TSTP Solution File: LAT399-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT399-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 18:33:43 EDT 2022
% Result : Unsatisfiable 1.71s 1.32s
% Output : Proof 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 115
% Syntax : Number of formulae : 463 ( 358 unt; 8 typ; 0 def)
% Number of atoms : 570 ( 560 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 188 ( 82 ~; 78 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 10 ( 4 >; 6 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 400 ( 377 !; 0 ?; 400 :)
% Comments :
%------------------------------------------------------------------------------
tff(lome_type,type,
lome: ( $i * $i * $i ) > $i ).
tff(z3_type,type,
z3: $i ).
tff(z2_type,type,
z2: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(z1_type,type,
z1: $i ).
tff(a_type,type,
a: $i ).
tff(upme_type,type,
upme: ( $i * $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i,X1: $i] :
refl(
( ( lome(X,Y,X1) = join(meet(X,Y),meet(X,X1)) )
<=> ( lome(X,Y,X1) = join(meet(X,Y),meet(X,X1)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i,X1: $i] : ( lome(X,Y,X1) = join(meet(X,Y),meet(X,X1)) )
<=> ! [Y: $i,X: $i,X1: $i] : ( lome(X,Y,X1) = join(meet(X,Y),meet(X,X1)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i,X1: $i] : ( lome(X,Y,X1) = join(meet(X,Y),meet(X,X1)) )
<=> ! [Y: $i,X: $i,X1: $i] : ( lome(X,Y,X1) = join(meet(X,Y),meet(X,X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i,X1: $i] : ( lome(X,Y,X1) = join(meet(X,Y),meet(X,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_lome) ).
tff(5,plain,
! [Y: $i,X: $i,X1: $i] : ( lome(X,Y,X1) = join(meet(X,Y),meet(X,X1)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i,X1: $i] : ( lome(X,Y,X1) = join(meet(X,Y),meet(X,X1)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i,X1: $i] : ( lome(X,Y,X1) = join(meet(X,Y),meet(X,X1)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i,X1: $i] : ( lome(X,Y,X1) = join(meet(X,Y),meet(X,X1)) )
| ( lome(meet(a,z1),z2,z3) = join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
lome(meet(a,z1),z2,z3) = join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)) = lome(meet(a,z1),z2,z3),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption_003) ).
tff(15,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(z3,join(z3,meet(meet(a,z1),z2))) = z3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
meet(z3,join(z3,meet(meet(a,z1),z2))) = z3,
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(21,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)],[20]) ).
tff(22,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(23,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity) ).
tff(24,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,z1) = meet(z1,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
meet(a,z1) = meet(z1,a),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
meet(z1,a) = meet(a,z1),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
meet(meet(z1,a),meet(z3,join(z3,meet(meet(a,z1),z2)))) = meet(meet(a,z1),z3),
inference(monotonicity,[status(thm)],[29,19]) ).
tff(31,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
<=> ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(z1,a),meet(z3,join(z3,meet(meet(a,z1),z2)))) = meet(meet(meet(z1,a),z3),join(z3,meet(meet(a,z1),z2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
meet(meet(z1,a),meet(z3,join(z3,meet(meet(a,z1),z2)))) = meet(meet(meet(z1,a),z3),join(z3,meet(meet(a,z1),z2))),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
meet(meet(meet(z1,a),z3),join(z3,meet(meet(a,z1),z2))) = meet(meet(z1,a),meet(z3,join(z3,meet(meet(a,z1),z2)))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
meet(meet(z1,a),z3) = meet(meet(a,z1),z3),
inference(monotonicity,[status(thm)],[29]) ).
tff(42,plain,
meet(meet(a,z1),z3) = meet(meet(z1,a),z3),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
meet(meet(meet(a,z1),z3),join(z3,meet(meet(a,z1),z2))) = meet(meet(meet(z1,a),z3),join(z3,meet(meet(a,z1),z2))),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)) = meet(meet(meet(a,z1),z3),join(z3,meet(meet(a,z1),z2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
meet(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)) = meet(meet(meet(a,z1),z3),join(z3,meet(meet(a,z1),z2))),
inference(unit_resolution,[status(thm)],[44,26]) ).
tff(46,plain,
meet(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)) = meet(meet(a,z1),z3),
inference(transitivity,[status(thm)],[45,43,40,30]) ).
tff(47,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(meet(a,z1),z2),join(meet(meet(a,z1),z2),z3)) = meet(meet(a,z1),z2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
meet(meet(meet(a,z1),z2),join(meet(meet(a,z1),z2),z3)) = meet(meet(a,z1),z2),
inference(unit_resolution,[status(thm)],[47,17]) ).
tff(49,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption) ).
tff(53,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(z3,meet(z3,meet(z1,a))) = z3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
join(z3,meet(z3,meet(z1,a))) = z3,
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(z1,a),z3) = meet(z3,meet(z1,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
meet(meet(z1,a),z3) = meet(z3,meet(z1,a)),
inference(unit_resolution,[status(thm)],[58,26]) ).
tff(60,plain,
meet(meet(a,z1),z3) = meet(z3,meet(z1,a)),
inference(transitivity,[status(thm)],[42,59]) ).
tff(61,plain,
join(z3,meet(meet(a,z1),z3)) = join(z3,meet(z3,meet(z1,a))),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
join(z3,meet(meet(a,z1),z3)) = z3,
inference(transitivity,[status(thm)],[61,57]) ).
tff(63,plain,
join(meet(meet(a,z1),z2),join(z3,meet(meet(a,z1),z3))) = join(meet(meet(a,z1),z2),z3),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(X,join(Y,Z)) = join(join(X,Y),Z) )
<=> ( join(X,join(Y,Z)) = join(join(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_002) ).
tff(68,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) )
| ( join(meet(meet(a,z1),z2),join(z3,meet(meet(a,z1),z3))) = join(join(meet(meet(a,z1),z2),z3),meet(meet(a,z1),z3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
join(meet(meet(a,z1),z2),join(z3,meet(meet(a,z1),z3))) = join(join(meet(meet(a,z1),z2),z3),meet(meet(a,z1),z3)),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
join(join(meet(meet(a,z1),z2),z3),meet(meet(a,z1),z3)) = join(meet(meet(a,z1),z2),join(z3,meet(meet(a,z1),z3))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(75,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)],[74]) ).
tff(76,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(77,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_001) ).
tff(78,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(meet(a,z1),z2),z3) = join(z3,meet(meet(a,z1),z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
join(meet(meet(a,z1),z2),z3) = join(z3,meet(meet(a,z1),z2)),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
join(z3,meet(meet(a,z1),z2)) = join(meet(meet(a,z1),z2),z3),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
join(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)) = join(join(meet(meet(a,z1),z2),z3),meet(meet(a,z1),z3)),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
join(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)) = join(meet(meet(a,z1),z2),z3),
inference(transitivity,[status(thm)],[84,73,63]) ).
tff(86,plain,
meet(meet(meet(a,z1),z2),join(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3))) = meet(meet(meet(a,z1),z2),join(meet(meet(a,z1),z2),z3)),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( upme(X,Y,Z) = meet(X,join(Y,Z)) )
<=> ( upme(X,Y,Z) = meet(X,join(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,axiom,
! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_upme) ).
tff(91,plain,
! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) )
| ( upme(meet(meet(a,z1),z2),join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)) = meet(meet(meet(a,z1),z2),join(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
upme(meet(meet(a,z1),z2),join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)) = meet(meet(meet(a,z1),z2),join(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3))),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(a,meet(z1,z2)) = meet(meet(a,z1),z2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
meet(a,meet(z1,z2)) = meet(meet(a,z1),z2),
inference(unit_resolution,[status(thm)],[96,37]) ).
tff(98,plain,
upme(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)) = upme(meet(meet(a,z1),z2),join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
upme(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)) = meet(meet(a,z1),z2),
inference(transitivity,[status(thm)],[98,95,86,48]) ).
tff(100,plain,
join(upme(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)),meet(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3))) = join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),
inference(monotonicity,[status(thm)],[99,46]) ).
tff(101,plain,
^ [W: $i,Y1: $i,X1: $i] :
refl(
( ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) )
<=> ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) )
<=> ! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) )
<=> ! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,axiom,
! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture) ).
tff(105,plain,
! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
( ~ ! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) )
| ( join(upme(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)),meet(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3))) = meet(join(meet(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2))),meet(meet(a,z1),z3)),join(meet(meet(a,meet(z1,z2)),meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
join(upme(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)),meet(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3))) = meet(join(meet(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2))),meet(meet(a,z1),z3)),join(meet(meet(a,meet(z1,z2)),meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2)))),
inference(unit_resolution,[status(thm)],[108,107]) ).
tff(110,plain,
meet(join(meet(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2))),meet(meet(a,z1),z3)),join(meet(meet(a,meet(z1,z2)),meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2)))) = join(upme(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3)),meet(join(z3,meet(meet(a,z1),z2)),meet(meet(a,z1),z3))),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
meet(meet(z1,a),z2) = meet(meet(a,z1),z2),
inference(monotonicity,[status(thm)],[29]) ).
tff(112,plain,
meet(meet(a,z1),z2) = meet(meet(z1,a),z2),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
meet(a,meet(z1,z2)) = meet(meet(z1,a),z2),
inference(transitivity,[status(thm)],[97,112]) ).
tff(114,plain,
meet(meet(a,meet(z1,z2)),z3) = meet(meet(meet(z1,a),z2),z3),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
meet(meet(meet(z1,a),z2),z3) = meet(meet(a,meet(z1,z2)),z3),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(z1,a),meet(z2,z3)) = meet(meet(meet(z1,a),z2),z3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
meet(meet(z1,a),meet(z2,z3)) = meet(meet(meet(z1,a),z2),z3),
inference(unit_resolution,[status(thm)],[116,37]) ).
tff(118,plain,
meet(meet(z1,a),meet(z2,z3)) = meet(meet(a,z1),meet(z2,z3)),
inference(monotonicity,[status(thm)],[29]) ).
tff(119,plain,
meet(meet(a,z1),meet(z2,z3)) = meet(meet(z1,a),meet(z2,z3)),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(z2,z3) = meet(z3,z2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
meet(z2,z3) = meet(z3,z2),
inference(unit_resolution,[status(thm)],[120,26]) ).
tff(122,plain,
meet(meet(a,z1),meet(z2,z3)) = meet(meet(z1,a),meet(z3,z2)),
inference(monotonicity,[status(thm)],[28,121]) ).
tff(123,plain,
meet(meet(z1,a),meet(z3,z2)) = meet(meet(a,z1),meet(z2,z3)),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(z1,a),meet(z3,z2)) = meet(meet(meet(z1,a),z3),z2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
meet(meet(z1,a),meet(z3,z2)) = meet(meet(meet(z1,a),z3),z2),
inference(unit_resolution,[status(thm)],[124,37]) ).
tff(126,plain,
meet(meet(meet(z1,a),z3),z2) = meet(meet(z1,a),meet(z3,z2)),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
meet(meet(meet(a,z1),z3),z2) = meet(meet(meet(z1,a),z3),z2),
inference(monotonicity,[status(thm)],[42]) ).
tff(128,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(meet(a,z1),z3),join(meet(meet(a,z1),z3),z2)) = meet(meet(a,z1),z3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
meet(meet(meet(a,z1),z3),join(meet(meet(a,z1),z3),z2)) = meet(meet(a,z1),z3),
inference(unit_resolution,[status(thm)],[128,17]) ).
tff(130,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(meet(a,z1),z3),z2) = join(z2,meet(meet(a,z1),z3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
join(meet(meet(a,z1),z3),z2) = join(z2,meet(meet(a,z1),z3)),
inference(unit_resolution,[status(thm)],[130,80]) ).
tff(132,plain,
join(z2,meet(meet(a,z1),z3)) = join(meet(meet(a,z1),z3),z2),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
meet(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z3))) = meet(meet(meet(a,z1),z3),join(meet(meet(a,z1),z3),z2)),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
meet(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z3))) = meet(meet(a,z1),z3),
inference(transitivity,[status(thm)],[133,129]) ).
tff(135,plain,
meet(meet(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z3))),z2) = meet(meet(meet(a,z1),z3),z2),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(meet(a,z1),z3),meet(join(z2,meet(meet(a,z1),z3)),z2)) = meet(meet(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z3))),z2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
meet(meet(meet(a,z1),z3),meet(join(z2,meet(meet(a,z1),z3)),z2)) = meet(meet(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z3))),z2),
inference(unit_resolution,[status(thm)],[136,37]) ).
tff(138,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(z1,a),join(meet(z1,a),meet(meet(a,z1),z2))) = meet(z1,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
meet(meet(z1,a),join(meet(z1,a),meet(meet(a,z1),z2))) = meet(z1,a),
inference(unit_resolution,[status(thm)],[138,17]) ).
tff(140,plain,
join(meet(z1,a),meet(meet(a,z1),z2)) = join(meet(z1,a),meet(meet(z1,a),z2)),
inference(monotonicity,[status(thm)],[112]) ).
tff(141,plain,
join(meet(z1,a),meet(meet(z1,a),z2)) = join(meet(z1,a),meet(meet(a,z1),z2)),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(z1,a),meet(meet(z1,a),z2)) = meet(z1,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
join(meet(z1,a),meet(meet(z1,a),z2)) = meet(z1,a),
inference(unit_resolution,[status(thm)],[142,55]) ).
tff(144,plain,
meet(z1,a) = join(meet(z1,a),meet(meet(z1,a),z2)),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
meet(z1,a) = join(meet(z1,a),meet(meet(a,z1),z2)),
inference(transitivity,[status(thm)],[144,141]) ).
tff(146,plain,
meet(meet(z1,a),meet(z1,a)) = meet(meet(z1,a),join(meet(z1,a),meet(meet(a,z1),z2))),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
meet(meet(z1,a),meet(z1,a)) = meet(a,z1),
inference(transitivity,[status(thm)],[146,139,29]) ).
tff(148,plain,
meet(meet(meet(z1,a),meet(z1,a)),z3) = meet(meet(a,z1),z3),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(z1,a),meet(meet(z1,a),z3)) = meet(meet(meet(z1,a),meet(z1,a)),z3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
meet(meet(z1,a),meet(meet(z1,a),z3)) = meet(meet(meet(z1,a),meet(z1,a)),z3),
inference(unit_resolution,[status(thm)],[149,37]) ).
tff(151,plain,
meet(meet(a,z1),meet(meet(a,z1),z3)) = meet(meet(z1,a),meet(meet(z1,a),z3)),
inference(monotonicity,[status(thm)],[28,42]) ).
tff(152,plain,
meet(meet(z1,a),meet(meet(a,z1),z3)) = meet(meet(a,z1),meet(meet(a,z1),z3)),
inference(monotonicity,[status(thm)],[29]) ).
tff(153,plain,
meet(meet(z1,a),meet(meet(a,z1),z3)) = meet(meet(a,z1),z3),
inference(transitivity,[status(thm)],[152,151,150,148]) ).
tff(154,plain,
meet(meet(meet(z1,a),meet(meet(a,z1),z3)),meet(join(z2,meet(meet(a,z1),z3)),z2)) = meet(meet(meet(a,z1),z3),meet(join(z2,meet(meet(a,z1),z3)),z2)),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(z1,a),meet(meet(meet(a,z1),z3),meet(join(z2,meet(meet(a,z1),z3)),z2))) = meet(meet(meet(z1,a),meet(meet(a,z1),z3)),meet(join(z2,meet(meet(a,z1),z3)),z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
meet(meet(z1,a),meet(meet(meet(a,z1),z3),meet(join(z2,meet(meet(a,z1),z3)),z2))) = meet(meet(meet(z1,a),meet(meet(a,z1),z3)),meet(join(z2,meet(meet(a,z1),z3)),z2)),
inference(unit_resolution,[status(thm)],[155,37]) ).
tff(157,plain,
meet(meet(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z3))),z2) = meet(meet(meet(a,z1),z3),meet(join(z2,meet(meet(a,z1),z3)),z2)),
inference(symmetry,[status(thm)],[137]) ).
tff(158,plain,
meet(meet(meet(a,z1),z3),z2) = meet(meet(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z3))),z2),
inference(symmetry,[status(thm)],[135]) ).
tff(159,plain,
meet(meet(meet(z1,a),z3),z2) = meet(meet(meet(a,z1),z3),z2),
inference(symmetry,[status(thm)],[127]) ).
tff(160,plain,
meet(meet(z1,a),meet(z3,z2)) = meet(meet(meet(a,z1),z3),meet(join(z2,meet(meet(a,z1),z3)),z2)),
inference(transitivity,[status(thm)],[125,159,158,157]) ).
tff(161,plain,
meet(meet(z1,a),meet(meet(z1,a),meet(z3,z2))) = meet(meet(z1,a),meet(meet(meet(a,z1),z3),meet(join(z2,meet(meet(a,z1),z3)),z2))),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
meet(z3,meet(z1,a)) = meet(meet(z1,a),z3),
inference(symmetry,[status(thm)],[59]) ).
tff(163,plain,
meet(z3,meet(z1,a)) = meet(meet(a,z1),z3),
inference(transitivity,[status(thm)],[162,41]) ).
tff(164,plain,
meet(meet(z3,meet(z1,a)),z2) = meet(meet(meet(a,z1),z3),z2),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(z3,meet(meet(z1,a),z2)) = meet(meet(z3,meet(z1,a)),z2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
meet(z3,meet(meet(z1,a),z2)) = meet(meet(z3,meet(z1,a)),z2),
inference(unit_resolution,[status(thm)],[165,37]) ).
tff(167,plain,
meet(z3,meet(meet(a,z1),z2)) = meet(z3,meet(meet(z1,a),z2)),
inference(monotonicity,[status(thm)],[112]) ).
tff(168,plain,
meet(z3,meet(meet(a,z1),z2)) = meet(meet(z1,a),meet(z3,z2)),
inference(transitivity,[status(thm)],[167,166,164,127,126]) ).
tff(169,plain,
meet(meet(z1,a),meet(z3,meet(meet(a,z1),z2))) = meet(meet(z1,a),meet(meet(z1,a),meet(z3,z2))),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(z1,a),meet(z3,meet(meet(a,z1),z2))) = meet(meet(meet(z1,a),z3),meet(meet(a,z1),z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
meet(meet(z1,a),meet(z3,meet(meet(a,z1),z2))) = meet(meet(meet(z1,a),z3),meet(meet(a,z1),z2)),
inference(unit_resolution,[status(thm)],[170,37]) ).
tff(172,plain,
meet(meet(meet(z1,a),z3),meet(meet(a,z1),z2)) = meet(meet(z1,a),meet(z3,meet(meet(a,z1),z2))),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(a,meet(z1,z3)) = meet(meet(a,z1),z3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
meet(a,meet(z1,z3)) = meet(meet(a,z1),z3),
inference(unit_resolution,[status(thm)],[173,37]) ).
tff(175,plain,
meet(a,meet(z1,z3)) = meet(meet(z1,a),z3),
inference(transitivity,[status(thm)],[174,42]) ).
tff(176,plain,
meet(meet(a,meet(z1,z3)),meet(meet(a,z1),z2)) = meet(meet(meet(z1,a),z3),meet(meet(a,z1),z2)),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
meet(meet(a,z1),z3) = meet(a,meet(z1,z3)),
inference(symmetry,[status(thm)],[174]) ).
tff(178,plain,
meet(meet(meet(a,z1),z3),meet(meet(a,z1),z2)) = meet(meet(a,meet(z1,z3)),meet(meet(a,z1),z2)),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(meet(a,z1),z3),meet(meet(a,z1),z2)) = meet(meet(meet(a,z1),z2),meet(meet(a,z1),z3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(180,plain,
meet(meet(meet(a,z1),z3),meet(meet(a,z1),z2)) = meet(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),
inference(unit_resolution,[status(thm)],[179,26]) ).
tff(181,plain,
meet(meet(meet(a,z1),z2),meet(meet(a,z1),z3)) = meet(meet(meet(a,z1),z3),meet(meet(a,z1),z2)),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
meet(meet(a,meet(z1,z2)),meet(meet(a,z1),z3)) = meet(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),
inference(monotonicity,[status(thm)],[97]) ).
tff(183,plain,
meet(meet(a,meet(z1,z2)),meet(meet(a,z1),z3)) = meet(meet(a,meet(z1,z2)),z3),
inference(transitivity,[status(thm)],[182,181,178,176,172,169,161,156,154,137,135,127,126,123,119,117,115]) ).
tff(184,plain,
join(meet(meet(a,meet(z1,z2)),meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2))) = join(meet(meet(a,meet(z1,z2)),z3),join(z3,meet(meet(a,z1),z2))),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
join(meet(meet(a,meet(z1,z2)),z3),join(z3,meet(meet(a,z1),z2))) = join(meet(meet(a,meet(z1,z2)),meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2))),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
meet(meet(meet(z1,a),z2),z3) = meet(meet(z1,a),meet(z2,z3)),
inference(symmetry,[status(thm)],[117]) ).
tff(187,plain,
meet(meet(a,meet(z1,z2)),z3) = meet(meet(z1,a),meet(z3,z2)),
inference(transitivity,[status(thm)],[114,186,118,122]) ).
tff(188,plain,
join(meet(meet(a,meet(z1,z2)),z3),join(z3,meet(meet(a,z1),z2))) = join(meet(meet(z1,a),meet(z3,z2)),join(z3,meet(meet(a,z1),z2))),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
join(meet(meet(z1,a),meet(z3,z2)),join(z3,meet(meet(a,z1),z2))) = join(meet(meet(a,meet(z1,z2)),z3),join(z3,meet(meet(a,z1),z2))),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) )
| ( join(meet(meet(z1,a),meet(z3,z2)),join(z3,meet(meet(a,z1),z2))) = join(join(meet(meet(z1,a),meet(z3,z2)),z3),meet(meet(a,z1),z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
join(meet(meet(z1,a),meet(z3,z2)),join(z3,meet(meet(a,z1),z2))) = join(join(meet(meet(z1,a),meet(z3,z2)),z3),meet(meet(a,z1),z2)),
inference(unit_resolution,[status(thm)],[190,70]) ).
tff(192,plain,
join(join(meet(meet(z1,a),meet(z3,z2)),z3),meet(meet(a,z1),z2)) = join(meet(meet(z1,a),meet(z3,z2)),join(z3,meet(meet(a,z1),z2))),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(z3,meet(z3,meet(meet(a,z1),z2))) = z3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(194,plain,
join(z3,meet(z3,meet(meet(a,z1),z2))) = z3,
inference(unit_resolution,[status(thm)],[193,55]) ).
tff(195,plain,
meet(z3,meet(meet(z1,a),z2)) = meet(z3,meet(meet(a,z1),z2)),
inference(symmetry,[status(thm)],[167]) ).
tff(196,plain,
meet(meet(z3,meet(z1,a)),z2) = meet(z3,meet(meet(z1,a),z2)),
inference(symmetry,[status(thm)],[166]) ).
tff(197,plain,
meet(meet(meet(a,z1),z3),z2) = meet(meet(z3,meet(z1,a)),z2),
inference(symmetry,[status(thm)],[164]) ).
tff(198,plain,
meet(meet(z1,a),meet(z3,z2)) = meet(z3,meet(meet(a,z1),z2)),
inference(transitivity,[status(thm)],[125,159,197,196,195]) ).
tff(199,plain,
join(z3,meet(meet(z1,a),meet(z3,z2))) = join(z3,meet(z3,meet(meet(a,z1),z2))),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(meet(z1,a),meet(z3,z2)),z3) = join(z3,meet(meet(z1,a),meet(z3,z2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(201,plain,
join(meet(meet(z1,a),meet(z3,z2)),z3) = join(z3,meet(meet(z1,a),meet(z3,z2))),
inference(unit_resolution,[status(thm)],[200,80]) ).
tff(202,plain,
join(meet(meet(z1,a),meet(z3,z2)),z3) = z3,
inference(transitivity,[status(thm)],[201,199,194]) ).
tff(203,plain,
join(join(meet(meet(z1,a),meet(z3,z2)),z3),meet(meet(a,z1),z2)) = join(z3,meet(meet(a,z1),z2)),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
join(z3,meet(meet(a,z1),z2)) = join(join(meet(meet(z1,a),meet(z3,z2)),z3),meet(meet(a,z1),z2)),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
join(z3,meet(meet(a,z1),z2)) = join(meet(meet(a,meet(z1,z2)),meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2))),
inference(transitivity,[status(thm)],[204,192,189,185]) ).
tff(206,plain,
meet(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2))) = meet(meet(meet(a,z1),z2),join(meet(meet(a,z1),z2),z3)),
inference(monotonicity,[status(thm)],[97,83]) ).
tff(207,plain,
meet(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2))) = meet(meet(a,z1),z2),
inference(transitivity,[status(thm)],[206,48]) ).
tff(208,plain,
join(meet(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2))),meet(meet(a,z1),z3)) = join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)) = join(meet(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2))),meet(meet(a,z1),z3)),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2))) = meet(join(meet(meet(a,meet(z1,z2)),join(z3,meet(meet(a,z1),z2))),meet(meet(a,z1),z3)),join(meet(meet(a,meet(z1,z2)),meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2)))),
inference(monotonicity,[status(thm)],[209,205]) ).
tff(211,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)) = join(meet(meet(a,z1),z3),meet(meet(a,z1),z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(212,plain,
join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)) = join(meet(meet(a,z1),z3),meet(meet(a,z1),z2)),
inference(unit_resolution,[status(thm)],[211,80]) ).
tff(213,plain,
join(meet(meet(a,z1),z3),meet(meet(a,z1),z2)) = join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(meet(a,z1),z2),join(meet(meet(a,z1),z2),meet(z1,a))) = meet(meet(a,z1),z2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(215,plain,
meet(meet(meet(a,z1),z2),join(meet(meet(a,z1),z2),meet(z1,a))) = meet(meet(a,z1),z2),
inference(unit_resolution,[status(thm)],[214,17]) ).
tff(216,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(z1,a),meet(meet(a,z1),z2)) = join(meet(meet(a,z1),z2),meet(z1,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(217,plain,
join(meet(z1,a),meet(meet(a,z1),z2)) = join(meet(meet(a,z1),z2),meet(z1,a)),
inference(unit_resolution,[status(thm)],[216,80]) ).
tff(218,plain,
meet(z1,a) = join(meet(meet(a,z1),z2),meet(z1,a)),
inference(transitivity,[status(thm)],[144,141,217]) ).
tff(219,plain,
meet(meet(meet(a,z1),z2),meet(z1,a)) = meet(meet(meet(a,z1),z2),join(meet(meet(a,z1),z2),meet(z1,a))),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(z1,a),meet(meet(a,z1),z2)) = meet(meet(meet(a,z1),z2),meet(z1,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(221,plain,
meet(meet(z1,a),meet(meet(a,z1),z2)) = meet(meet(meet(a,z1),z2),meet(z1,a)),
inference(unit_resolution,[status(thm)],[220,26]) ).
tff(222,plain,
meet(meet(z1,a),meet(meet(a,z1),z2)) = meet(meet(a,z1),z2),
inference(transitivity,[status(thm)],[221,219,215]) ).
tff(223,plain,
meet(meet(z1,a),meet(z3,meet(z1,a))) = meet(meet(a,z1),meet(meet(a,z1),z3)),
inference(monotonicity,[status(thm)],[29,163]) ).
tff(224,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(z1,a),meet(z3,meet(z1,a))) = meet(meet(meet(z1,a),z3),meet(z1,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(225,plain,
meet(meet(z1,a),meet(z3,meet(z1,a))) = meet(meet(meet(z1,a),z3),meet(z1,a)),
inference(unit_resolution,[status(thm)],[224,37]) ).
tff(226,plain,
meet(meet(meet(z1,a),z3),meet(z1,a)) = meet(meet(z1,a),meet(z3,meet(z1,a))),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
join(meet(z1,a),meet(meet(a,z1),z2)) = meet(z1,a),
inference(transitivity,[status(thm)],[140,143]) ).
tff(228,plain,
meet(meet(meet(a,z1),z3),join(meet(z1,a),meet(meet(a,z1),z2))) = meet(meet(meet(z1,a),z3),meet(z1,a)),
inference(monotonicity,[status(thm)],[42,227]) ).
tff(229,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) )
| ( upme(meet(meet(a,z1),z3),meet(z1,a),meet(meet(a,z1),z2)) = meet(meet(meet(a,z1),z3),join(meet(z1,a),meet(meet(a,z1),z2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(230,plain,
upme(meet(meet(a,z1),z3),meet(z1,a),meet(meet(a,z1),z2)) = meet(meet(meet(a,z1),z3),join(meet(z1,a),meet(meet(a,z1),z2))),
inference(unit_resolution,[status(thm)],[229,93]) ).
tff(231,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,meet(z1,a))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(232,plain,
meet(a,join(a,meet(z1,a))) = a,
inference(unit_resolution,[status(thm)],[231,17]) ).
tff(233,plain,
join(a,meet(z1,a)) = join(a,meet(a,z1)),
inference(monotonicity,[status(thm)],[29]) ).
tff(234,plain,
join(a,meet(a,z1)) = join(a,meet(z1,a)),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(a,meet(a,z1)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(236,plain,
join(a,meet(a,z1)) = a,
inference(unit_resolution,[status(thm)],[235,55]) ).
tff(237,plain,
a = join(a,meet(a,z1)),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
a = join(a,meet(z1,a)),
inference(transitivity,[status(thm)],[237,234]) ).
tff(239,plain,
meet(a,a) = meet(a,join(a,meet(z1,a))),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
meet(a,a) = a,
inference(transitivity,[status(thm)],[239,232]) ).
tff(241,plain,
meet(meet(a,a),meet(z1,z3)) = meet(a,meet(z1,z3)),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(a,meet(a,meet(z1,z3))) = meet(meet(a,a),meet(z1,z3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(243,plain,
meet(a,meet(a,meet(z1,z3))) = meet(meet(a,a),meet(z1,z3)),
inference(unit_resolution,[status(thm)],[242,37]) ).
tff(244,plain,
meet(a,meet(meet(a,z1),z3)) = meet(a,meet(a,meet(z1,z3))),
inference(monotonicity,[status(thm)],[177]) ).
tff(245,plain,
meet(a,meet(meet(a,z1),z3)) = meet(meet(a,z1),z3),
inference(transitivity,[status(thm)],[244,243,241,174]) ).
tff(246,plain,
upme(meet(a,meet(meet(a,z1),z3)),meet(z1,a),meet(meet(a,z1),z2)) = upme(meet(meet(a,z1),z3),meet(z1,a),meet(meet(a,z1),z2)),
inference(monotonicity,[status(thm)],[245]) ).
tff(247,plain,
upme(meet(a,meet(meet(a,z1),z3)),meet(z1,a),meet(meet(a,z1),z2)) = meet(meet(a,z1),z3),
inference(transitivity,[status(thm)],[246,230,228,226,223,151,150,148]) ).
tff(248,plain,
join(upme(meet(a,meet(meet(a,z1),z3)),meet(z1,a),meet(meet(a,z1),z2)),meet(meet(z1,a),meet(meet(a,z1),z2))) = join(meet(meet(a,z1),z3),meet(meet(a,z1),z2)),
inference(monotonicity,[status(thm)],[247,222]) ).
tff(249,plain,
( ~ ! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) )
| ( join(upme(meet(a,meet(meet(a,z1),z3)),meet(z1,a),meet(meet(a,z1),z2)),meet(meet(z1,a),meet(meet(a,z1),z2))) = meet(join(meet(meet(a,meet(meet(a,z1),z3)),meet(z1,a)),meet(meet(a,z1),z2)),join(meet(meet(a,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),meet(z1,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(250,plain,
join(upme(meet(a,meet(meet(a,z1),z3)),meet(z1,a),meet(meet(a,z1),z2)),meet(meet(z1,a),meet(meet(a,z1),z2))) = meet(join(meet(meet(a,meet(meet(a,z1),z3)),meet(z1,a)),meet(meet(a,z1),z2)),join(meet(meet(a,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),meet(z1,a))),
inference(unit_resolution,[status(thm)],[249,107]) ).
tff(251,plain,
meet(join(meet(meet(a,meet(meet(a,z1),z3)),meet(z1,a)),meet(meet(a,z1),z2)),join(meet(meet(a,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),meet(z1,a))) = join(upme(meet(a,meet(meet(a,z1),z3)),meet(z1,a),meet(meet(a,z1),z2)),meet(meet(z1,a),meet(meet(a,z1),z2))),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
meet(a,meet(meet(a,z1),z3)) = meet(a,meet(z1,z3)),
inference(transitivity,[status(thm)],[244,243,241]) ).
tff(253,plain,
meet(meet(a,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)) = meet(meet(a,meet(z1,z3)),meet(meet(a,z1),z2)),
inference(monotonicity,[status(thm)],[252]) ).
tff(254,plain,
meet(meet(a,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)) = meet(meet(z1,a),meet(z3,z2)),
inference(transitivity,[status(thm)],[253,176,172,169,161,156,154,137,135,127,126]) ).
tff(255,plain,
join(meet(meet(a,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),meet(z1,a)) = join(meet(meet(z1,a),meet(z3,z2)),meet(z1,a)),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
join(meet(meet(z1,a),meet(z3,z2)),meet(z1,a)) = join(meet(meet(a,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),meet(z1,a)),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(z1,a),meet(meet(z1,a),meet(z3,z2))) = join(meet(meet(z1,a),meet(z3,z2)),meet(z1,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(258,plain,
join(meet(z1,a),meet(meet(z1,a),meet(z3,z2))) = join(meet(meet(z1,a),meet(z3,z2)),meet(z1,a)),
inference(unit_resolution,[status(thm)],[257,80]) ).
tff(259,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(z1,a),meet(meet(z1,a),meet(z3,z2))) = meet(z1,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(260,plain,
join(meet(z1,a),meet(meet(z1,a),meet(z3,z2))) = meet(z1,a),
inference(unit_resolution,[status(thm)],[259,55]) ).
tff(261,plain,
meet(z1,a) = join(meet(z1,a),meet(meet(z1,a),meet(z3,z2))),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
meet(z1,a) = join(meet(meet(a,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),meet(z1,a)),
inference(transitivity,[status(thm)],[261,258,256]) ).
tff(263,plain,
meet(a,meet(meet(a,z1),z3)) = meet(meet(z1,a),z3),
inference(transitivity,[status(thm)],[244,243,241,174,42]) ).
tff(264,plain,
meet(meet(a,meet(meet(a,z1),z3)),meet(z1,a)) = meet(meet(meet(z1,a),z3),meet(z1,a)),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
meet(meet(a,meet(meet(a,z1),z3)),meet(z1,a)) = meet(meet(a,z1),z3),
inference(transitivity,[status(thm)],[264,226,223,151,150,148]) ).
tff(266,plain,
join(meet(meet(a,meet(meet(a,z1),z3)),meet(z1,a)),meet(meet(a,z1),z2)) = join(meet(meet(a,z1),z3),meet(meet(a,z1),z2)),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
join(meet(meet(a,z1),z3),meet(meet(a,z1),z2)) = join(meet(meet(a,meet(meet(a,z1),z3)),meet(z1,a)),meet(meet(a,z1),z2)),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)) = join(meet(meet(a,meet(meet(a,z1),z3)),meet(z1,a)),meet(meet(a,z1),z2)),
inference(transitivity,[status(thm)],[212,267]) ).
tff(269,plain,
meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),meet(z1,a)) = meet(join(meet(meet(a,meet(meet(a,z1),z3)),meet(z1,a)),meet(meet(a,z1),z2)),join(meet(meet(a,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),meet(z1,a))),
inference(monotonicity,[status(thm)],[268,262]) ).
tff(270,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(z1,a),join(meet(meet(a,z1),z2),meet(meet(a,z1),z3))) = meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),meet(z1,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(271,plain,
meet(meet(z1,a),join(meet(meet(a,z1),z2),meet(meet(a,z1),z3))) = meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),meet(z1,a)),
inference(unit_resolution,[status(thm)],[270,26]) ).
tff(272,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(z2,join(z2,meet(meet(a,z1),z3))) = z2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(273,plain,
meet(z2,join(z2,meet(meet(a,z1),z3))) = z2,
inference(unit_resolution,[status(thm)],[272,17]) ).
tff(274,plain,
meet(meet(z1,a),meet(z2,join(z2,meet(meet(a,z1),z3)))) = meet(meet(a,z1),z2),
inference(monotonicity,[status(thm)],[29,273]) ).
tff(275,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(z1,a),meet(z2,join(z2,meet(meet(a,z1),z3)))) = meet(meet(meet(z1,a),z2),join(z2,meet(meet(a,z1),z3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(276,plain,
meet(meet(z1,a),meet(z2,join(z2,meet(meet(a,z1),z3)))) = meet(meet(meet(z1,a),z2),join(z2,meet(meet(a,z1),z3))),
inference(unit_resolution,[status(thm)],[275,37]) ).
tff(277,plain,
meet(meet(meet(z1,a),z2),join(z2,meet(meet(a,z1),z3))) = meet(meet(z1,a),meet(z2,join(z2,meet(meet(a,z1),z3)))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
meet(meet(meet(a,z1),z2),join(z2,meet(meet(a,z1),z3))) = meet(meet(meet(z1,a),z2),join(z2,meet(meet(a,z1),z3))),
inference(monotonicity,[status(thm)],[112]) ).
tff(279,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)) = meet(meet(meet(a,z1),z2),join(z2,meet(meet(a,z1),z3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(280,plain,
meet(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)) = meet(meet(meet(a,z1),z2),join(z2,meet(meet(a,z1),z3))),
inference(unit_resolution,[status(thm)],[279,26]) ).
tff(281,plain,
meet(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)) = meet(meet(a,z1),z2),
inference(transitivity,[status(thm)],[280,278,277,274]) ).
tff(282,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(z2,meet(z2,meet(z1,a))) = z2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(283,plain,
join(z2,meet(z2,meet(z1,a))) = z2,
inference(unit_resolution,[status(thm)],[282,55]) ).
tff(284,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(z1,a),z2) = meet(z2,meet(z1,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(285,plain,
meet(meet(z1,a),z2) = meet(z2,meet(z1,a)),
inference(unit_resolution,[status(thm)],[284,26]) ).
tff(286,plain,
meet(meet(a,z1),z2) = meet(z2,meet(z1,a)),
inference(transitivity,[status(thm)],[112,285]) ).
tff(287,plain,
join(z2,meet(meet(a,z1),z2)) = join(z2,meet(z2,meet(z1,a))),
inference(monotonicity,[status(thm)],[286]) ).
tff(288,plain,
join(z2,meet(meet(a,z1),z2)) = z2,
inference(transitivity,[status(thm)],[287,283]) ).
tff(289,plain,
join(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z2))) = join(meet(meet(a,z1),z3),z2),
inference(monotonicity,[status(thm)],[288]) ).
tff(290,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) )
| ( join(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z2))) = join(join(meet(meet(a,z1),z3),z2),meet(meet(a,z1),z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(291,plain,
join(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z2))) = join(join(meet(meet(a,z1),z3),z2),meet(meet(a,z1),z2)),
inference(unit_resolution,[status(thm)],[290,70]) ).
tff(292,plain,
join(join(meet(meet(a,z1),z3),z2),meet(meet(a,z1),z2)) = join(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z2))),
inference(symmetry,[status(thm)],[291]) ).
tff(293,plain,
join(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)) = join(join(meet(meet(a,z1),z3),z2),meet(meet(a,z1),z2)),
inference(monotonicity,[status(thm)],[132]) ).
tff(294,plain,
join(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)) = join(meet(meet(a,z1),z3),z2),
inference(transitivity,[status(thm)],[293,292,289]) ).
tff(295,plain,
meet(meet(meet(a,z1),z3),join(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2))) = meet(meet(meet(a,z1),z3),join(meet(meet(a,z1),z3),z2)),
inference(monotonicity,[status(thm)],[294]) ).
tff(296,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) )
| ( upme(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)) = meet(meet(meet(a,z1),z3),join(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(297,plain,
upme(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)) = meet(meet(meet(a,z1),z3),join(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2))),
inference(unit_resolution,[status(thm)],[296,93]) ).
tff(298,plain,
upme(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)) = upme(meet(meet(a,z1),z3),join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),
inference(monotonicity,[status(thm)],[174]) ).
tff(299,plain,
upme(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)) = meet(meet(a,z1),z3),
inference(transitivity,[status(thm)],[298,297,295,129]) ).
tff(300,plain,
join(upme(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),meet(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2))) = join(meet(meet(a,z1),z3),meet(meet(a,z1),z2)),
inference(monotonicity,[status(thm)],[299,281]) ).
tff(301,plain,
( ~ ! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) )
| ( join(upme(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),meet(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2))) = meet(join(meet(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3))),meet(meet(a,z1),z2)),join(meet(meet(a,meet(z1,z3)),meet(meet(a,z1),z2)),join(z2,meet(meet(a,z1),z3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(302,plain,
join(upme(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),meet(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2))) = meet(join(meet(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3))),meet(meet(a,z1),z2)),join(meet(meet(a,meet(z1,z3)),meet(meet(a,z1),z2)),join(z2,meet(meet(a,z1),z3)))),
inference(unit_resolution,[status(thm)],[301,107]) ).
tff(303,plain,
meet(join(meet(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3))),meet(meet(a,z1),z2)),join(meet(meet(a,meet(z1,z3)),meet(meet(a,z1),z2)),join(z2,meet(meet(a,z1),z3)))) = join(upme(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2)),meet(join(z2,meet(meet(a,z1),z3)),meet(meet(a,z1),z2))),
inference(symmetry,[status(thm)],[302]) ).
tff(304,plain,
meet(meet(a,meet(z1,z3)),z2) = meet(meet(meet(a,z1),z3),z2),
inference(monotonicity,[status(thm)],[174]) ).
tff(305,plain,
meet(meet(meet(a,z1),z3),z2) = meet(meet(a,meet(z1,z3)),z2),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
meet(meet(a,meet(z1,z3)),meet(meet(a,z1),z2)) = meet(meet(a,meet(z1,z3)),z2),
inference(transitivity,[status(thm)],[176,172,169,161,156,154,137,135,305]) ).
tff(307,plain,
join(meet(meet(a,meet(z1,z3)),meet(meet(a,z1),z2)),join(z2,meet(meet(a,z1),z3))) = join(meet(meet(a,meet(z1,z3)),z2),join(z2,meet(meet(a,z1),z3))),
inference(monotonicity,[status(thm)],[306]) ).
tff(308,plain,
join(meet(meet(a,meet(z1,z3)),z2),join(z2,meet(meet(a,z1),z3))) = join(meet(meet(a,meet(z1,z3)),meet(meet(a,z1),z2)),join(z2,meet(meet(a,z1),z3))),
inference(symmetry,[status(thm)],[307]) ).
tff(309,plain,
meet(meet(a,meet(z1,z3)),z2) = meet(meet(z1,a),meet(z3,z2)),
inference(transitivity,[status(thm)],[304,127,126]) ).
tff(310,plain,
join(meet(meet(a,meet(z1,z3)),z2),join(z2,meet(meet(a,z1),z3))) = join(meet(meet(z1,a),meet(z3,z2)),join(z2,meet(meet(a,z1),z3))),
inference(monotonicity,[status(thm)],[309]) ).
tff(311,plain,
join(meet(meet(z1,a),meet(z3,z2)),join(z2,meet(meet(a,z1),z3))) = join(meet(meet(a,meet(z1,z3)),z2),join(z2,meet(meet(a,z1),z3))),
inference(symmetry,[status(thm)],[310]) ).
tff(312,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) )
| ( join(meet(meet(z1,a),meet(z3,z2)),join(z2,meet(meet(a,z1),z3))) = join(join(meet(meet(z1,a),meet(z3,z2)),z2),meet(meet(a,z1),z3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(313,plain,
join(meet(meet(z1,a),meet(z3,z2)),join(z2,meet(meet(a,z1),z3))) = join(join(meet(meet(z1,a),meet(z3,z2)),z2),meet(meet(a,z1),z3)),
inference(unit_resolution,[status(thm)],[312,70]) ).
tff(314,plain,
join(join(meet(meet(z1,a),meet(z3,z2)),z2),meet(meet(a,z1),z3)) = join(meet(meet(z1,a),meet(z3,z2)),join(z2,meet(meet(a,z1),z3))),
inference(symmetry,[status(thm)],[313]) ).
tff(315,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(z2,meet(z2,meet(meet(a,z1),z3))) = z2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(316,plain,
join(z2,meet(z2,meet(meet(a,z1),z3))) = z2,
inference(unit_resolution,[status(thm)],[315,55]) ).
tff(317,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(z2,meet(meet(a,z1),z3)) = meet(meet(meet(a,z1),z3),z2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(318,plain,
meet(z2,meet(meet(a,z1),z3)) = meet(meet(meet(a,z1),z3),z2),
inference(unit_resolution,[status(thm)],[317,26]) ).
tff(319,plain,
meet(meet(meet(a,z1),z3),z2) = meet(z2,meet(meet(a,z1),z3)),
inference(symmetry,[status(thm)],[318]) ).
tff(320,plain,
meet(meet(z1,a),meet(z3,z2)) = meet(z2,meet(meet(a,z1),z3)),
inference(transitivity,[status(thm)],[125,159,319]) ).
tff(321,plain,
join(z2,meet(meet(z1,a),meet(z3,z2))) = join(z2,meet(z2,meet(meet(a,z1),z3))),
inference(monotonicity,[status(thm)],[320]) ).
tff(322,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(z2,meet(meet(z1,a),meet(z3,z2))) = join(meet(meet(z1,a),meet(z3,z2)),z2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(323,plain,
join(z2,meet(meet(z1,a),meet(z3,z2))) = join(meet(meet(z1,a),meet(z3,z2)),z2),
inference(unit_resolution,[status(thm)],[322,80]) ).
tff(324,plain,
join(meet(meet(z1,a),meet(z3,z2)),z2) = join(z2,meet(meet(z1,a),meet(z3,z2))),
inference(symmetry,[status(thm)],[323]) ).
tff(325,plain,
join(meet(meet(z1,a),meet(z3,z2)),z2) = z2,
inference(transitivity,[status(thm)],[324,321,316]) ).
tff(326,plain,
join(join(meet(meet(z1,a),meet(z3,z2)),z2),meet(meet(a,z1),z3)) = join(z2,meet(meet(a,z1),z3)),
inference(monotonicity,[status(thm)],[325]) ).
tff(327,plain,
join(z2,meet(meet(a,z1),z3)) = join(join(meet(meet(z1,a),meet(z3,z2)),z2),meet(meet(a,z1),z3)),
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
meet(meet(a,z1),meet(meet(a,z1),z3)) = meet(meet(a,z1),z3),
inference(transitivity,[status(thm)],[151,150,148]) ).
tff(329,plain,
join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2) = join(meet(meet(a,z1),z3),z2),
inference(monotonicity,[status(thm)],[328]) ).
tff(330,plain,
join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2) = join(meet(meet(a,meet(z1,z3)),meet(meet(a,z1),z2)),join(z2,meet(meet(a,z1),z3))),
inference(transitivity,[status(thm)],[329,131,327,314,311,308]) ).
tff(331,plain,
meet(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3))) = meet(meet(meet(a,z1),z3),join(meet(meet(a,z1),z3),z2)),
inference(monotonicity,[status(thm)],[174,132]) ).
tff(332,plain,
meet(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3))) = meet(meet(a,z1),z3),
inference(transitivity,[status(thm)],[331,129]) ).
tff(333,plain,
join(meet(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3))),meet(meet(a,z1),z2)) = join(meet(meet(a,z1),z3),meet(meet(a,z1),z2)),
inference(monotonicity,[status(thm)],[332]) ).
tff(334,plain,
join(meet(meet(a,z1),z3),meet(meet(a,z1),z2)) = join(meet(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3))),meet(meet(a,z1),z2)),
inference(symmetry,[status(thm)],[333]) ).
tff(335,plain,
join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)) = join(meet(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3))),meet(meet(a,z1),z2)),
inference(transitivity,[status(thm)],[212,334]) ).
tff(336,plain,
meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2)) = meet(join(meet(meet(a,meet(z1,z3)),join(z2,meet(meet(a,z1),z3))),meet(meet(a,z1),z2)),join(meet(meet(a,meet(z1,z3)),meet(meet(a,z1),z2)),join(z2,meet(meet(a,z1),z3)))),
inference(monotonicity,[status(thm)],[335,330]) ).
tff(337,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2)) = meet(join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2),join(meet(meet(a,z1),z2),meet(meet(a,z1),z3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(338,plain,
meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2)) = meet(join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2),join(meet(meet(a,z1),z2),meet(meet(a,z1),z3))),
inference(unit_resolution,[status(thm)],[337,26]) ).
tff(339,plain,
meet(join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2),join(meet(meet(a,z1),z2),meet(meet(a,z1),z3))) = meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2)),
inference(symmetry,[status(thm)],[338]) ).
tff(340,plain,
meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2)) = join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),
inference(transitivity,[status(thm)],[336,303,300,213]) ).
tff(341,plain,
join(meet(meet(a,z1),z3),z2) = join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2),
inference(symmetry,[status(thm)],[329]) ).
tff(342,plain,
join(z2,meet(meet(a,z1),z3)) = join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2),
inference(transitivity,[status(thm)],[132,341]) ).
tff(343,plain,
meet(join(z2,meet(meet(a,z1),z3)),meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2))) = meet(join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2),join(meet(meet(a,z1),z2),meet(meet(a,z1),z3))),
inference(monotonicity,[status(thm)],[342,340]) ).
tff(344,plain,
meet(join(z2,meet(meet(a,z1),z3)),meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2))) = join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),
inference(transitivity,[status(thm)],[343,339,336,303,300,213]) ).
tff(345,plain,
meet(meet(z1,a),meet(join(z2,meet(meet(a,z1),z3)),meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2)))) = meet(meet(z1,a),join(meet(meet(a,z1),z2),meet(meet(a,z1),z3))),
inference(monotonicity,[status(thm)],[344]) ).
tff(346,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(z1,a),meet(join(z2,meet(meet(a,z1),z3)),meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2)))) = meet(meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))),meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(347,plain,
meet(meet(z1,a),meet(join(z2,meet(meet(a,z1),z3)),meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2)))) = meet(meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))),meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2))),
inference(unit_resolution,[status(thm)],[346,37]) ).
tff(348,plain,
meet(meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))),meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2))) = meet(meet(z1,a),meet(join(z2,meet(meet(a,z1),z3)),meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2)))),
inference(symmetry,[status(thm)],[347]) ).
tff(349,plain,
( ~ ! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) )
| ( join(upme(meet(a,z1),z2,meet(meet(a,z1),z3)),meet(z2,meet(meet(a,z1),z3))) = meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(350,plain,
join(upme(meet(a,z1),z2,meet(meet(a,z1),z3)),meet(z2,meet(meet(a,z1),z3))) = meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2)),
inference(unit_resolution,[status(thm)],[349,107]) ).
tff(351,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) )
| ( upme(meet(z1,a),z2,meet(meet(a,z1),z3)) = meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(352,plain,
upme(meet(z1,a),z2,meet(meet(a,z1),z3)) = meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))),
inference(unit_resolution,[status(thm)],[351,93]) ).
tff(353,plain,
upme(meet(z1,a),z2,meet(meet(a,z1),z3)) = upme(meet(a,z1),z2,meet(meet(a,z1),z3)),
inference(monotonicity,[status(thm)],[29]) ).
tff(354,plain,
upme(meet(a,z1),z2,meet(meet(a,z1),z3)) = upme(meet(z1,a),z2,meet(meet(a,z1),z3)),
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
upme(meet(a,z1),z2,meet(meet(a,z1),z3)) = meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))),
inference(transitivity,[status(thm)],[354,352]) ).
tff(356,plain,
meet(upme(meet(a,z1),z2,meet(meet(a,z1),z3)),join(upme(meet(a,z1),z2,meet(meet(a,z1),z3)),meet(z2,meet(meet(a,z1),z3)))) = meet(meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))),meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(meet(meet(a,z1),meet(meet(a,z1),z3)),z2))),
inference(monotonicity,[status(thm)],[355,350]) ).
tff(357,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(upme(meet(a,z1),z2,meet(meet(a,z1),z3)),join(upme(meet(a,z1),z2,meet(meet(a,z1),z3)),meet(z2,meet(meet(a,z1),z3)))) = upme(meet(a,z1),z2,meet(meet(a,z1),z3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(358,plain,
meet(upme(meet(a,z1),z2,meet(meet(a,z1),z3)),join(upme(meet(a,z1),z2,meet(meet(a,z1),z3)),meet(z2,meet(meet(a,z1),z3)))) = upme(meet(a,z1),z2,meet(meet(a,z1),z3)),
inference(unit_resolution,[status(thm)],[357,17]) ).
tff(359,plain,
upme(meet(a,z1),z2,meet(meet(a,z1),z3)) = meet(upme(meet(a,z1),z2,meet(meet(a,z1),z3)),join(upme(meet(a,z1),z2,meet(meet(a,z1),z3)),meet(z2,meet(meet(a,z1),z3)))),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))) = upme(meet(z1,a),z2,meet(meet(a,z1),z3)),
inference(symmetry,[status(thm)],[352]) ).
tff(361,plain,
meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))) = join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),
inference(transitivity,[status(thm)],[360,353,359,356,348,345,271,269,251,248,213]) ).
tff(362,plain,
meet(meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))),join(z3,meet(meet(a,z1),z2))) = meet(join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2))),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(z1,a),meet(join(z2,meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2)))) = meet(meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))),join(z3,meet(meet(a,z1),z2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(364,plain,
meet(meet(z1,a),meet(join(z2,meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2)))) = meet(meet(meet(z1,a),join(z2,meet(meet(a,z1),z3))),join(z3,meet(meet(a,z1),z2))),
inference(unit_resolution,[status(thm)],[363,37]) ).
tff(365,plain,
meet(join(z2,meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2))) = meet(join(meet(meet(a,z1),z3),z2),join(meet(meet(a,z1),z2),z3)),
inference(monotonicity,[status(thm)],[132,83]) ).
tff(366,plain,
meet(join(meet(meet(a,z1),z3),z2),join(meet(meet(a,z1),z2),z3)) = meet(join(z2,meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2))),
inference(symmetry,[status(thm)],[365]) ).
tff(367,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)) = meet(join(meet(meet(a,z1),z3),z2),join(meet(meet(a,z1),z2),z3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(368,plain,
meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)) = meet(join(meet(meet(a,z1),z3),z2),join(meet(meet(a,z1),z2),z3)),
inference(unit_resolution,[status(thm)],[367,26]) ).
tff(369,plain,
meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)) = meet(join(z2,meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2))),
inference(transitivity,[status(thm)],[368,366]) ).
tff(370,plain,
meet(meet(z1,a),meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2))) = meet(meet(z1,a),meet(join(z2,meet(meet(a,z1),z3)),join(z3,meet(meet(a,z1),z2)))),
inference(monotonicity,[status(thm)],[369]) ).
tff(371,plain,
( ~ ! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) )
| ( join(upme(meet(a,z1),z2,z3),meet(z2,z3)) = meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(372,plain,
join(upme(meet(a,z1),z2,z3),meet(z2,z3)) = meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)),
inference(unit_resolution,[status(thm)],[371,107]) ).
tff(373,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(z2,z3) = join(z3,z2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(374,plain,
join(z2,z3) = join(z3,z2),
inference(unit_resolution,[status(thm)],[373,80]) ).
tff(375,plain,
meet(join(z2,z3),meet(z2,z3)) = meet(join(z3,z2),meet(z3,z2)),
inference(monotonicity,[status(thm)],[374,121]) ).
tff(376,plain,
meet(join(z3,z2),meet(z3,z2)) = meet(join(z2,z3),meet(z2,z3)),
inference(symmetry,[status(thm)],[375]) ).
tff(377,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(z3,z2),meet(z3,z2)) = meet(meet(z3,z2),join(z3,z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(378,plain,
meet(join(z3,z2),meet(z3,z2)) = meet(meet(z3,z2),join(z3,z2)),
inference(unit_resolution,[status(thm)],[377,26]) ).
tff(379,plain,
meet(meet(z3,z2),join(z3,z2)) = meet(join(z3,z2),meet(z3,z2)),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
meet(meet(z2,z3),join(z2,z3)) = meet(meet(z3,z2),join(z3,z2)),
inference(monotonicity,[status(thm)],[121,374]) ).
tff(381,plain,
join(z3,z2) = join(z2,z3),
inference(symmetry,[status(thm)],[374]) ).
tff(382,plain,
meet(meet(z2,z3),join(z3,z2)) = meet(meet(z2,z3),join(z2,z3)),
inference(monotonicity,[status(thm)],[381]) ).
tff(383,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(z2,meet(z3,join(z3,z2))) = meet(meet(z2,z3),join(z3,z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(384,plain,
meet(z2,meet(z3,join(z3,z2))) = meet(meet(z2,z3),join(z3,z2)),
inference(unit_resolution,[status(thm)],[383,37]) ).
tff(385,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(z3,join(z3,z2)) = z3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(386,plain,
meet(z3,join(z3,z2)) = z3,
inference(unit_resolution,[status(thm)],[385,17]) ).
tff(387,plain,
z3 = meet(z3,join(z3,z2)),
inference(symmetry,[status(thm)],[386]) ).
tff(388,plain,
meet(z2,z3) = meet(z2,meet(z3,join(z3,z2))),
inference(monotonicity,[status(thm)],[387]) ).
tff(389,plain,
meet(z2,z3) = meet(join(z2,z3),meet(z2,z3)),
inference(transitivity,[status(thm)],[388,384,382,380,379,376]) ).
tff(390,plain,
upme(meet(a,z1),join(z2,z3),meet(z2,z3)) = upme(meet(z1,a),join(z3,z2),meet(z3,z2)),
inference(monotonicity,[status(thm)],[28,374,121]) ).
tff(391,plain,
upme(meet(z1,a),join(z3,z2),meet(z3,z2)) = upme(meet(a,z1),join(z2,z3),meet(z2,z3)),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) )
| ( upme(meet(z1,a),join(z3,z2),meet(z3,z2)) = meet(meet(z1,a),join(join(z3,z2),meet(z3,z2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(393,plain,
upme(meet(z1,a),join(z3,z2),meet(z3,z2)) = meet(meet(z1,a),join(join(z3,z2),meet(z3,z2))),
inference(unit_resolution,[status(thm)],[392,93]) ).
tff(394,plain,
meet(meet(z1,a),join(join(z3,z2),meet(z3,z2))) = upme(meet(z1,a),join(z3,z2),meet(z3,z2)),
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(z2,meet(z2,z3)) = z2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(396,plain,
join(z2,meet(z2,z3)) = z2,
inference(unit_resolution,[status(thm)],[395,55]) ).
tff(397,plain,
meet(z3,z2) = meet(z2,z3),
inference(symmetry,[status(thm)],[121]) ).
tff(398,plain,
join(z2,meet(z3,z2)) = join(z2,meet(z2,z3)),
inference(monotonicity,[status(thm)],[397]) ).
tff(399,plain,
join(z2,meet(z3,z2)) = z2,
inference(transitivity,[status(thm)],[398,396]) ).
tff(400,plain,
join(z3,join(z2,meet(z3,z2))) = join(z3,z2),
inference(monotonicity,[status(thm)],[399]) ).
tff(401,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) )
| ( join(z3,join(z2,meet(z3,z2))) = join(join(z3,z2),meet(z3,z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(402,plain,
join(z3,join(z2,meet(z3,z2))) = join(join(z3,z2),meet(z3,z2)),
inference(unit_resolution,[status(thm)],[401,70]) ).
tff(403,plain,
join(join(z3,z2),meet(z3,z2)) = join(z3,join(z2,meet(z3,z2))),
inference(symmetry,[status(thm)],[402]) ).
tff(404,plain,
join(join(z3,z2),meet(z3,z2)) = join(z2,z3),
inference(transitivity,[status(thm)],[403,400,381]) ).
tff(405,plain,
meet(meet(z1,a),join(join(z3,z2),meet(z3,z2))) = meet(meet(a,z1),join(z2,z3)),
inference(monotonicity,[status(thm)],[29,404]) ).
tff(406,plain,
meet(meet(a,z1),join(z2,z3)) = meet(meet(z1,a),join(join(z3,z2),meet(z3,z2))),
inference(symmetry,[status(thm)],[405]) ).
tff(407,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( upme(X,Y,Z) = meet(X,join(Y,Z)) )
| ( upme(meet(a,z1),z2,z3) = meet(meet(a,z1),join(z2,z3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(408,plain,
upme(meet(a,z1),z2,z3) = meet(meet(a,z1),join(z2,z3)),
inference(unit_resolution,[status(thm)],[407,93]) ).
tff(409,plain,
upme(meet(a,z1),z2,z3) = upme(meet(a,z1),join(z2,z3),meet(z2,z3)),
inference(transitivity,[status(thm)],[408,406,394,391]) ).
tff(410,plain,
join(upme(meet(a,z1),z2,z3),meet(z2,z3)) = join(upme(meet(a,z1),join(z2,z3),meet(z2,z3)),meet(join(z2,z3),meet(z2,z3))),
inference(monotonicity,[status(thm)],[409,389]) ).
tff(411,plain,
join(upme(meet(a,z1),join(z2,z3),meet(z2,z3)),meet(join(z2,z3),meet(z2,z3))) = join(upme(meet(a,z1),z2,z3),meet(z2,z3)),
inference(symmetry,[status(thm)],[410]) ).
tff(412,plain,
( ~ ! [W: $i,Y1: $i,X1: $i] : ( join(upme(meet(a,X1),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1),Y1),W),join(meet(meet(a,X1),W),Y1)) )
| ( join(upme(meet(a,z1),join(z2,z3),meet(z2,z3)),meet(join(z2,z3),meet(z2,z3))) = meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(413,plain,
join(upme(meet(a,z1),join(z2,z3),meet(z2,z3)),meet(join(z2,z3),meet(z2,z3))) = meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),
inference(unit_resolution,[status(thm)],[412,107]) ).
tff(414,plain,
meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))) = join(upme(meet(a,z1),join(z2,z3),meet(z2,z3)),meet(join(z2,z3),meet(z2,z3))),
inference(symmetry,[status(thm)],[413]) ).
tff(415,plain,
meet(meet(a,z1),join(z2,z3)) = upme(meet(a,z1),z2,z3),
inference(symmetry,[status(thm)],[408]) ).
tff(416,plain,
join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)) = join(upme(meet(a,z1),z2,z3),meet(z2,z3)),
inference(monotonicity,[status(thm)],[415]) ).
tff(417,plain,
join(upme(meet(a,z1),z2,z3),meet(z2,z3)) = join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),
inference(symmetry,[status(thm)],[416]) ).
tff(418,plain,
meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))) = join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),
inference(transitivity,[status(thm)],[414,411,417]) ).
tff(419,plain,
meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))) = meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),
inference(monotonicity,[status(thm)],[418]) ).
tff(420,plain,
meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))) = meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)),
inference(transitivity,[status(thm)],[419,414,411,372]) ).
tff(421,plain,
meet(meet(z1,a),meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)))) = meet(meet(z1,a),meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2))),
inference(monotonicity,[status(thm)],[420]) ).
tff(422,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(z1,a),meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)))) = meet(meet(meet(z1,a),meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)))),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(423,plain,
meet(meet(z1,a),meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)))) = meet(meet(meet(z1,a),meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)))),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),
inference(unit_resolution,[status(thm)],[422,37]) ).
tff(424,plain,
meet(meet(meet(z1,a),meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)))),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))) = meet(meet(z1,a),meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)))),
inference(symmetry,[status(thm)],[423]) ).
tff(425,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,join(Y,Z)) = join(join(X,Y),Z) )
| ( join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)) = join(join(meet(meet(a,z1),meet(z2,z3)),z2),z3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(426,plain,
join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)) = join(join(meet(meet(a,z1),meet(z2,z3)),z2),z3),
inference(unit_resolution,[status(thm)],[425,70]) ).
tff(427,plain,
join(join(meet(meet(a,z1),meet(z2,z3)),z2),z3) = join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
join(meet(meet(a,z1),meet(z2,z3)),z2) = join(meet(meet(z1,a),meet(z3,z2)),z2),
inference(monotonicity,[status(thm)],[122]) ).
tff(429,plain,
join(meet(meet(a,z1),meet(z2,z3)),z2) = z2,
inference(transitivity,[status(thm)],[428,324,321,316]) ).
tff(430,plain,
join(join(meet(meet(a,z1),meet(z2,z3)),z2),z3) = join(z2,z3),
inference(monotonicity,[status(thm)],[429]) ).
tff(431,plain,
join(z2,z3) = join(join(meet(meet(a,z1),meet(z2,z3)),z2),z3),
inference(symmetry,[status(thm)],[430]) ).
tff(432,plain,
join(z3,z2) = join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)),
inference(transitivity,[status(thm)],[381,431,427]) ).
tff(433,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(z1,a),meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)))) = meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),meet(z1,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(434,plain,
meet(meet(z1,a),meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)))) = meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),meet(z1,a)),
inference(unit_resolution,[status(thm)],[433,26]) ).
tff(435,plain,
meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),meet(z1,a)) = meet(meet(z1,a),meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)))),
inference(symmetry,[status(thm)],[434]) ).
tff(436,plain,
meet(meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),meet(z1,a)),join(z3,z2)) = meet(meet(meet(z1,a),meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3)))),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),
inference(monotonicity,[status(thm)],[435,432]) ).
tff(437,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,meet(Y,Z)) = meet(meet(X,Y),Z) )
| ( meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),meet(meet(z1,a),join(z3,z2))) = meet(meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),meet(z1,a)),join(z3,z2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(438,plain,
meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),meet(meet(z1,a),join(z3,z2))) = meet(meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),meet(z1,a)),join(z3,z2)),
inference(unit_resolution,[status(thm)],[437,37]) ).
tff(439,plain,
meet(meet(z1,a),join(z3,z2)) = meet(meet(a,z1),join(z2,z3)),
inference(monotonicity,[status(thm)],[29,381]) ).
tff(440,plain,
meet(meet(a,z1),join(z2,z3)) = meet(meet(z1,a),join(z3,z2)),
inference(symmetry,[status(thm)],[439]) ).
tff(441,plain,
meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)) = join(upme(meet(a,z1),z2,z3),meet(z2,z3)),
inference(symmetry,[status(thm)],[372]) ).
tff(442,plain,
meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)) = meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),
inference(transitivity,[status(thm)],[441,410,413]) ).
tff(443,plain,
meet(meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)),meet(meet(a,z1),join(z2,z3))) = meet(meet(join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)),join(meet(meet(a,z1),meet(z2,z3)),join(z2,z3))),meet(meet(z1,a),join(z3,z2))),
inference(monotonicity,[status(thm)],[442,440]) ).
tff(444,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(meet(a,z1),join(z2,z3)),meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2))) = meet(meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)),meet(meet(a,z1),join(z2,z3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(445,plain,
meet(meet(meet(a,z1),join(z2,z3)),meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2))) = meet(meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)),meet(meet(a,z1),join(z2,z3))),
inference(unit_resolution,[status(thm)],[444,26]) ).
tff(446,plain,
join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3)) = meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2)),
inference(transitivity,[status(thm)],[416,372]) ).
tff(447,plain,
meet(meet(meet(a,z1),join(z2,z3)),join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3))) = meet(meet(meet(a,z1),join(z2,z3)),meet(join(meet(meet(a,z1),z2),z3),join(meet(meet(a,z1),z3),z2))),
inference(monotonicity,[status(thm)],[446]) ).
tff(448,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(meet(a,z1),join(z2,z3)),join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3))) = meet(meet(a,z1),join(z2,z3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(449,plain,
meet(meet(meet(a,z1),join(z2,z3)),join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3))) = meet(meet(a,z1),join(z2,z3)),
inference(unit_resolution,[status(thm)],[448,17]) ).
tff(450,plain,
meet(meet(a,z1),join(z2,z3)) = meet(meet(meet(a,z1),join(z2,z3)),join(meet(meet(a,z1),join(z2,z3)),meet(z2,z3))),
inference(symmetry,[status(thm)],[449]) ).
tff(451,plain,
upme(meet(a,z1),z2,z3) = lome(meet(a,z1),z2,z3),
inference(transitivity,[status(thm)],[408,450,447,445,443,438,436,424,421,370,364,362,210,110,100,10]) ).
tff(452,plain,
( ( upme(meet(a,z1),z2,z3) != lome(meet(a,z1),z2,z3) )
<=> ( upme(meet(a,z1),z2,z3) != lome(meet(a,z1),z2,z3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(453,axiom,
upme(meet(a,z1),z2,z3) != lome(meet(a,z1),z2,z3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
tff(454,plain,
upme(meet(a,z1),z2,z3) != lome(meet(a,z1),z2,z3),
inference(modus_ponens,[status(thm)],[453,452]) ).
tff(455,plain,
$false,
inference(unit_resolution,[status(thm)],[454,451]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT399-1 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 17:18:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.71/1.32 % SZS status Unsatisfiable
% 1.71/1.32 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------