%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT026-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:45 AM UTC 2025
% Result : Unsatisfiable 1.62s 1.81s
% Output : Proof 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 89
% Syntax : Number of formulae : 404 ( 323 unt; 0 typ; 0 def)
% Number of atoms : 499 ( 491 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 158 ( 70 ~; 66 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 288 ( 273 !; 0 ?; 288 :)
% 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,
^ [X: $i] :
refl(( ( join(X,X) = X )
<=> ( join(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( join(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',idempotence_of_join) ).
tff(5,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( join(X,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(a,meet(b,c)),meet(a,meet(b,c))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
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(( ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
<=> ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',wal_1) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
meet(meet(join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',commutativity_of_meet) ).
tff(23,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c)))))) = meet(meet(join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c)))))) = meet(meet(join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
<=> ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
<=> ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',commutativity_of_join) ).
tff(32,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))) = join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
join(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))) = join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
^ [X: $i] :
refl(( ( meet(X,X) = X )
<=> ( meet(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
! [X: $i] : ( meet(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',idempotence_of_meet) ).
tff(41,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(join(meet(meet(b,c),a),meet(b,a)),join(meet(meet(b,c),a),meet(b,a))) = join(meet(meet(b,c),a),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
meet(join(meet(meet(b,c),a),meet(b,a)),join(meet(meet(b,c),a),meet(b,a))) = join(meet(meet(b,c),a),meet(b,a)),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
join(meet(meet(b,c),a),meet(b,a)) = meet(join(meet(meet(b,c),a),meet(b,a)),join(meet(meet(b,c),a),meet(b,a))),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,a) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
meet(b,a) = meet(a,b),
inference(unit_resolution,[status(thm)],[47,25]) ).
tff(49,plain,
meet(a,b) = meet(b,a),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
<=> ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',wal_2) ).
tff(54,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(c,meet(a,b)),meet(c,meet(a,b))),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
join(join(meet(c,meet(a,b)),meet(c,meet(a,b))),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,meet(a,b)) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
meet(c,meet(a,b)) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[59,25]) ).
tff(61,plain,
join(meet(c,meet(a,b)),meet(c,meet(a,b))) = join(meet(meet(a,b),c),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[60,60]) ).
tff(62,plain,
join(meet(meet(a,b),c),meet(meet(a,b),c)) = join(meet(c,meet(a,b)),meet(c,meet(a,b))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(meet(a,b),c),meet(meet(a,b),c)) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
join(meet(meet(a,b),c),meet(meet(a,b),c)) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
meet(meet(a,b),c) = join(meet(meet(a,b),c),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
meet(meet(a,b),c) = join(meet(c,meet(a,b)),meet(c,meet(a,b))),
inference(transitivity,[status(thm)],[65,62]) ).
tff(67,plain,
join(meet(meet(a,b),c),meet(a,b)) = join(join(meet(c,meet(a,b)),meet(c,meet(a,b))),meet(a,b)),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
join(meet(meet(a,b),c),meet(a,b)) = meet(b,a),
inference(transitivity,[status(thm)],[67,58,49]) ).
tff(69,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(b,c),a) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
meet(meet(b,c),a) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[69,25]) ).
tff(71,plain,
meet(a,meet(b,c)) = meet(meet(b,c),a),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = meet(meet(b,c),a),
inference(transitivity,[status(thm)],[9,71]) ).
tff(73,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(a,b))) = join(meet(meet(b,c),a),meet(b,a)),
inference(monotonicity,[status(thm)],[72,68]) ).
tff(74,plain,
join(meet(meet(b,c),a),meet(b,a)) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(a,b))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))) = meet(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(a,b)))),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
meet(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,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(78,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)],[77]) ).
tff(79,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(80,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion) ).
tff(81,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
meet(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
meet(meet(a,b),c) = meet(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(a,b)))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
meet(meet(a,b),c) = meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),
inference(transitivity,[status(thm)],[86,76]) ).
tff(88,plain,
join(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))) = join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(join(meet(meet(b,c),a),meet(b,a)),join(meet(meet(b,c),a),meet(b,a)))),
inference(monotonicity,[status(thm)],[87,46]) ).
tff(89,plain,
join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(join(meet(meet(b,c),a),meet(b,a)),join(meet(meet(b,c),a),meet(b,a)))) = join(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[75,85]) ).
tff(91,plain,
join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a)))) = join(meet(meet(a,b),c),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[90,90]) ).
tff(92,plain,
join(meet(meet(a,b),c),meet(meet(a,b),c)) = join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a)))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))) = join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a)))),
inference(transitivity,[status(thm)],[75,85,65,92]) ).
tff(94,plain,
join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(join(meet(meet(b,c),a),meet(b,a)),join(meet(meet(b,c),a),meet(b,a)))) = join(join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a)))),join(meet(meet(b,c),a),meet(b,a))),
inference(monotonicity,[status(thm)],[93,45]) ).
tff(95,plain,
join(join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a)))),join(meet(meet(b,c),a),meet(b,a))) = join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(join(meet(meet(b,c),a),meet(b,a)),join(meet(meet(b,c),a),meet(b,a)))),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a)))),join(meet(meet(b,c),a),meet(b,a))) = join(meet(meet(b,c),a),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
join(join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a)))),join(meet(meet(b,c),a),meet(b,a))) = join(meet(meet(b,c),a),meet(b,a)),
inference(unit_resolution,[status(thm)],[96,56]) ).
tff(98,plain,
join(meet(meet(b,c),a),meet(b,a)) = join(join(meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),meet(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a)))),join(meet(meet(b,c),a),meet(b,a))),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b)) = join(meet(meet(b,c),a),meet(b,a)),
inference(monotonicity,[status(thm)],[72,49]) ).
tff(100,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b)),
inference(unit_resolution,[status(thm)],[100,34]) ).
tff(102,plain,
join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c)),
inference(transitivity,[status(thm)],[101,99,98,95,89,36]) ).
tff(103,plain,
join(c,meet(meet(a,b),c)) = join(c,join(meet(meet(a,b),c),meet(meet(a,b),c))),
inference(monotonicity,[status(thm)],[65]) ).
tff(104,plain,
join(c,join(meet(meet(a,b),c),meet(meet(a,b),c))) = join(c,meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,join(meet(meet(a,b),c),meet(meet(a,b),c))) = join(join(meet(meet(a,b),c),meet(meet(a,b),c)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
join(c,join(meet(meet(a,b),c),meet(meet(a,b),c))) = join(join(meet(meet(a,b),c),meet(meet(a,b),c)),c),
inference(unit_resolution,[status(thm)],[105,34]) ).
tff(107,plain,
join(join(meet(meet(a,b),c),meet(meet(a,b),c)),c) = join(c,join(meet(meet(a,b),c),meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,b),c),meet(meet(a,b),c)),c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
join(join(meet(meet(a,b),c),meet(meet(a,b),c)),c) = c,
inference(unit_resolution,[status(thm)],[108,56]) ).
tff(110,plain,
c = join(join(meet(meet(a,b),c),meet(meet(a,b),c)),c),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c)),c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
join(join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c)),c) = c,
inference(unit_resolution,[status(thm)],[111,56]) ).
tff(113,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(c,c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
meet(c,c) = c,
inference(unit_resolution,[status(thm)],[113,43]) ).
tff(115,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(c,join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(c,join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[115,83]) ).
tff(117,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(b,c),meet(b,c)) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
join(meet(b,c),meet(b,c)) = meet(b,c),
inference(unit_resolution,[status(thm)],[117,7]) ).
tff(119,plain,
meet(b,c) = join(meet(b,c),meet(b,c)),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)) = meet(b,c),
inference(unit_resolution,[status(thm)],[120,56]) ).
tff(122,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)) = join(meet(b,c),meet(b,c)),
inference(transitivity,[status(thm)],[121,119]) ).
tff(123,plain,
join(c,join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))) = join(c,join(meet(b,c),meet(b,c))),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
join(c,join(meet(b,c),meet(b,c))) = join(c,join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,join(meet(b,c),meet(b,c))) = join(join(meet(b,c),meet(b,c)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
join(c,join(meet(b,c),meet(b,c))) = join(join(meet(b,c),meet(b,c)),c),
inference(unit_resolution,[status(thm)],[125,34]) ).
tff(127,plain,
join(join(meet(b,c),meet(b,c)),c) = join(c,join(meet(b,c),meet(b,c))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(b,c),meet(b,c)),c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
join(join(meet(b,c),meet(b,c)),c) = c,
inference(unit_resolution,[status(thm)],[128,56]) ).
tff(130,plain,
c = join(join(meet(b,c),meet(b,c)),c),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
c = join(c,join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))),
inference(transitivity,[status(thm)],[130,127,124]) ).
tff(132,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c) = meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(c,join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[132,116,9]) ).
tff(134,plain,
join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c)) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[133,133]) ).
tff(135,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c)),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c) = join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c)),
inference(transitivity,[status(thm)],[132,116,135]) ).
tff(137,plain,
join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c),meet(c,c)) = join(join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c)),c),
inference(monotonicity,[status(thm)],[136,114]) ).
tff(138,plain,
c = meet(c,c),
inference(symmetry,[status(thm)],[114]) ).
tff(139,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(c,join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))) = meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c),
inference(symmetry,[status(thm)],[132]) ).
tff(140,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(c,join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))),
inference(symmetry,[status(thm)],[116]) ).
tff(141,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c),
inference(transitivity,[status(thm)],[140,139]) ).
tff(142,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c) = join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c),meet(c,c)),
inference(monotonicity,[status(thm)],[141,138]) ).
tff(143,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c) = join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c) = join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(unit_resolution,[status(thm)],[143,34]) ).
tff(145,plain,
join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),c),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(c,meet(meet(a,b),c)),
inference(transitivity,[status(thm)],[145,142,137,112,110,107,104]) ).
tff(147,plain,
meet(join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(join(c,meet(meet(a,b),c)),join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c))),
inference(monotonicity,[status(thm)],[146,102]) ).
tff(148,plain,
meet(join(c,meet(meet(a,b),c)),join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c))) = meet(join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c)) = join(meet(meet(a,b),c),join(meet(meet(b,c),a),meet(b,a))),
inference(symmetry,[status(thm)],[36]) ).
tff(150,plain,
join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c)) = join(meet(meet(b,c),a),meet(b,a)),
inference(transitivity,[status(thm)],[149,88,94,97]) ).
tff(151,plain,
join(c,meet(meet(a,b),c)) = c,
inference(transitivity,[status(thm)],[103,106,109]) ).
tff(152,plain,
meet(join(c,meet(meet(a,b),c)),join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c))) = meet(c,join(meet(meet(b,c),a),meet(b,a))),
inference(monotonicity,[status(thm)],[151,150]) ).
tff(153,plain,
meet(c,join(meet(meet(b,c),a),meet(b,a))) = meet(join(c,meet(meet(a,b),c)),join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(meet(b,c),a),meet(b,a)),c) = meet(c,join(meet(meet(b,c),a),meet(b,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
meet(join(meet(meet(b,c),a),meet(b,a)),c) = meet(c,join(meet(meet(b,c),a),meet(b,a))),
inference(unit_resolution,[status(thm)],[154,25]) ).
tff(156,plain,
c = join(c,meet(meet(a,b),c)),
inference(transitivity,[status(thm)],[110,107,104]) ).
tff(157,plain,
join(meet(meet(b,c),a),meet(b,a)) = join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c)),
inference(transitivity,[status(thm)],[98,95,89,36]) ).
tff(158,plain,
meet(join(meet(meet(b,c),a),meet(b,a)),c) = meet(join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c)),join(c,meet(meet(a,b),c))),
inference(monotonicity,[status(thm)],[157,156]) ).
tff(159,plain,
meet(join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c)),join(c,meet(meet(a,b),c))) = meet(join(meet(meet(b,c),a),meet(b,a)),c),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,b),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(a,b),meet(a,b)))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,plain,
meet(meet(a,b),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(a,b),meet(a,b)))) = meet(a,b),
inference(unit_resolution,[status(thm)],[160,83]) ).
tff(162,plain,
join(meet(meet(b,c),a),meet(b,a)) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b)),
inference(symmetry,[status(thm)],[99]) ).
tff(163,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(a,b),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
join(meet(a,b),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[163,7]) ).
tff(165,plain,
join(meet(a,b),meet(a,b)) = meet(b,a),
inference(transitivity,[status(thm)],[164,49]) ).
tff(166,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(a,b),meet(a,b))) = join(meet(meet(b,c),a),meet(b,a)),
inference(monotonicity,[status(thm)],[72,165]) ).
tff(167,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(a,b),meet(a,b))) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b)),
inference(transitivity,[status(thm)],[166,162]) ).
tff(168,plain,
meet(a,b) = join(meet(a,b),meet(a,b)),
inference(symmetry,[status(thm)],[164]) ).
tff(169,plain,
meet(meet(a,b),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(a,b),meet(a,b)))) = meet(join(meet(a,b),meet(a,b)),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b))),
inference(monotonicity,[status(thm)],[168,167]) ).
tff(170,plain,
meet(join(meet(a,b),meet(a,b)),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b))) = meet(meet(a,b),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(a,b),meet(a,b)))),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(meet(b,c),a),meet(b,a)),b),meet(join(meet(meet(b,c),a),meet(b,a)),b)),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
join(join(meet(join(meet(meet(b,c),a),meet(b,a)),b),meet(join(meet(meet(b,c),a),meet(b,a)),b)),b) = b,
inference(unit_resolution,[status(thm)],[171,56]) ).
tff(173,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(b,b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
meet(b,b) = b,
inference(unit_resolution,[status(thm)],[173,43]) ).
tff(175,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(join(meet(meet(b,c),a),meet(b,a)),b),meet(join(meet(meet(b,c),a),meet(b,a)),b)) = meet(join(meet(meet(b,c),a),meet(b,a)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
join(meet(join(meet(meet(b,c),a),meet(b,a)),b),meet(join(meet(meet(b,c),a),meet(b,a)),b)) = meet(join(meet(meet(b,c),a),meet(b,a)),b),
inference(unit_resolution,[status(thm)],[175,7]) ).
tff(177,plain,
meet(join(meet(meet(b,c),a),meet(b,a)),b) = join(meet(join(meet(meet(b,c),a),meet(b,a)),b),meet(join(meet(meet(b,c),a),meet(b,a)),b)),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
join(meet(join(meet(meet(b,c),a),meet(b,a)),b),meet(b,b)) = join(join(meet(join(meet(meet(b,c),a),meet(b,a)),b),meet(join(meet(meet(b,c),a),meet(b,a)),b)),b),
inference(monotonicity,[status(thm)],[177,174]) ).
tff(179,plain,
b = meet(b,b),
inference(symmetry,[status(thm)],[174]) ).
tff(180,plain,
join(meet(join(meet(meet(b,c),a),meet(b,a)),b),b) = join(meet(join(meet(meet(b,c),a),meet(b,a)),b),meet(b,b)),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(meet(meet(b,c),a),meet(b,a)),b),b) = join(b,meet(join(meet(meet(b,c),a),meet(b,a)),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(182,plain,
join(meet(join(meet(meet(b,c),a),meet(b,a)),b),b) = join(b,meet(join(meet(meet(b,c),a),meet(b,a)),b)),
inference(unit_resolution,[status(thm)],[181,34]) ).
tff(183,plain,
join(b,meet(join(meet(meet(b,c),a),meet(b,a)),b)) = join(meet(join(meet(meet(b,c),a),meet(b,a)),b),b),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
join(meet(b,b),meet(join(meet(meet(b,c),a),meet(b,a)),b)) = join(b,meet(join(meet(meet(b,c),a),meet(b,a)),b)),
inference(monotonicity,[status(thm)],[174]) ).
tff(185,plain,
join(b,meet(a,b)) = join(b,join(meet(a,b),meet(a,b))),
inference(monotonicity,[status(thm)],[168]) ).
tff(186,plain,
join(b,join(meet(a,b),meet(a,b))) = join(b,meet(a,b)),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,join(meet(a,b),meet(a,b))) = join(join(meet(a,b),meet(a,b)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(188,plain,
join(b,join(meet(a,b),meet(a,b))) = join(join(meet(a,b),meet(a,b)),b),
inference(unit_resolution,[status(thm)],[187,34]) ).
tff(189,plain,
join(join(meet(a,b),meet(a,b)),b) = join(b,join(meet(a,b),meet(a,b))),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(a,b),meet(a,b)),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(191,plain,
join(join(meet(a,b),meet(a,b)),b) = b,
inference(unit_resolution,[status(thm)],[190,56]) ).
tff(192,plain,
b = join(join(meet(a,b),meet(a,b)),b),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
b = join(b,meet(a,b)),
inference(transitivity,[status(thm)],[192,189,186]) ).
tff(194,plain,
meet(join(meet(meet(b,c),a),meet(b,a)),b) = meet(join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b)),join(b,meet(a,b))),
inference(monotonicity,[status(thm)],[162,193]) ).
tff(195,plain,
meet(join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b)),join(b,meet(a,b))) = meet(join(meet(meet(b,c),a),meet(b,a)),b),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,b),join(meet(c,b),meet(a,b))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(c,b),meet(a,b)))),join(meet(c,b),meet(a,b))) = join(meet(c,b),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
join(join(meet(meet(a,b),join(meet(c,b),meet(a,b))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(c,b),meet(a,b)))),join(meet(c,b),meet(a,b))) = join(meet(c,b),meet(a,b)),
inference(unit_resolution,[status(thm)],[196,56]) ).
tff(198,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(a,b),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(a,b),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[198,83]) ).
tff(200,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,b) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
meet(c,b) = meet(b,c),
inference(unit_resolution,[status(thm)],[200,25]) ).
tff(202,plain,
meet(b,c) = meet(c,b),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)) = meet(c,b),
inference(transitivity,[status(thm)],[121,202]) ).
tff(204,plain,
join(meet(a,b),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))) = join(meet(a,b),meet(c,b)),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
join(meet(a,b),meet(c,b)) = join(meet(a,b),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
join(meet(a,b),meet(c,b)) = join(meet(a,b),meet(b,c)),
inference(monotonicity,[status(thm)],[201]) ).
tff(207,plain,
join(meet(a,b),meet(b,c)) = join(meet(a,b),meet(c,b)),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,c),meet(a,b)) = join(meet(a,b),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
join(meet(b,c),meet(a,b)) = join(meet(a,b),meet(b,c)),
inference(unit_resolution,[status(thm)],[208,34]) ).
tff(210,plain,
join(meet(b,c),meet(a,b)) = join(meet(c,b),meet(a,b)),
inference(monotonicity,[status(thm)],[202]) ).
tff(211,plain,
join(meet(c,b),meet(a,b)) = join(meet(b,c),meet(a,b)),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
join(meet(c,b),meet(a,b)) = join(meet(a,b),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))),
inference(transitivity,[status(thm)],[211,209,207,205]) ).
tff(213,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(c,b),meet(a,b))) = meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(a,b),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(c,b),meet(a,b))) = meet(meet(b,c),a),
inference(transitivity,[status(thm)],[213,199,9,71]) ).
tff(215,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,b),join(meet(b,c),join(meet(a,b),meet(a,b)))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
meet(meet(a,b),join(meet(b,c),join(meet(a,b),meet(a,b)))) = meet(a,b),
inference(unit_resolution,[status(thm)],[215,83]) ).
tff(217,plain,
join(meet(b,c),join(meet(a,b),meet(a,b))) = join(meet(c,b),meet(a,b)),
inference(monotonicity,[status(thm)],[202,164]) ).
tff(218,plain,
join(meet(c,b),meet(a,b)) = join(meet(b,c),join(meet(a,b),meet(a,b))),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
join(meet(b,c),meet(a,b)) = join(meet(b,c),join(meet(a,b),meet(a,b))),
inference(transitivity,[status(thm)],[210,218]) ).
tff(220,plain,
meet(join(meet(a,b),meet(a,b)),join(meet(b,c),meet(a,b))) = meet(meet(a,b),join(meet(b,c),join(meet(a,b),meet(a,b)))),
inference(monotonicity,[status(thm)],[164,219]) ).
tff(221,plain,
meet(meet(a,b),join(meet(c,b),meet(a,b))) = meet(join(meet(a,b),meet(a,b)),join(meet(b,c),meet(a,b))),
inference(monotonicity,[status(thm)],[168,211]) ).
tff(222,plain,
meet(meet(a,b),join(meet(c,b),meet(a,b))) = meet(b,a),
inference(transitivity,[status(thm)],[221,220,216,49]) ).
tff(223,plain,
join(meet(meet(a,b),join(meet(c,b),meet(a,b))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(c,b),meet(a,b)))) = join(meet(b,a),meet(meet(b,c),a)),
inference(monotonicity,[status(thm)],[222,214]) ).
tff(224,plain,
join(meet(b,a),meet(meet(b,c),a)) = join(meet(meet(a,b),join(meet(c,b),meet(a,b))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(c,b),meet(a,b)))),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
meet(a,meet(b,c)) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(symmetry,[status(thm)],[9]) ).
tff(226,plain,
meet(meet(b,c),a) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(transitivity,[status(thm)],[70,225]) ).
tff(227,plain,
join(meet(b,a),meet(meet(b,c),a)) = join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(monotonicity,[status(thm)],[48,226]) ).
tff(228,plain,
join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(meet(b,a),meet(meet(b,c),a)),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b)) = join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(symmetry,[status(thm)],[101]) ).
tff(230,plain,
join(meet(meet(b,c),a),meet(b,a)) = join(meet(meet(a,b),join(meet(c,b),meet(a,b))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(c,b),meet(a,b)))),
inference(transitivity,[status(thm)],[162,229,228,224]) ).
tff(231,plain,
join(join(meet(meet(b,c),a),meet(b,a)),join(meet(c,b),meet(a,b))) = join(join(meet(meet(a,b),join(meet(c,b),meet(a,b))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(c,b),meet(a,b)))),join(meet(c,b),meet(a,b))),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
join(join(meet(meet(b,c),a),meet(b,a)),join(meet(c,b),meet(a,b))) = join(meet(c,b),meet(a,b)),
inference(transitivity,[status(thm)],[231,197]) ).
tff(233,plain,
join(b,join(join(meet(meet(b,c),a),meet(b,a)),join(meet(c,b),meet(a,b)))) = join(b,join(meet(c,b),meet(a,b))),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
join(b,join(meet(c,b),meet(a,b))) = join(b,join(join(meet(meet(b,c),a),meet(b,a)),join(meet(c,b),meet(a,b)))),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,join(meet(c,b),meet(a,b))) = join(join(meet(c,b),meet(a,b)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(236,plain,
join(b,join(meet(c,b),meet(a,b))) = join(join(meet(c,b),meet(a,b)),b),
inference(unit_resolution,[status(thm)],[235,34]) ).
tff(237,plain,
join(join(meet(c,b),meet(a,b)),b) = join(b,join(meet(c,b),meet(a,b))),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(c,b),meet(a,b)),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
join(join(meet(c,b),meet(a,b)),b) = b,
inference(unit_resolution,[status(thm)],[238,56]) ).
tff(240,plain,
b = join(join(meet(c,b),meet(a,b)),b),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
join(b,meet(a,b)) = join(b,join(join(meet(meet(b,c),a),meet(b,a)),join(meet(c,b),meet(a,b)))),
inference(transitivity,[status(thm)],[185,188,191,240,237,234]) ).
tff(242,plain,
meet(join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b)),join(b,meet(a,b))) = meet(join(meet(meet(b,c),a),meet(b,a)),join(b,join(join(meet(meet(b,c),a),meet(b,a)),join(meet(c,b),meet(a,b))))),
inference(monotonicity,[status(thm)],[99,241]) ).
tff(243,plain,
meet(join(meet(meet(b,c),a),meet(b,a)),join(b,join(join(meet(meet(b,c),a),meet(b,a)),join(meet(c,b),meet(a,b))))) = meet(join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b)),join(b,meet(a,b))),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(meet(b,c),a),meet(b,a)),join(b,join(join(meet(meet(b,c),a),meet(b,a)),join(meet(c,b),meet(a,b))))) = join(meet(meet(b,c),a),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(245,plain,
meet(join(meet(meet(b,c),a),meet(b,a)),join(b,join(join(meet(meet(b,c),a),meet(b,a)),join(meet(c,b),meet(a,b))))) = join(meet(meet(b,c),a),meet(b,a)),
inference(unit_resolution,[status(thm)],[244,83]) ).
tff(246,plain,
join(meet(meet(b,c),a),meet(b,a)) = meet(join(meet(meet(b,c),a),meet(b,a)),join(b,join(join(meet(meet(b,c),a),meet(b,a)),join(meet(c,b),meet(a,b))))),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
join(meet(meet(b,c),a),meet(b,a)) = meet(join(meet(meet(b,c),a),meet(b,a)),b),
inference(transitivity,[status(thm)],[246,243,195]) ).
tff(248,plain,
join(b,join(meet(meet(b,c),a),meet(b,a))) = join(meet(b,b),meet(join(meet(meet(b,c),a),meet(b,a)),b)),
inference(monotonicity,[status(thm)],[179,247]) ).
tff(249,plain,
join(b,join(meet(meet(b,c),a),meet(b,a))) = b,
inference(transitivity,[status(thm)],[248,184,183,180,178,172]) ).
tff(250,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(b,c),a),meet(b,a)),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(251,plain,
join(join(meet(meet(b,c),a),meet(b,a)),a) = a,
inference(unit_resolution,[status(thm)],[250,56]) ).
tff(252,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,join(meet(meet(b,c),a),meet(b,a))) = join(join(meet(meet(b,c),a),meet(b,a)),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(253,plain,
join(a,join(meet(meet(b,c),a),meet(b,a))) = join(join(meet(meet(b,c),a),meet(b,a)),a),
inference(unit_resolution,[status(thm)],[252,34]) ).
tff(254,plain,
join(a,join(meet(meet(b,c),a),meet(b,a))) = a,
inference(transitivity,[status(thm)],[253,251]) ).
tff(255,plain,
meet(join(a,join(meet(meet(b,c),a),meet(b,a))),join(b,join(meet(meet(b,c),a),meet(b,a)))) = meet(a,b),
inference(monotonicity,[status(thm)],[254,249]) ).
tff(256,plain,
meet(a,b) = meet(join(a,join(meet(meet(b,c),a),meet(b,a))),join(b,join(meet(meet(b,c),a),meet(b,a)))),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
join(meet(a,b),meet(a,b)) = meet(join(a,join(meet(meet(b,c),a),meet(b,a))),join(b,join(meet(meet(b,c),a),meet(b,a)))),
inference(transitivity,[status(thm)],[164,256]) ).
tff(258,plain,
meet(join(meet(a,b),meet(a,b)),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b))) = meet(meet(join(a,join(meet(meet(b,c),a),meet(b,a))),join(b,join(meet(meet(b,c),a),meet(b,a)))),join(meet(meet(b,c),a),meet(b,a))),
inference(monotonicity,[status(thm)],[257,99]) ).
tff(259,plain,
meet(meet(join(a,join(meet(meet(b,c),a),meet(b,a))),join(b,join(meet(meet(b,c),a),meet(b,a)))),join(meet(meet(b,c),a),meet(b,a))) = meet(join(meet(a,b),meet(a,b)),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(a,b))),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(a,join(meet(meet(b,c),a),meet(b,a))),join(b,join(meet(meet(b,c),a),meet(b,a)))),join(meet(meet(b,c),a),meet(b,a))) = join(meet(meet(b,c),a),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(261,plain,
meet(meet(join(a,join(meet(meet(b,c),a),meet(b,a))),join(b,join(meet(meet(b,c),a),meet(b,a)))),join(meet(meet(b,c),a),meet(b,a))) = join(meet(meet(b,c),a),meet(b,a)),
inference(unit_resolution,[status(thm)],[260,16]) ).
tff(262,plain,
join(meet(meet(b,c),a),meet(b,a)) = meet(meet(join(a,join(meet(meet(b,c),a),meet(b,a))),join(b,join(meet(meet(b,c),a),meet(b,a)))),join(meet(meet(b,c),a),meet(b,a))),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c)) = meet(a,b),
inference(transitivity,[status(thm)],[149,88,94,97,262,259,170,161]) ).
tff(264,plain,
meet(join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c)),join(c,meet(meet(a,b),c))) = meet(meet(a,b),c),
inference(monotonicity,[status(thm)],[263,151]) ).
tff(265,plain,
meet(meet(a,b),c) = meet(join(join(meet(meet(b,c),a),meet(b,a)),meet(meet(a,b),c)),join(c,meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
meet(meet(a,b),c) = meet(join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(transitivity,[status(thm)],[265,159,155,153,148]) ).
tff(267,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(meet(meet(a,b),c),meet(b,c)),join(meet(meet(a,b),c),meet(b,c))),meet(b,c)) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(268,plain,
meet(meet(join(meet(meet(a,b),c),meet(b,c)),join(meet(meet(a,b),c),meet(b,c))),meet(b,c)) = meet(b,c),
inference(unit_resolution,[status(thm)],[267,16]) ).
tff(269,plain,
meet(b,c) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)),
inference(symmetry,[status(thm)],[121]) ).
tff(270,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(join(meet(meet(a,b),c),meet(b,c)),join(meet(meet(a,b),c),meet(b,c))) = join(meet(meet(a,b),c),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(271,plain,
meet(join(meet(meet(a,b),c),meet(b,c)),join(meet(meet(a,b),c),meet(b,c))) = join(meet(meet(a,b),c),meet(b,c)),
inference(unit_resolution,[status(thm)],[270,43]) ).
tff(272,plain,
meet(meet(join(meet(meet(a,b),c),meet(b,c)),join(meet(meet(a,b),c),meet(b,c))),meet(b,c)) = meet(join(meet(meet(a,b),c),meet(b,c)),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))),
inference(monotonicity,[status(thm)],[271,269]) ).
tff(273,plain,
meet(join(meet(meet(a,b),c),meet(b,c)),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))) = meet(meet(join(meet(meet(a,b),c),meet(b,c)),join(meet(meet(a,b),c),meet(b,c))),meet(b,c)),
inference(symmetry,[status(thm)],[272]) ).
tff(274,plain,
meet(join(meet(meet(a,b),c),meet(b,c)),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))) = meet(join(meet(meet(a,b),c),meet(b,c)),meet(b,c)),
inference(monotonicity,[status(thm)],[121]) ).
tff(275,plain,
meet(join(meet(meet(a,b),c),meet(b,c)),meet(b,c)) = meet(join(meet(meet(a,b),c),meet(b,c)),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(meet(a,b),c),meet(b,c)),meet(b,c)) = meet(meet(b,c),join(meet(meet(a,b),c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(277,plain,
meet(join(meet(meet(a,b),c),meet(b,c)),meet(b,c)) = meet(meet(b,c),join(meet(meet(a,b),c),meet(b,c))),
inference(unit_resolution,[status(thm)],[276,25]) ).
tff(278,plain,
meet(meet(b,c),join(meet(meet(a,b),c),meet(b,c))) = meet(join(meet(meet(a,b),c),meet(b,c)),meet(b,c)),
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
meet(meet(b,c),join(meet(meet(a,b),c),meet(b,c))) = meet(join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)),join(meet(meet(a,b),c),meet(b,c))),
inference(monotonicity,[status(thm)],[269]) ).
tff(280,plain,
meet(join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)),join(meet(meet(a,b),c),meet(b,c))) = meet(meet(b,c),join(meet(meet(a,b),c),meet(b,c))),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(c,b),meet(meet(meet(a,b),c),b)),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(282,plain,
join(join(meet(c,b),meet(meet(meet(a,b),c),b)),b) = b,
inference(unit_resolution,[status(thm)],[281,56]) ).
tff(283,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(meet(a,b),c),join(b,join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(284,plain,
meet(meet(meet(a,b),c),join(b,join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[283,83]) ).
tff(285,plain,
join(meet(meet(a,b),c),meet(a,b)) = join(meet(a,b),meet(a,b)),
inference(transitivity,[status(thm)],[67,58,168]) ).
tff(286,plain,
join(b,join(meet(meet(a,b),c),meet(a,b))) = join(b,join(meet(a,b),meet(a,b))),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
join(b,join(meet(a,b),meet(a,b))) = join(b,join(meet(meet(a,b),c),meet(a,b))),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
b = join(b,join(meet(meet(a,b),c),meet(a,b))),
inference(transitivity,[status(thm)],[192,189,287]) ).
tff(289,plain,
meet(meet(meet(a,b),c),b) = meet(meet(meet(a,b),c),join(b,join(meet(meet(a,b),c),meet(a,b)))),
inference(monotonicity,[status(thm)],[288]) ).
tff(290,plain,
meet(meet(meet(a,b),c),b) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[289,284]) ).
tff(291,plain,
join(meet(c,b),meet(meet(meet(a,b),c),b)) = join(meet(b,c),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[201,290]) ).
tff(292,plain,
join(meet(b,c),meet(meet(a,b),c)) = join(meet(c,b),meet(meet(meet(a,b),c),b)),
inference(symmetry,[status(thm)],[291]) ).
tff(293,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,c),meet(meet(a,b),c)) = join(meet(meet(a,b),c),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(294,plain,
join(meet(b,c),meet(meet(a,b),c)) = join(meet(meet(a,b),c),meet(b,c)),
inference(unit_resolution,[status(thm)],[293,34]) ).
tff(295,plain,
join(meet(meet(a,b),c),meet(b,c)) = join(meet(b,c),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
join(meet(meet(a,b),c),meet(b,c)) = join(meet(c,b),meet(meet(meet(a,b),c),b)),
inference(transitivity,[status(thm)],[295,292]) ).
tff(297,plain,
join(join(meet(meet(a,b),c),meet(b,c)),b) = join(join(meet(c,b),meet(meet(meet(a,b),c),b)),b),
inference(monotonicity,[status(thm)],[296]) ).
tff(298,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,join(meet(meet(a,b),c),meet(b,c))) = join(join(meet(meet(a,b),c),meet(b,c)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(299,plain,
join(b,join(meet(meet(a,b),c),meet(b,c))) = join(join(meet(meet(a,b),c),meet(b,c)),b),
inference(unit_resolution,[status(thm)],[298,34]) ).
tff(300,plain,
join(b,join(meet(meet(a,b),c),meet(b,c))) = b,
inference(transitivity,[status(thm)],[299,297,282]) ).
tff(301,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,b),c),meet(b,c)),c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(302,plain,
join(join(meet(meet(a,b),c),meet(b,c)),c) = c,
inference(unit_resolution,[status(thm)],[301,56]) ).
tff(303,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,join(meet(meet(a,b),c),meet(b,c))) = join(join(meet(meet(a,b),c),meet(b,c)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(304,plain,
join(c,join(meet(meet(a,b),c),meet(b,c))) = join(join(meet(meet(a,b),c),meet(b,c)),c),
inference(unit_resolution,[status(thm)],[303,34]) ).
tff(305,plain,
join(c,join(meet(meet(a,b),c),meet(b,c))) = c,
inference(transitivity,[status(thm)],[304,302]) ).
tff(306,plain,
meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))) = meet(c,b),
inference(monotonicity,[status(thm)],[305,300]) ).
tff(307,plain,
meet(c,b) = meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))),
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)) = meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))),
inference(transitivity,[status(thm)],[121,202,307]) ).
tff(309,plain,
meet(join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)),join(meet(meet(a,b),c),meet(b,c))) = meet(meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))),
inference(monotonicity,[status(thm)],[308]) ).
tff(310,plain,
meet(meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))) = meet(join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)),join(meet(meet(a,b),c),meet(b,c))),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))) = join(meet(meet(a,b),c),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(312,plain,
meet(meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))) = join(meet(meet(a,b),c),meet(b,c)),
inference(unit_resolution,[status(thm)],[311,16]) ).
tff(313,plain,
join(meet(meet(a,b),c),meet(b,c)) = meet(meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))),
inference(symmetry,[status(thm)],[312]) ).
tff(314,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))) = join(meet(meet(a,b),c),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(315,plain,
join(join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))) = join(meet(meet(a,b),c),meet(b,c)),
inference(unit_resolution,[status(thm)],[314,56]) ).
tff(316,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(317,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[316,83]) ).
tff(318,plain,
join(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))) = join(meet(meet(a,b),c),meet(b,c)),
inference(monotonicity,[status(thm)],[121]) ).
tff(319,plain,
join(meet(meet(a,b),c),meet(b,c)) = join(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[318]) ).
tff(320,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))) = meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))),
inference(monotonicity,[status(thm)],[319]) ).
tff(321,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[320,317,9]) ).
tff(322,plain,
join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c)))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[321,321]) ).
tff(323,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c)))),
inference(symmetry,[status(thm)],[322]) ).
tff(324,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))) = join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c)))),
inference(transitivity,[status(thm)],[320,317,323]) ).
tff(325,plain,
join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(meet(a,b),c),meet(b,c)),join(meet(meet(a,b),c),meet(b,c)))) = join(join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))),
inference(monotonicity,[status(thm)],[324,271]) ).
tff(326,plain,
join(meet(meet(a,b),c),meet(b,c)) = meet(join(meet(meet(a,b),c),meet(b,c)),join(meet(meet(a,b),c),meet(b,c))),
inference(symmetry,[status(thm)],[271]) ).
tff(327,plain,
meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))) = meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),
inference(symmetry,[status(thm)],[320]) ).
tff(328,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(b,c)))),
inference(symmetry,[status(thm)],[317]) ).
tff(329,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),
inference(transitivity,[status(thm)],[328,327]) ).
tff(330,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))) = join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(meet(a,b),c),meet(b,c)),join(meet(meet(a,b),c),meet(b,c)))),
inference(monotonicity,[status(thm)],[329,326]) ).
tff(331,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))) = join(join(meet(meet(a,b),c),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(332,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))) = join(join(meet(meet(a,b),c),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(unit_resolution,[status(thm)],[331,34]) ).
tff(333,plain,
join(join(meet(meet(a,b),c),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),
inference(symmetry,[status(thm)],[332]) ).
tff(334,plain,
join(join(meet(meet(a,b),c),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = meet(b,c),
inference(transitivity,[status(thm)],[333,330,325,315,313,310,280,278,275,273,268]) ).
tff(335,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(b,c),a),meet(meet(b,c),a)),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(336,plain,
join(join(meet(meet(b,c),a),meet(meet(b,c),a)),a) = a,
inference(unit_resolution,[status(thm)],[335,56]) ).
tff(337,plain,
join(meet(meet(b,c),a),meet(meet(b,c),a)) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[70,70]) ).
tff(338,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = join(meet(meet(b,c),a),meet(meet(b,c),a)),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),a) = join(join(meet(meet(b,c),a),meet(meet(b,c),a)),a),
inference(monotonicity,[status(thm)],[338]) ).
tff(340,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(341,plain,
join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),a),
inference(unit_resolution,[status(thm)],[340,34]) ).
tff(342,plain,
join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = a,
inference(transitivity,[status(thm)],[341,339,336]) ).
tff(343,plain,
meet(join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(join(meet(meet(a,b),c),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(a,meet(b,c)),
inference(monotonicity,[status(thm)],[342,334]) ).
tff(344,plain,
join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(meet(a,b),c),meet(b,c)),join(meet(meet(a,b),c),meet(b,c)))) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),
inference(symmetry,[status(thm)],[330]) ).
tff(345,plain,
join(join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))) = join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(meet(a,b),c),meet(b,c)),join(meet(meet(a,b),c),meet(b,c)))),
inference(symmetry,[status(thm)],[325]) ).
tff(346,plain,
join(meet(meet(a,b),c),meet(b,c)) = join(join(meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c))),meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))),
inference(symmetry,[status(thm)],[315]) ).
tff(347,plain,
join(meet(meet(a,b),c),meet(b,c)) = join(join(meet(meet(a,b),c),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[346,345,344,332]) ).
tff(348,plain,
join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),a) = join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(symmetry,[status(thm)],[341]) ).
tff(349,plain,
join(join(meet(meet(b,c),a),meet(meet(b,c),a)),a) = join(join(meet(a,meet(b,c)),meet(a,meet(b,c))),a),
inference(symmetry,[status(thm)],[339]) ).
tff(350,plain,
a = join(join(meet(meet(b,c),a),meet(meet(b,c),a)),a),
inference(symmetry,[status(thm)],[336]) ).
tff(351,plain,
a = join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[350,349,348]) ).
tff(352,plain,
meet(a,join(meet(meet(a,b),c),meet(b,c))) = meet(join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(join(meet(meet(a,b),c),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(monotonicity,[status(thm)],[351,347]) ).
tff(353,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(meet(a,b),c),meet(b,c)),a) = meet(a,join(meet(meet(a,b),c),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(354,plain,
meet(join(meet(meet(a,b),c),meet(b,c)),a) = meet(a,join(meet(meet(a,b),c),meet(b,c))),
inference(unit_resolution,[status(thm)],[353,25]) ).
tff(355,plain,
join(join(meet(meet(a,b),c),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(meet(meet(a,b),c),meet(b,c)),
inference(transitivity,[status(thm)],[333,330,325,315]) ).
tff(356,plain,
meet(join(join(meet(meet(a,b),c),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(join(meet(meet(a,b),c),meet(b,c)),a),
inference(monotonicity,[status(thm)],[355,342]) ).
tff(357,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(meet(a,b),c),a),meet(meet(meet(a,b),c),a)),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(358,plain,
join(join(meet(meet(meet(a,b),c),a),meet(meet(meet(a,b),c),a)),a) = a,
inference(unit_resolution,[status(thm)],[357,56]) ).
tff(359,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(a,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(360,plain,
meet(a,a) = a,
inference(unit_resolution,[status(thm)],[359,43]) ).
tff(361,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(meet(a,b),c),join(a,join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(362,plain,
meet(meet(meet(a,b),c),join(a,join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[361,83]) ).
tff(363,plain,
join(meet(meet(a,b),c),meet(a,b)) = meet(a,b),
inference(transitivity,[status(thm)],[67,58]) ).
tff(364,plain,
join(a,join(meet(meet(a,b),c),meet(a,b))) = join(a,meet(a,b)),
inference(monotonicity,[status(thm)],[363]) ).
tff(365,plain,
join(a,meet(a,b)) = join(a,join(meet(meet(a,b),c),meet(a,b))),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,meet(a,b)) = join(meet(a,b),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(367,plain,
join(a,meet(a,b)) = join(meet(a,b),a),
inference(unit_resolution,[status(thm)],[366,34]) ).
tff(368,plain,
join(meet(a,b),a) = join(a,meet(a,b)),
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
join(meet(b,a),meet(b,a)) = join(meet(a,b),meet(a,b)),
inference(monotonicity,[status(thm)],[48,48]) ).
tff(370,plain,
join(meet(a,b),meet(a,b)) = join(meet(b,a),meet(b,a)),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
meet(a,b) = join(meet(b,a),meet(b,a)),
inference(transitivity,[status(thm)],[168,370]) ).
tff(372,plain,
join(meet(a,b),a) = join(join(meet(b,a),meet(b,a)),a),
inference(monotonicity,[status(thm)],[371]) ).
tff(373,plain,
join(join(meet(b,a),meet(b,a)),a) = join(meet(a,b),a),
inference(symmetry,[status(thm)],[372]) ).
tff(374,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(b,a),meet(b,a)),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(375,plain,
join(join(meet(b,a),meet(b,a)),a) = a,
inference(unit_resolution,[status(thm)],[374,56]) ).
tff(376,plain,
a = join(join(meet(b,a),meet(b,a)),a),
inference(symmetry,[status(thm)],[375]) ).
tff(377,plain,
a = join(a,join(meet(meet(a,b),c),meet(a,b))),
inference(transitivity,[status(thm)],[376,373,368,365]) ).
tff(378,plain,
meet(meet(meet(a,b),c),a) = meet(meet(meet(a,b),c),join(a,join(meet(meet(a,b),c),meet(a,b)))),
inference(monotonicity,[status(thm)],[377]) ).
tff(379,plain,
meet(meet(meet(a,b),c),a) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[378,362]) ).
tff(380,plain,
join(meet(meet(meet(a,b),c),a),meet(meet(meet(a,b),c),a)) = join(meet(meet(a,b),c),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[379,379]) ).
tff(381,plain,
join(meet(meet(a,b),c),meet(meet(a,b),c)) = join(meet(meet(meet(a,b),c),a),meet(meet(meet(a,b),c),a)),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
meet(meet(meet(a,b),c),a) = join(meet(meet(meet(a,b),c),a),meet(meet(meet(a,b),c),a)),
inference(transitivity,[status(thm)],[378,362,65,381]) ).
tff(383,plain,
join(meet(meet(meet(a,b),c),a),meet(a,a)) = join(join(meet(meet(meet(a,b),c),a),meet(meet(meet(a,b),c),a)),a),
inference(monotonicity,[status(thm)],[382,360]) ).
tff(384,plain,
a = meet(a,a),
inference(symmetry,[status(thm)],[360]) ).
tff(385,plain,
meet(meet(meet(a,b),c),join(a,join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(meet(a,b),c),a),
inference(symmetry,[status(thm)],[378]) ).
tff(386,plain,
meet(meet(a,b),c) = meet(meet(meet(a,b),c),join(a,join(meet(meet(a,b),c),meet(a,b)))),
inference(symmetry,[status(thm)],[362]) ).
tff(387,plain,
meet(meet(a,b),c) = meet(meet(meet(a,b),c),a),
inference(transitivity,[status(thm)],[386,385]) ).
tff(388,plain,
join(meet(meet(a,b),c),a) = join(meet(meet(meet(a,b),c),a),meet(a,a)),
inference(monotonicity,[status(thm)],[387,384]) ).
tff(389,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(meet(a,b),c),a) = join(a,meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(390,plain,
join(meet(meet(a,b),c),a) = join(a,meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[389,34]) ).
tff(391,plain,
join(a,meet(meet(a,b),c)) = join(meet(meet(a,b),c),a),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
join(a,meet(meet(a,b),c)) = join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[391,388,383,358,350,349,348]) ).
tff(393,plain,
join(meet(b,c),meet(meet(a,b),c)) = join(join(meet(meet(a,b),c),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[294,346,345,344,332]) ).
tff(394,plain,
meet(join(meet(b,c),meet(meet(a,b),c)),join(a,meet(meet(a,b),c))) = meet(join(join(meet(meet(a,b),c),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(a,join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(monotonicity,[status(thm)],[393,392]) ).
tff(395,plain,
meet(join(meet(b,c),meet(meet(a,b),c)),join(a,meet(meet(a,b),c))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(transitivity,[status(thm)],[394,356,354,352,343,225]) ).
tff(396,plain,
meet(meet(join(meet(b,c),meet(meet(a,b),c)),join(a,meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(join(meet(a,meet(b,c)),meet(a,meet(b,c))),meet(join(c,join(meet(a,meet(b,c)),meet(a,meet(b,c)))),join(meet(a,b),join(meet(a,meet(b,c)),meet(a,meet(b,c)))))),
inference(monotonicity,[status(thm)],[395,266]) ).
tff(397,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(meet(b,c),meet(meet(a,b),c)),join(a,meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(398,plain,
meet(meet(join(meet(b,c),meet(meet(a,b),c)),join(a,meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[397,16]) ).
tff(399,plain,
meet(meet(a,b),c) = meet(meet(join(meet(b,c),meet(meet(a,b),c)),join(a,meet(meet(a,b),c))),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[398]) ).
tff(400,plain,
meet(meet(a,b),c) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[399,396,27,18,9]) ).
tff(401,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(402,axiom,
meet(meet(a,b),c) != meet(a,meet(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_meet) ).
tff(403,plain,
meet(meet(a,b),c) != meet(a,meet(b,c)),
inference(modus_ponens,[status(thm)],[402,401]) ).
tff(404,plain,
$false,
inference(unit_resolution,[status(thm)],[403,400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT026-1 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:28:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.62/1.81 % SZS status Unsatisfiable
% 1.62/1.81 % SZS output start Proof
% See solution above
% 1.69/1.85 % E exiting
%------------------------------------------------------------------------------