
tff(908,plain,
meet(meet(meet(a,b),c),meet(meet(a,b),c)) = meet(meet(meet(a,b),c),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[907]) ).
tff(909,plain,
meet(meet(meet(a,b),c),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(meet(a,b),c),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[908]) ).
tff(910,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(meet(a,b),c),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(911,plain,
meet(meet(meet(a,b),c),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[910,7]) ).
tff(912,plain,
meet(meet(a,b),c) = meet(meet(meet(a,b),c),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(symmetry,[status(thm)],[911]) ).
tff(913,plain,
join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))) = meet(meet(meet(a,b),c),meet(meet(a,b),c)),
inference(transitivity,[status(thm)],[891,885,912,909]) ).
tff(914,plain,
join(meet(a,b),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))) = join(meet(a,b),meet(meet(meet(a,b),c),meet(meet(a,b),c))),
inference(monotonicity,[status(thm)],[913]) ).
tff(915,plain,
join(meet(a,b),meet(meet(meet(a,b),c),meet(meet(a,b),c))) = join(meet(a,b),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(symmetry,[status(thm)],[914]) ).
tff(916,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(a,b),meet(meet(meet(a,b),c),meet(meet(a,b),c))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(917,plain,
join(meet(a,b),meet(meet(meet(a,b),c),meet(meet(a,b),c))) = meet(a,b),
inference(unit_resolution,[status(thm)],[916,16]) ).
tff(918,plain,
meet(a,b) = join(meet(a,b),meet(meet(meet(a,b),c),meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[917]) ).
tff(919,plain,
meet(b,meet(a,b)) = join(meet(a,b),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[79,74,918,915]) ).
tff(920,plain,
meet(meet(meet(a,b),c),meet(b,meet(a,b))) = meet(meet(meet(a,b),c),join(meet(a,b),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(monotonicity,[status(thm)],[919]) ).
tff(921,plain,
meet(meet(meet(a,b),c),join(meet(a,b),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(meet(a,b),c),meet(b,meet(a,b))),
inference(symmetry,[status(thm)],[920]) ).
tff(922,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(meet(a,b),c),join(meet(a,b),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(923,plain,
meet(meet(meet(a,b),c),join(meet(a,b),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[922,7]) ).
tff(924,plain,
meet(meet(a,b),c) = meet(meet(meet(a,b),c),join(meet(a,b),join(meet(meet(a,b),c),meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a))))),
inference(symmetry,[status(thm)],[923]) ).
tff(925,plain,
meet(meet(a,b),c) = meet(meet(meet(a,b),c),meet(b,meet(a,b))),
inference(transitivity,[status(thm)],[924,921]) ).
tff(926,plain,
join(b,meet(meet(a,b),c)) = join(b,meet(meet(meet(a,b),c),meet(b,meet(a,b)))),
inference(monotonicity,[status(thm)],[925]) ).
tff(927,plain,
join(b,meet(meet(a,b),c)) = b,
inference(transitivity,[status(thm)],[926,903]) ).
tff(928,plain,
meet(join(b,meet(meet(a,b),c)),join(meet(meet(a,b),c),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c)))) = meet(b,meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[927,901]) ).
tff(929,plain,
meet(join(b,meet(meet(a,b),c)),join(meet(meet(a,b),c),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c)))) = join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),
inference(transitivity,[status(thm)],[928,879,876,852]) ).
tff(930,plain,
meet(meet(join(b,meet(meet(a,b),c)),join(meet(meet(a,b),c),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c)))),meet(meet(a,b),c)) = meet(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),join(join(meet(meet(b,meet(meet(a,b),c)),a),meet(a,meet(join(join(meet(b,meet(b,c)),meet(meet(b,c),meet(b,c))),meet(a,meet(b,c))),join(meet(a,meet(b,c)),a)))),meet(meet(a,b),c)))),
inference(monotonicity,[status(thm)],[929,850]) ).
tff(931,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(b,meet(meet(a,b),c)),join(meet(meet(a,b),c),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c)))),meet(meet(a,b),c)) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(932,plain,
meet(meet(join(b,meet(meet(a,b),c)),join(meet(meet(a,b),c),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c)))),meet(meet(a,b),c)) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[931,25]) ).
tff(933,plain,
meet(meet(a,b),c) = meet(meet(join(b,meet(meet(a,b),c)),join(meet(meet(a,b),c),meet(join(meet(a,meet(b,c)),a),meet(meet(a,b),c)))),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[932]) ).
tff(934,plain,
meet(meet(a,b),c) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[933,930,845,843,840,337,335,332,9]) ).
tff(935,plain,
( ( meet(meet(a,b),c) != meet(a,meet(b,c)) )
<=> ( meet(meet(a,b),c) != meet(a,meet(b,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(936,axiom,
meet(meet(a,b),c) != meet(a,meet(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_meet) ).
tff(937,plain,
meet(meet(a,b),c) != meet(a,meet(b,c)),
inference(modus_ponens,[status(thm)],[936,935]) ).
tff(938,plain,
$false,
inference(unit_resolution,[status(thm)],[937,934]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT013-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 10:52:01 EDT 2022
% 0.12/0.34 % 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.
% 0.94/0.85 % SZS status Unsatisfiable
% 0.94/0.85 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------