TSTP Solution File: LAT009-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT009-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:31:42 EDT 2022
% Result : Unsatisfiable 71.35s 46.15s
% Output : Proof 71.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 175
% Syntax : Number of formulae : 831 ( 666 unt; 5 typ; 0 def)
% Number of atoms : 1004 ( 994 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 314 ( 145 ~; 141 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 503 ( 484 !; 0 ?; 503 :)
% Comments :
%------------------------------------------------------------------------------
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(5,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(a,c),meet(join(a,c),join(a,b))) = join(a,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
join(join(a,c),meet(join(a,c),join(a,b))) = join(a,c),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(14,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,c),join(a,b)) = meet(join(a,b),join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
meet(join(a,c),join(a,b)) = meet(join(a,b),join(a,c)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
meet(join(a,b),join(a,c)) = meet(join(a,c),join(a,b)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(21,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)],[20]) ).
tff(22,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(23,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(24,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,a) = join(a,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
join(c,a) = join(a,c),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
join(join(c,a),meet(join(a,b),join(a,c))) = join(join(a,c),meet(join(a,c),join(a,b))),
inference(monotonicity,[status(thm)],[28,19]) ).
tff(30,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(c,a),meet(join(a,b),join(a,c))) = join(c,join(a,meet(join(a,b),join(a,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
join(join(c,a),meet(join(a,b),join(a,c))) = join(c,join(a,meet(join(a,b),join(a,c)))),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
join(c,join(a,meet(join(a,b),join(a,c)))) = join(join(c,a),meet(join(a,b),join(a,c))),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
join(c,join(a,meet(join(a,b),join(a,c)))) = join(a,c),
inference(transitivity,[status(thm)],[39,29,9]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(a,b),meet(join(a,b),a)) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
join(join(a,b),meet(join(a,b),a)) = join(a,b),
inference(unit_resolution,[status(thm)],[41,7]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),a) = meet(a,join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
meet(join(a,b),a) = meet(a,join(a,b)),
inference(unit_resolution,[status(thm)],[43,16]) ).
tff(45,plain,
meet(a,join(a,b)) = meet(join(a,b),a),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(47,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)],[46]) ).
tff(48,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(49,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(50,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,b)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
meet(a,join(a,b)) = a,
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
a = meet(a,join(a,b)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
a = meet(join(a,b),a),
inference(transitivity,[status(thm)],[55,45]) ).
tff(57,plain,
join(join(a,b),a) = join(join(a,b),meet(join(a,b),a)),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(a,b),a) = join(a,join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
join(join(a,b),a) = join(a,join(a,b)),
inference(unit_resolution,[status(thm)],[58,26]) ).
tff(60,plain,
join(a,join(a,b)) = join(join(a,b),a),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(a,join(a,b)),meet(join(a,join(a,b)),c)) = join(a,join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
join(join(a,join(a,b)),meet(join(a,join(a,b)),c)) = join(a,join(a,b)),
inference(unit_resolution,[status(thm)],[61,7]) ).
tff(63,plain,
join(join(a,b),meet(join(a,b),a)) = join(join(a,b),a),
inference(symmetry,[status(thm)],[57]) ).
tff(64,plain,
join(a,b) = join(join(a,b),meet(join(a,b),a)),
inference(symmetry,[status(thm)],[42]) ).
tff(65,plain,
join(a,b) = join(a,join(a,b)),
inference(transitivity,[status(thm)],[64,63,59]) ).
tff(66,plain,
join(join(a,b),meet(join(a,join(a,b)),c)) = join(join(a,join(a,b)),meet(join(a,join(a,b)),c)),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(a,b),meet(join(a,join(a,b)),c)) = join(meet(join(a,join(a,b)),c),join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
join(join(a,b),meet(join(a,join(a,b)),c)) = join(meet(join(a,join(a,b)),c),join(a,b)),
inference(unit_resolution,[status(thm)],[67,26]) ).
tff(69,plain,
join(meet(join(a,join(a,b)),c),join(a,b)) = join(join(a,b),meet(join(a,join(a,b)),c)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
meet(join(a,b),c) = meet(join(a,join(a,b)),c),
inference(monotonicity,[status(thm)],[65]) ).
tff(71,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(a,b),meet(join(a,b),join(a,c))) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
join(join(a,b),meet(join(a,b),join(a,c))) = join(a,b),
inference(unit_resolution,[status(thm)],[71,7]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,b),join(a,c)),join(a,b)) = join(join(a,b),meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
join(meet(join(a,b),join(a,c)),join(a,b)) = join(join(a,b),meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[73,26]) ).
tff(75,plain,
join(meet(join(a,b),join(a,c)),join(a,b)) = join(a,b),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
join(a,join(meet(join(a,b),join(a,c)),join(a,b))) = join(a,join(a,b)),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(a,meet(join(a,b),join(a,c))),join(a,b)) = join(a,join(meet(join(a,b),join(a,c)),join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
join(join(a,meet(join(a,b),join(a,c))),join(a,b)) = join(a,join(meet(join(a,b),join(a,c)),join(a,b))),
inference(unit_resolution,[status(thm)],[77,36]) ).
tff(79,plain,
join(join(a,meet(join(a,b),join(a,c))),join(a,b)) = join(a,b),
inference(transitivity,[status(thm)],[78,76,60,57,42]) ).
tff(80,plain,
meet(join(join(a,meet(join(a,b),join(a,c))),join(a,b)),c) = meet(join(a,b),c),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
meet(join(join(a,meet(join(a,b),join(a,c))),join(a,b)),c) = meet(join(a,join(a,b)),c),
inference(transitivity,[status(thm)],[80,70]) ).
tff(82,plain,
join(meet(join(join(a,meet(join(a,b),join(a,c))),join(a,b)),c),join(a,b)) = join(meet(join(a,join(a,b)),c),join(a,b)),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
join(meet(join(join(a,meet(join(a,b),join(a,c))),join(a,b)),c),join(a,b)) = join(a,b),
inference(transitivity,[status(thm)],[82,69,66,62,60,57,42]) ).
tff(84,plain,
meet(join(meet(join(join(a,meet(join(a,b),join(a,c))),join(a,b)),c),join(a,b)),join(c,join(a,meet(join(a,b),join(a,c))))) = meet(join(a,b),join(a,c)),
inference(monotonicity,[status(thm)],[83,40]) ).
tff(85,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
<=> ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_dual) ).
tff(89,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(join(a,meet(join(a,b),join(a,c))),join(a,b)),c),join(a,b)),meet(c,join(a,meet(join(a,b),join(a,c))))) = meet(join(meet(join(join(a,meet(join(a,b),join(a,c))),join(a,b)),c),join(a,b)),join(c,join(a,meet(join(a,b),join(a,c))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
join(meet(join(meet(join(a,meet(join(a,b),join(a,c))),join(a,b)),c),join(a,b)),meet(c,join(a,meet(join(a,b),join(a,c))))) = meet(join(meet(join(join(a,meet(join(a,b),join(a,c))),join(a,b)),c),join(a,b)),join(c,join(a,meet(join(a,b),join(a,c))))),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(join(a,b),join(a,c)),meet(meet(join(a,b),join(a,c)),a)) = meet(join(a,b),join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
join(meet(join(a,b),join(a,c)),meet(meet(join(a,b),join(a,c)),a)) = meet(join(a,b),join(a,c)),
inference(unit_resolution,[status(thm)],[94,7]) ).
tff(96,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(join(a,b),join(a,c)),a) = meet(a,meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
meet(meet(join(a,b),join(a,c)),a) = meet(a,meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[96,16]) ).
tff(98,plain,
meet(a,meet(join(a,b),join(a,c))) = meet(meet(join(a,b),join(a,c)),a),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
tff(103,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,join(a,b)),join(a,c)) = meet(a,meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
meet(meet(a,join(a,b)),join(a,c)) = meet(a,meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
meet(meet(a,join(a,b)),join(a,c)) = meet(a,join(a,c)),
inference(monotonicity,[status(thm)],[54]) ).
tff(109,plain,
meet(a,join(a,c)) = meet(meet(a,join(a,b)),join(a,c)),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,c)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
meet(a,join(a,c)) = a,
inference(unit_resolution,[status(thm)],[110,52]) ).
tff(112,plain,
a = meet(a,join(a,c)),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
a = meet(meet(join(a,b),join(a,c)),a),
inference(transitivity,[status(thm)],[112,109,107,98]) ).
tff(114,plain,
join(meet(join(a,b),join(a,c)),a) = join(meet(join(a,b),join(a,c)),meet(meet(join(a,b),join(a,c)),a)),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,b),join(a,c)),a) = join(a,meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
join(meet(join(a,b),join(a,c)),a) = join(a,meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[115,26]) ).
tff(117,plain,
join(a,meet(join(a,b),join(a,c))) = join(meet(join(a,b),join(a,c)),a),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
join(a,meet(join(a,b),join(a,c))) = meet(join(a,b),join(a,c)),
inference(transitivity,[status(thm)],[117,114,95]) ).
tff(119,plain,
meet(c,join(a,meet(join(a,b),join(a,c)))) = meet(c,meet(join(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
meet(c,meet(join(a,b),join(a,c))) = meet(c,join(a,meet(join(a,b),join(a,c)))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
meet(c,meet(join(a,b),join(a,c))) = meet(c,meet(join(a,c),join(a,b))),
inference(monotonicity,[status(thm)],[19]) ).
tff(122,plain,
meet(c,meet(join(a,c),join(a,b))) = meet(c,meet(join(a,b),join(a,c))),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(c,join(a,c)),join(a,b)) = meet(c,meet(join(a,c),join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
meet(meet(c,join(a,c)),join(a,b)) = meet(c,meet(join(a,c),join(a,b))),
inference(unit_resolution,[status(thm)],[123,105]) ).
tff(125,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(c,join(c,a)) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
meet(c,join(c,a)) = c,
inference(unit_resolution,[status(thm)],[125,52]) ).
tff(127,plain,
join(a,c) = join(c,a),
inference(symmetry,[status(thm)],[28]) ).
tff(128,plain,
meet(c,join(a,c)) = meet(c,join(c,a)),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
meet(c,join(a,c)) = c,
inference(transitivity,[status(thm)],[128,126]) ).
tff(130,plain,
meet(meet(c,join(a,c)),join(a,b)) = meet(c,join(a,b)),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
meet(c,join(a,b)) = meet(meet(c,join(a,c)),join(a,b)),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
meet(c,join(a,b)) = meet(c,join(a,join(a,b))),
inference(monotonicity,[status(thm)],[65]) ).
tff(133,plain,
meet(c,join(a,join(a,b))) = meet(c,join(a,b)),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,join(a,join(a,b))) = meet(join(a,join(a,b)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
meet(c,join(a,join(a,b))) = meet(join(a,join(a,b)),c),
inference(unit_resolution,[status(thm)],[134,16]) ).
tff(136,plain,
meet(join(a,join(a,b)),c) = meet(c,join(a,join(a,b))),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
meet(join(a,join(a,b)),c) = meet(c,join(a,meet(join(a,b),join(a,c)))),
inference(transitivity,[status(thm)],[136,133,131,124,122,120]) ).
tff(138,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(a,meet(join(a,b),join(a,c))),c) = join(c,join(a,meet(join(a,b),join(a,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
join(join(a,meet(join(a,b),join(a,c))),c) = join(c,join(a,meet(join(a,b),join(a,c)))),
inference(unit_resolution,[status(thm)],[138,26]) ).
tff(140,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(join(a,meet(join(a,b),join(a,c))),join(join(a,meet(join(a,b),join(a,c))),join(a,b))) = join(a,meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
meet(join(a,meet(join(a,b),join(a,c))),join(join(a,meet(join(a,b),join(a,c))),join(a,b))) = join(a,meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[140,52]) ).
tff(142,plain,
join(a,join(meet(join(a,b),join(a,c)),join(a,b))) = join(join(a,meet(join(a,b),join(a,c))),join(a,b)),
inference(symmetry,[status(thm)],[78]) ).
tff(143,plain,
join(a,join(a,b)) = join(a,join(meet(join(a,b),join(a,c)),join(a,b))),
inference(symmetry,[status(thm)],[76]) ).
tff(144,plain,
join(a,join(a,b)) = join(join(a,meet(join(a,b),join(a,c))),join(a,b)),
inference(transitivity,[status(thm)],[143,142]) ).
tff(145,plain,
meet(join(join(a,b),meet(join(a,b),join(a,c))),a) = meet(join(a,b),a),
inference(monotonicity,[status(thm)],[72]) ).
tff(146,plain,
meet(join(join(a,b),meet(join(a,b),join(a,c))),a) = a,
inference(transitivity,[status(thm)],[145,44,54]) ).
tff(147,plain,
join(meet(join(join(a,b),meet(join(a,b),join(a,c))),a),meet(join(a,b),join(a,c))) = join(a,meet(join(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
meet(join(meet(join(join(a,b),meet(join(a,b),join(a,c))),a),meet(join(a,b),join(a,c))),join(a,join(a,b))) = meet(join(a,meet(join(a,b),join(a,c))),join(join(a,meet(join(a,b),join(a,c))),join(a,b))),
inference(monotonicity,[status(thm)],[147,144]) ).
tff(149,plain,
join(a,meet(join(a,b),join(a,c))) = join(meet(join(join(a,b),meet(join(a,b),join(a,c))),a),meet(join(a,b),join(a,c))),
inference(symmetry,[status(thm)],[147]) ).
tff(150,plain,
meet(join(a,meet(join(a,b),join(a,c))),join(a,b)) = meet(join(meet(join(join(a,b),meet(join(a,b),join(a,c))),a),meet(join(a,b),join(a,c))),join(a,join(a,b))),
inference(monotonicity,[status(thm)],[149,65]) ).
tff(151,plain,
meet(join(a,meet(join(a,b),join(a,c))),join(a,b)) = join(a,meet(join(a,b),join(a,c))),
inference(transitivity,[status(thm)],[150,148,141]) ).
tff(152,plain,
join(meet(join(a,meet(join(a,b),join(a,c))),join(a,b)),c) = join(join(a,meet(join(a,b),join(a,c))),c),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
join(meet(join(a,meet(join(a,b),join(a,c))),join(a,b)),c) = join(a,c),
inference(transitivity,[status(thm)],[152,139,39,29,9]) ).
tff(154,plain,
meet(join(meet(join(a,meet(join(a,b),join(a,c))),join(a,b)),c),join(a,b)) = meet(join(a,c),join(a,b)),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
meet(join(a,c),join(a,b)) = meet(join(meet(join(a,meet(join(a,b),join(a,c))),join(a,b)),c),join(a,b)),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
meet(join(a,b),join(a,c)) = meet(join(meet(join(a,meet(join(a,b),join(a,c))),join(a,b)),c),join(a,b)),
inference(transitivity,[status(thm)],[19,155]) ).
tff(157,plain,
join(meet(join(a,b),join(a,c)),meet(join(a,join(a,b)),c)) = join(meet(join(meet(join(a,meet(join(a,b),join(a,c))),join(a,b)),c),join(a,b)),meet(c,join(a,meet(join(a,b),join(a,c))))),
inference(monotonicity,[status(thm)],[156,137]) ).
tff(158,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,b),join(a,c)),meet(join(a,join(a,b)),c)) = join(meet(join(a,join(a,b)),c),meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
join(meet(join(a,b),join(a,c)),meet(join(a,join(a,b)),c)) = join(meet(join(a,join(a,b)),c),meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[158,26]) ).
tff(160,plain,
join(meet(join(a,join(a,b)),c),meet(join(a,b),join(a,c))) = join(meet(join(a,b),join(a,c)),meet(join(a,join(a,b)),c)),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
join(join(a,c),meet(join(a,b),join(a,c))) = join(join(a,c),meet(join(a,c),join(a,b))),
inference(monotonicity,[status(thm)],[19]) ).
tff(162,plain,
join(join(a,c),meet(join(a,b),join(a,c))) = join(a,c),
inference(transitivity,[status(thm)],[161,9]) ).
tff(163,plain,
meet(join(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)) = meet(join(a,b),join(a,c)),
inference(monotonicity,[status(thm)],[75]) ).
tff(164,plain,
join(meet(join(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)),join(a,b)) = join(meet(join(a,b),join(a,c)),join(a,b)),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
join(meet(join(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)),join(a,b)) = join(a,b),
inference(transitivity,[status(thm)],[164,74,72]) ).
tff(166,plain,
meet(join(meet(join(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)),join(a,b)),join(join(a,c),meet(join(a,b),join(a,c)))) = meet(join(a,b),join(a,c)),
inference(monotonicity,[status(thm)],[165,162]) ).
tff(167,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)),join(a,b)),meet(join(a,c),meet(join(a,b),join(a,c)))) = meet(join(meet(join(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)),join(a,b)),join(join(a,c),meet(join(a,b),join(a,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
join(meet(join(meet(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)),join(a,b)),meet(join(a,c),meet(join(a,b),join(a,c)))) = meet(join(meet(join(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)),join(a,b)),join(join(a,c),meet(join(a,b),join(a,c)))),
inference(unit_resolution,[status(thm)],[167,91]) ).
tff(169,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,b),join(a,c)),join(a,c)) = join(join(a,c),meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
join(meet(join(a,b),join(a,c)),join(a,c)) = join(join(a,c),meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[169,26]) ).
tff(171,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(join(a,b),join(a,c)),join(meet(join(a,b),join(a,c)),join(a,b))) = meet(join(a,b),join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(172,plain,
meet(meet(join(a,b),join(a,c)),join(meet(join(a,b),join(a,c)),join(a,b))) = meet(join(a,b),join(a,c)),
inference(unit_resolution,[status(thm)],[171,52]) ).
tff(173,plain,
join(join(a,b),meet(join(a,b),join(a,c))) = join(meet(join(a,b),join(a,c)),join(a,b)),
inference(symmetry,[status(thm)],[74]) ).
tff(174,plain,
join(a,b) = join(join(a,b),meet(join(a,b),join(a,c))),
inference(symmetry,[status(thm)],[72]) ).
tff(175,plain,
join(a,b) = join(meet(join(a,b),join(a,c)),join(a,b)),
inference(transitivity,[status(thm)],[174,173]) ).
tff(176,plain,
meet(meet(join(a,b),join(a,c)),join(a,b)) = meet(meet(join(a,b),join(a,c)),join(meet(join(a,b),join(a,c)),join(a,b))),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
meet(meet(join(a,b),join(a,c)),join(a,b)) = meet(join(a,b),join(a,c)),
inference(transitivity,[status(thm)],[176,172]) ).
tff(178,plain,
join(meet(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)) = join(meet(join(a,b),join(a,c)),join(a,c)),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
join(meet(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)) = join(a,c),
inference(transitivity,[status(thm)],[178,170,161,9]) ).
tff(180,plain,
meet(join(meet(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)),join(a,b)) = meet(join(a,c),join(a,b)),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
meet(join(a,c),join(a,b)) = meet(join(meet(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)),join(a,b)),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
meet(join(a,b),join(a,c)) = meet(join(meet(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)),join(a,b)),
inference(transitivity,[status(thm)],[19,181]) ).
tff(183,plain,
join(meet(join(a,b),join(a,c)),meet(join(a,c),meet(join(a,b),join(a,c)))) = join(meet(join(meet(meet(join(a,b),join(a,c)),join(a,b)),join(a,c)),join(a,b)),meet(join(a,c),meet(join(a,b),join(a,c)))),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,b),join(a,c)),meet(join(a,c),meet(join(a,b),join(a,c)))) = join(meet(join(a,c),meet(join(a,b),join(a,c))),meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
join(meet(join(a,b),join(a,c)),meet(join(a,c),meet(join(a,b),join(a,c)))) = join(meet(join(a,c),meet(join(a,b),join(a,c))),meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[184,26]) ).
tff(186,plain,
join(meet(join(a,c),meet(join(a,b),join(a,c))),meet(join(a,b),join(a,c))) = join(meet(join(a,b),join(a,c)),meet(join(a,c),meet(join(a,b),join(a,c)))),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(join(a,b),join(join(a,b),meet(join(a,b),join(a,c)))) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
meet(join(a,b),join(join(a,b),meet(join(a,b),join(a,c)))) = join(a,b),
inference(unit_resolution,[status(thm)],[187,52]) ).
tff(189,plain,
meet(join(a,b),join(a,b)) = meet(join(a,b),join(join(a,b),meet(join(a,b),join(a,c)))),
inference(monotonicity,[status(thm)],[174]) ).
tff(190,plain,
meet(join(a,b),join(a,b)) = join(a,b),
inference(transitivity,[status(thm)],[189,188]) ).
tff(191,plain,
meet(meet(join(a,b),join(a,b)),join(a,c)) = meet(join(a,b),join(a,c)),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,b),join(a,b)),join(a,c)) = meet(join(a,b),meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(193,plain,
meet(meet(join(a,b),join(a,b)),join(a,c)) = meet(join(a,b),meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[192,105]) ).
tff(194,plain,
meet(join(a,b),meet(join(a,b),join(a,c))) = meet(meet(join(a,b),join(a,b)),join(a,c)),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
meet(join(a,b),meet(join(a,b),join(a,c))) = meet(join(a,b),join(a,c)),
inference(transitivity,[status(thm)],[194,191]) ).
tff(196,plain,
join(meet(join(a,b),meet(join(a,b),join(a,c))),join(a,c)) = join(meet(join(a,b),join(a,c)),join(a,c)),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
join(meet(join(a,b),meet(join(a,b),join(a,c))),join(a,c)) = join(a,c),
inference(transitivity,[status(thm)],[196,170,161,9]) ).
tff(198,plain,
meet(join(meet(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))) = meet(join(a,c),meet(join(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
join(meet(join(meet(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))),meet(join(a,c),join(a,b))) = join(meet(join(a,c),meet(join(a,b),join(a,c))),meet(join(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[198,18]) ).
tff(200,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))),meet(join(a,c),join(a,b))) = meet(join(meet(join(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))),join(join(a,c),join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(201,plain,
join(meet(join(meet(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))),meet(join(a,c),join(a,b))) = meet(join(meet(join(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))),join(join(a,c),join(a,b))),
inference(unit_resolution,[status(thm)],[200,91]) ).
tff(202,plain,
meet(join(meet(join(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))),join(join(a,c),join(a,b))) = join(meet(join(meet(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))),meet(join(a,c),join(a,b))),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(a,c),a),b) = join(join(a,c),join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
join(join(join(a,c),a),b) = join(join(a,c),join(a,b)),
inference(unit_resolution,[status(thm)],[203,36]) ).
tff(205,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,c),a) = meet(a,join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(206,plain,
meet(join(a,c),a) = meet(a,join(a,c)),
inference(unit_resolution,[status(thm)],[205,16]) ).
tff(207,plain,
meet(a,join(a,c)) = meet(join(a,c),a),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
a = meet(join(a,c),a),
inference(transitivity,[status(thm)],[112,207]) ).
tff(209,plain,
join(join(a,c),a) = join(join(a,c),meet(join(a,c),a)),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,plain,
join(join(a,c),meet(join(a,c),a)) = join(join(a,c),a),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(a,c),meet(join(a,c),a)) = join(a,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(212,plain,
join(join(a,c),meet(join(a,c),a)) = join(a,c),
inference(unit_resolution,[status(thm)],[211,7]) ).
tff(213,plain,
join(a,c) = join(join(a,c),meet(join(a,c),a)),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
join(a,c) = join(join(a,c),a),
inference(transitivity,[status(thm)],[213,210]) ).
tff(215,plain,
join(join(a,c),b) = join(join(join(a,c),a),b),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
join(join(a,c),b) = join(join(a,c),join(a,b)),
inference(transitivity,[status(thm)],[215,204]) ).
tff(217,plain,
meet(join(join(a,b),meet(join(a,b),join(a,c))),join(a,c)) = meet(join(a,b),join(a,c)),
inference(monotonicity,[status(thm)],[72]) ).
tff(218,plain,
join(meet(join(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))) = join(meet(join(a,b),join(a,c)),meet(join(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
join(meet(join(a,b),join(a,c)),meet(join(a,b),join(a,c))) = join(meet(join(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
^ [X: $i] :
refl(
( ( join(X,X) = X )
<=> ( join(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(221,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(quant_intro,[status(thm)],[220]) ).
tff(222,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(223,axiom,
! [X: $i] : ( join(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
tff(224,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
! [X: $i] : ( join(X,X) = X ),
inference(skolemize,[status(sab)],[224]) ).
tff(226,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[225,221]) ).
tff(227,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(join(a,b),join(a,c)),meet(join(a,b),join(a,c))) = meet(join(a,b),join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
join(meet(join(a,b),join(a,c)),meet(join(a,b),join(a,c))) = meet(join(a,b),join(a,c)),
inference(unit_resolution,[status(thm)],[227,226]) ).
tff(229,plain,
meet(join(a,b),join(a,c)) = join(meet(join(a,b),join(a,c)),meet(join(a,b),join(a,c))),
inference(symmetry,[status(thm)],[228]) ).
tff(230,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,a) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(231,plain,
join(b,a) = join(a,b),
inference(unit_resolution,[status(thm)],[230,26]) ).
tff(232,plain,
meet(join(b,a),join(a,c)) = meet(join(a,b),join(a,c)),
inference(monotonicity,[status(thm)],[231]) ).
tff(233,plain,
join(meet(join(b,a),join(a,c)),a) = join(meet(join(a,b),join(a,c)),a),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
join(meet(join(b,a),join(a,c)),a) = join(meet(join(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))),
inference(transitivity,[status(thm)],[233,114,95,229,219]) ).
tff(235,plain,
meet(join(meet(join(b,a),join(a,c)),a),join(join(a,c),b)) = meet(join(meet(join(join(a,b),meet(join(a,b),join(a,c))),join(a,c)),meet(join(a,b),join(a,c))),join(join(a,c),join(a,b))),
inference(monotonicity,[status(thm)],[234,216]) ).
tff(236,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(b,a),join(a,c)),a),meet(join(a,c),b)) = meet(join(meet(join(b,a),join(a,c)),a),join(join(a,c),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(237,plain,
join(meet(join(meet(b,a),join(a,c)),a),meet(join(a,c),b)) = meet(join(meet(join(b,a),join(a,c)),a),join(join(a,c),b)),
inference(unit_resolution,[status(thm)],[236,91]) ).
tff(238,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(a,c),a) = join(a,join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(239,plain,
join(join(a,c),a) = join(a,join(a,c)),
inference(unit_resolution,[status(thm)],[238,26]) ).
tff(240,plain,
join(a,c) = join(a,join(a,c)),
inference(transitivity,[status(thm)],[213,210,239]) ).
tff(241,plain,
meet(join(a,c),b) = meet(join(a,join(a,c)),b),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
meet(join(a,join(a,c)),b) = meet(join(a,c),b),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,join(a,join(a,c))) = meet(join(a,join(a,c)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(244,plain,
meet(b,join(a,join(a,c))) = meet(join(a,join(a,c)),b),
inference(unit_resolution,[status(thm)],[243,16]) ).
tff(245,plain,
meet(b,join(a,c)) = meet(b,join(a,join(a,c))),
inference(monotonicity,[status(thm)],[240]) ).
tff(246,plain,
meet(b,join(a,c)) = meet(join(a,c),b),
inference(transitivity,[status(thm)],[245,244,242]) ).
tff(247,plain,
join(a,join(a,c)) = join(join(a,c),a),
inference(symmetry,[status(thm)],[239]) ).
tff(248,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(a,join(a,c)),meet(join(a,join(a,c)),b)) = join(a,join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(249,plain,
join(join(a,join(a,c)),meet(join(a,join(a,c)),b)) = join(a,join(a,c)),
inference(unit_resolution,[status(thm)],[248,7]) ).
tff(250,plain,
join(join(a,c),meet(join(a,join(a,c)),b)) = join(join(a,join(a,c)),meet(join(a,join(a,c)),b)),
inference(monotonicity,[status(thm)],[240]) ).
tff(251,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(a,c),meet(join(a,join(a,c)),b)) = join(meet(join(a,join(a,c)),b),join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(252,plain,
join(join(a,c),meet(join(a,join(a,c)),b)) = join(meet(join(a,join(a,c)),b),join(a,c)),
inference(unit_resolution,[status(thm)],[251,26]) ).
tff(253,plain,
join(meet(join(a,join(a,c)),b),join(a,c)) = join(join(a,c),meet(join(a,join(a,c)),b)),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
join(meet(join(a,join(a,c)),b),join(a,c)) = join(a,c),
inference(transitivity,[status(thm)],[253,250,249,247,209,212]) ).
tff(255,plain,
meet(join(meet(join(a,join(a,c)),b),join(a,c)),join(b,a)) = meet(join(a,c),join(a,b)),
inference(monotonicity,[status(thm)],[254,231]) ).
tff(256,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(a,join(a,c)),b),join(a,c)),meet(b,a)) = meet(join(meet(join(a,join(a,c)),b),join(a,c)),join(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(257,plain,
join(meet(join(meet(a,join(a,c)),b),join(a,c)),meet(b,a)) = meet(join(meet(join(a,join(a,c)),b),join(a,c)),join(b,a)),
inference(unit_resolution,[status(thm)],[256,91]) ).
tff(258,plain,
join(meet(a,join(a,c)),b) = join(a,b),
inference(monotonicity,[status(thm)],[111]) ).
tff(259,plain,
meet(join(meet(a,join(a,c)),b),join(a,c)) = meet(join(a,b),join(a,c)),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
meet(join(a,b),join(a,c)) = meet(join(meet(a,join(a,c)),b),join(a,c)),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
join(meet(join(a,b),join(a,c)),meet(b,a)) = join(meet(join(meet(a,join(a,c)),b),join(a,c)),meet(b,a)),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,a),meet(join(a,b),join(a,c))) = join(meet(join(a,b),join(a,c)),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
join(meet(b,a),meet(join(a,b),join(a,c))) = join(meet(join(a,b),join(a,c)),meet(b,a)),
inference(unit_resolution,[status(thm)],[262,26]) ).
tff(264,plain,
join(meet(b,a),meet(join(a,b),join(a,c))) = meet(join(a,b),join(a,c)),
inference(transitivity,[status(thm)],[263,261,257,255,18]) ).
tff(265,plain,
join(join(meet(b,a),meet(join(a,b),join(a,c))),join(a,c)) = join(meet(join(a,b),join(a,c)),join(a,c)),
inference(monotonicity,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(b,a),meet(join(a,b),join(a,c))),join(a,c)) = join(meet(b,a),join(meet(join(a,b),join(a,c)),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(267,plain,
join(join(meet(b,a),meet(join(a,b),join(a,c))),join(a,c)) = join(meet(b,a),join(meet(join(a,b),join(a,c)),join(a,c))),
inference(unit_resolution,[status(thm)],[266,36]) ).
tff(268,plain,
join(meet(b,a),join(meet(join(a,b),join(a,c)),join(a,c))) = join(join(meet(b,a),meet(join(a,b),join(a,c))),join(a,c)),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
join(join(a,c),meet(join(a,b),join(a,c))) = join(meet(join(a,b),join(a,c)),join(a,c)),
inference(symmetry,[status(thm)],[170]) ).
tff(270,plain,
join(join(a,c),meet(join(a,c),join(a,b))) = join(join(a,c),meet(join(a,b),join(a,c))),
inference(symmetry,[status(thm)],[161]) ).
tff(271,plain,
join(a,c) = join(join(a,c),meet(join(a,c),join(a,b))),
inference(symmetry,[status(thm)],[9]) ).
tff(272,plain,
join(a,c) = join(meet(join(a,b),join(a,c)),join(a,c)),
inference(transitivity,[status(thm)],[271,270,269]) ).
tff(273,plain,
join(meet(b,a),join(a,c)) = join(meet(b,a),join(meet(join(a,b),join(a,c)),join(a,c))),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
join(meet(b,a),join(a,c)) = join(a,c),
inference(transitivity,[status(thm)],[273,268,265,170,161,9]) ).
tff(275,plain,
meet(join(meet(b,a),join(a,c)),a) = meet(join(a,c),a),
inference(monotonicity,[status(thm)],[274]) ).
tff(276,plain,
meet(join(a,c),a) = meet(join(meet(b,a),join(a,c)),a),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
meet(join(a,c),a) = a,
inference(transitivity,[status(thm)],[206,111]) ).
tff(278,plain,
join(meet(join(a,c),a),b) = join(a,b),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
meet(join(meet(join(a,c),a),b),a) = meet(join(a,b),a),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
meet(join(meet(join(a,c),a),b),a) = meet(join(meet(b,a),join(a,c)),a),
inference(transitivity,[status(thm)],[279,44,54,112,207,276]) ).
tff(281,plain,
join(meet(join(meet(join(a,c),a),b),a),meet(b,join(a,c))) = join(meet(join(meet(b,a),join(a,c)),a),meet(join(a,c),b)),
inference(monotonicity,[status(thm)],[280,246]) ).
tff(282,plain,
meet(b,join(a,join(a,c))) = meet(b,join(a,c)),
inference(symmetry,[status(thm)],[245]) ).
tff(283,plain,
meet(join(a,join(a,c)),b) = meet(b,join(a,join(a,c))),
inference(symmetry,[status(thm)],[244]) ).
tff(284,plain,
meet(join(a,join(a,c)),b) = meet(b,join(a,c)),
inference(transitivity,[status(thm)],[283,282]) ).
tff(285,plain,
meet(join(a,b),a) = meet(join(meet(join(a,c),a),b),a),
inference(symmetry,[status(thm)],[279]) ).
tff(286,plain,
a = meet(join(meet(join(a,c),a),b),a),
inference(transitivity,[status(thm)],[55,45,285]) ).
tff(287,plain,
join(a,meet(join(a,join(a,c)),b)) = join(meet(join(meet(join(a,c),a),b),a),meet(b,join(a,c))),
inference(monotonicity,[status(thm)],[286,284]) ).
tff(288,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,meet(join(a,join(a,c)),b)) = join(meet(join(a,join(a,c)),b),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(289,plain,
join(a,meet(join(a,join(a,c)),b)) = join(meet(join(a,join(a,c)),b),a),
inference(unit_resolution,[status(thm)],[288,26]) ).
tff(290,plain,
join(meet(join(a,join(a,c)),b),a) = join(a,meet(join(a,join(a,c)),b)),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
join(meet(join(a,join(a,c)),b),a) = meet(join(a,b),join(a,c)),
inference(transitivity,[status(thm)],[290,287,281,237,235,202,199,186,183,168,166]) ).
tff(292,plain,
join(meet(join(a,join(a,b)),c),join(meet(join(a,join(a,c)),b),a)) = join(meet(join(a,join(a,b)),c),meet(join(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[291]) ).
tff(293,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,join(a,b)),c),meet(join(a,join(a,c)),b)),a) = join(meet(join(a,join(a,b)),c),join(meet(join(a,join(a,c)),b),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(294,plain,
join(join(meet(join(a,join(a,b)),c),meet(join(a,join(a,c)),b)),a) = join(meet(join(a,join(a,b)),c),join(meet(join(a,join(a,c)),b),a)),
inference(unit_resolution,[status(thm)],[293,36]) ).
tff(295,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(b,join(b,a)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(296,plain,
meet(b,join(b,a)) = b,
inference(unit_resolution,[status(thm)],[295,52]) ).
tff(297,plain,
join(a,b) = join(b,a),
inference(symmetry,[status(thm)],[231]) ).
tff(298,plain,
meet(b,join(a,b)) = meet(b,join(b,a)),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),b) = meet(b,join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(300,plain,
meet(join(a,b),b) = meet(b,join(a,b)),
inference(unit_resolution,[status(thm)],[299,16]) ).
tff(301,plain,
meet(join(a,b),b) = b,
inference(transitivity,[status(thm)],[300,298,296]) ).
tff(302,plain,
meet(join(a,c),meet(join(a,b),b)) = meet(join(a,c),b),
inference(monotonicity,[status(thm)],[301]) ).
tff(303,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,c),join(a,b)),b) = meet(join(a,c),meet(join(a,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(304,plain,
meet(meet(join(a,c),join(a,b)),b) = meet(join(a,c),meet(join(a,b),b)),
inference(unit_resolution,[status(thm)],[303,105]) ).
tff(305,plain,
meet(meet(join(a,b),join(a,c)),b) = meet(meet(join(a,c),join(a,b)),b),
inference(monotonicity,[status(thm)],[19]) ).
tff(306,plain,
meet(join(a,meet(join(a,b),join(a,c))),b) = meet(meet(join(a,b),join(a,c)),b),
inference(monotonicity,[status(thm)],[118]) ).
tff(307,plain,
meet(join(a,meet(join(a,b),join(a,c))),b) = meet(join(a,join(a,c)),b),
inference(transitivity,[status(thm)],[306,305,304,302,241]) ).
tff(308,plain,
join(meet(join(a,join(a,b)),c),meet(join(a,meet(join(a,b),join(a,c))),b)) = join(meet(join(a,join(a,b)),c),meet(join(a,join(a,c)),b)),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
join(join(meet(join(a,join(a,b)),c),meet(join(a,meet(join(a,b),join(a,c))),b)),a) = join(join(meet(join(a,join(a,b)),c),meet(join(a,join(a,c)),b)),a),
inference(monotonicity,[status(thm)],[308]) ).
tff(310,plain,
meet(meet(join(a,b),join(a,c)),b) = meet(join(a,meet(join(a,b),join(a,c))),b),
inference(symmetry,[status(thm)],[306]) ).
tff(311,plain,
meet(meet(join(a,c),join(a,b)),b) = meet(meet(join(a,b),join(a,c)),b),
inference(symmetry,[status(thm)],[305]) ).
tff(312,plain,
meet(join(a,c),meet(join(a,b),b)) = meet(meet(join(a,c),join(a,b)),b),
inference(symmetry,[status(thm)],[304]) ).
tff(313,plain,
meet(join(a,c),b) = meet(join(a,c),meet(join(a,b),b)),
inference(symmetry,[status(thm)],[302]) ).
tff(314,plain,
meet(b,join(a,b)) = b,
inference(transitivity,[status(thm)],[298,296]) ).
tff(315,plain,
meet(meet(b,join(a,b)),join(a,c)) = meet(b,join(a,c)),
inference(monotonicity,[status(thm)],[314]) ).
tff(316,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(b,join(a,b)),join(a,c)) = meet(b,meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(317,plain,
meet(meet(b,join(a,b)),join(a,c)) = meet(b,meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[316,105]) ).
tff(318,plain,
meet(b,meet(join(a,b),join(a,c))) = meet(meet(b,join(a,b)),join(a,c)),
inference(symmetry,[status(thm)],[317]) ).
tff(319,plain,
meet(b,join(meet(join(a,join(a,c)),b),a)) = meet(b,meet(join(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[291]) ).
tff(320,plain,
meet(b,join(meet(join(a,join(a,c)),b),a)) = meet(join(a,meet(join(a,b),join(a,c))),b),
inference(transitivity,[status(thm)],[319,318,315,245,244,242,313,312,311,310]) ).
tff(321,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(join(a,join(a,b)),c),join(meet(join(a,join(a,b)),c),b)) = meet(join(a,join(a,b)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(322,plain,
meet(meet(join(a,join(a,b)),c),join(meet(join(a,join(a,b)),c),b)) = meet(join(a,join(a,b)),c),
inference(unit_resolution,[status(thm)],[321,52]) ).
tff(323,plain,
meet(c,join(a,b)) = meet(join(a,join(a,b)),c),
inference(transitivity,[status(thm)],[132,135]) ).
tff(324,plain,
meet(meet(c,join(a,b)),join(meet(join(a,join(a,b)),c),b)) = meet(meet(join(a,join(a,b)),c),join(meet(join(a,join(a,b)),c),b)),
inference(monotonicity,[status(thm)],[323]) ).
tff(325,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(c,join(a,b)),join(meet(join(a,join(a,b)),c),b)) = meet(c,meet(join(a,b),join(meet(join(a,join(a,b)),c),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(326,plain,
meet(meet(c,join(a,b)),join(meet(join(a,join(a,b)),c),b)) = meet(c,meet(join(a,b),join(meet(join(a,join(a,b)),c),b))),
inference(unit_resolution,[status(thm)],[325,105]) ).
tff(327,plain,
meet(c,meet(join(a,b),join(meet(join(a,join(a,b)),c),b))) = meet(meet(c,join(a,b)),join(meet(join(a,join(a,b)),c),b)),
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,meet(join(a,join(a,b)),c)) = join(meet(join(a,join(a,b)),c),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(329,plain,
join(b,meet(join(a,join(a,b)),c)) = join(meet(join(a,join(a,b)),c),b),
inference(unit_resolution,[status(thm)],[328,26]) ).
tff(330,plain,
join(meet(join(a,join(a,b)),c),b) = join(b,meet(join(a,join(a,b)),c)),
inference(symmetry,[status(thm)],[329]) ).
tff(331,plain,
join(meet(join(a,join(a,b)),c),join(a,b)) = join(a,b),
inference(transitivity,[status(thm)],[69,66,62,60,57,42]) ).
tff(332,plain,
meet(join(meet(join(a,join(a,b)),c),join(a,b)),b) = meet(join(a,b),b),
inference(monotonicity,[status(thm)],[331]) ).
tff(333,plain,
meet(join(meet(join(a,join(a,b)),c),join(a,b)),b) = b,
inference(transitivity,[status(thm)],[332,300,298,296]) ).
tff(334,plain,
join(meet(join(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)) = join(b,join(a,b)),
inference(monotonicity,[status(thm)],[333]) ).
tff(335,plain,
join(b,join(a,b)) = join(meet(join(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,join(a,b)) = join(join(a,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(337,plain,
join(b,join(a,b)) = join(join(a,b),b),
inference(unit_resolution,[status(thm)],[336,26]) ).
tff(338,plain,
join(join(a,b),b) = join(b,join(a,b)),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,join(a,b)),c),a),b) = join(meet(join(a,join(a,b)),c),join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(340,plain,
join(join(meet(join(a,join(a,b)),c),a),b) = join(meet(join(a,join(a,b)),c),join(a,b)),
inference(unit_resolution,[status(thm)],[339,36]) ).
tff(341,plain,
join(meet(join(a,join(a,b)),c),join(a,b)) = join(join(meet(join(a,join(a,b)),c),a),b),
inference(symmetry,[status(thm)],[340]) ).
tff(342,plain,
join(join(a,join(a,b)),meet(join(a,join(a,b)),c)) = join(join(a,b),meet(join(a,join(a,b)),c)),
inference(symmetry,[status(thm)],[66]) ).
tff(343,plain,
join(a,join(a,b)) = join(join(a,join(a,b)),meet(join(a,join(a,b)),c)),
inference(symmetry,[status(thm)],[62]) ).
tff(344,plain,
join(a,b) = join(join(meet(join(a,join(a,b)),c),a),b),
inference(transitivity,[status(thm)],[64,63,59,343,342,68,341]) ).
tff(345,plain,
join(join(a,b),b) = join(join(join(meet(join(a,join(a,b)),c),a),b),b),
inference(monotonicity,[status(thm)],[344]) ).
tff(346,plain,
join(join(join(meet(join(a,join(a,b)),c),a),b),b) = join(join(a,b),b),
inference(symmetry,[status(thm)],[345]) ).
tff(347,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(meet(join(a,join(a,b)),c),a),b),b) = join(join(meet(join(a,join(a,b)),c),a),join(b,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(348,plain,
join(join(join(meet(join(a,join(a,b)),c),a),b),b) = join(join(meet(join(a,join(a,b)),c),a),join(b,b)),
inference(unit_resolution,[status(thm)],[347,36]) ).
tff(349,plain,
join(join(meet(join(a,join(a,b)),c),a),join(b,b)) = join(join(join(meet(join(a,join(a,b)),c),a),b),b),
inference(symmetry,[status(thm)],[348]) ).
tff(350,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(b,meet(b,b)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(351,plain,
join(b,meet(b,b)) = b,
inference(unit_resolution,[status(thm)],[350,7]) ).
tff(352,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(b,meet(b,c)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(353,plain,
join(b,meet(b,c)) = b,
inference(unit_resolution,[status(thm)],[352,7]) ).
tff(354,plain,
b = join(b,meet(b,c)),
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
meet(b,b) = meet(b,join(b,meet(b,c))),
inference(monotonicity,[status(thm)],[354]) ).
tff(356,plain,
meet(b,join(b,meet(b,c))) = meet(b,b),
inference(symmetry,[status(thm)],[355]) ).
tff(357,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(b,join(b,meet(b,c))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(358,plain,
meet(b,join(b,meet(b,c))) = b,
inference(unit_resolution,[status(thm)],[357,52]) ).
tff(359,plain,
b = meet(b,join(b,meet(b,c))),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
b = meet(b,b),
inference(transitivity,[status(thm)],[359,356]) ).
tff(361,plain,
join(b,b) = join(b,meet(b,b)),
inference(monotonicity,[status(thm)],[360]) ).
tff(362,plain,
join(b,b) = b,
inference(transitivity,[status(thm)],[361,351]) ).
tff(363,plain,
join(join(meet(join(a,join(a,b)),c),a),join(b,b)) = join(join(meet(join(a,join(a,b)),c),a),b),
inference(monotonicity,[status(thm)],[362]) ).
tff(364,plain,
join(join(meet(join(a,join(a,b)),c),a),b) = join(join(meet(join(a,join(a,b)),c),a),join(b,b)),
inference(symmetry,[status(thm)],[363]) ).
tff(365,plain,
join(a,b) = join(meet(join(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),
inference(transitivity,[status(thm)],[64,63,59,343,342,68,341,364,349,346,338,335]) ).
tff(366,plain,
meet(join(a,b),join(meet(join(a,join(a,b)),c),b)) = meet(join(meet(join(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),join(b,meet(join(a,join(a,b)),c))),
inference(monotonicity,[status(thm)],[365,330]) ).
tff(367,plain,
meet(join(meet(join(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),join(b,meet(join(a,join(a,b)),c))) = meet(join(a,b),join(meet(join(a,join(a,b)),c),b)),
inference(symmetry,[status(thm)],[366]) ).
tff(368,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),meet(b,meet(join(a,join(a,b)),c))) = meet(join(meet(join(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),join(b,meet(join(a,join(a,b)),c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(369,plain,
join(meet(join(meet(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),meet(b,meet(join(a,join(a,b)),c))) = meet(join(meet(join(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),join(b,meet(join(a,join(a,b)),c))),
inference(unit_resolution,[status(thm)],[368,91]) ).
tff(370,plain,
meet(meet(b,join(a,b)),c) = meet(b,c),
inference(monotonicity,[status(thm)],[314]) ).
tff(371,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(b,join(a,b)),c) = meet(b,meet(join(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(372,plain,
meet(meet(b,join(a,b)),c) = meet(b,meet(join(a,b),c)),
inference(unit_resolution,[status(thm)],[371,105]) ).
tff(373,plain,
meet(b,meet(join(a,b),c)) = meet(meet(b,join(a,b)),c),
inference(symmetry,[status(thm)],[372]) ).
tff(374,plain,
meet(join(a,join(a,b)),c) = meet(join(a,b),c),
inference(symmetry,[status(thm)],[70]) ).
tff(375,plain,
meet(b,meet(join(a,join(a,b)),c)) = meet(b,meet(join(a,b),c)),
inference(monotonicity,[status(thm)],[374]) ).
tff(376,plain,
meet(b,meet(join(a,join(a,b)),c)) = meet(b,c),
inference(transitivity,[status(thm)],[375,373,370]) ).
tff(377,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(join(meet(join(a,join(a,b)),c),b),join(join(meet(join(a,join(a,b)),c),b),join(a,meet(b,c)))) = join(meet(join(a,join(a,b)),c),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(378,plain,
meet(join(meet(join(a,join(a,b)),c),b),join(join(meet(join(a,join(a,b)),c),b),join(a,meet(b,c)))) = join(meet(join(a,join(a,b)),c),b),
inference(unit_resolution,[status(thm)],[377,52]) ).
tff(379,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,join(a,b)),c),b),join(a,meet(b,c))) = join(meet(join(a,join(a,b)),c),join(b,join(a,meet(b,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(380,plain,
join(join(meet(join(a,join(a,b)),c),b),join(a,meet(b,c))) = join(meet(join(a,join(a,b)),c),join(b,join(a,meet(b,c)))),
inference(unit_resolution,[status(thm)],[379,36]) ).
tff(381,plain,
join(meet(join(a,join(a,b)),c),join(b,join(a,meet(b,c)))) = join(join(meet(join(a,join(a,b)),c),b),join(a,meet(b,c))),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
join(join(b,meet(b,c)),a) = join(b,a),
inference(monotonicity,[status(thm)],[353]) ).
tff(383,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(b,meet(b,c)),a) = join(b,join(meet(b,c),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(384,plain,
join(join(b,meet(b,c)),a) = join(b,join(meet(b,c),a)),
inference(unit_resolution,[status(thm)],[383,36]) ).
tff(385,plain,
join(b,join(meet(b,c),a)) = join(join(b,meet(b,c)),a),
inference(symmetry,[status(thm)],[384]) ).
tff(386,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,c),a) = join(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(387,plain,
join(meet(b,c),a) = join(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[386,26]) ).
tff(388,plain,
join(a,meet(b,c)) = join(meet(b,c),a),
inference(symmetry,[status(thm)],[387]) ).
tff(389,plain,
join(b,join(a,meet(b,c))) = join(b,join(meet(b,c),a)),
inference(monotonicity,[status(thm)],[388]) ).
tff(390,plain,
join(b,join(a,meet(b,c))) = join(a,b),
inference(transitivity,[status(thm)],[389,385,382,231]) ).
tff(391,plain,
join(meet(join(a,join(a,b)),c),join(b,join(a,meet(b,c)))) = join(meet(join(a,join(a,b)),c),join(a,b)),
inference(monotonicity,[status(thm)],[390]) ).
tff(392,plain,
join(meet(join(a,join(a,b)),c),join(a,b)) = join(meet(join(a,join(a,b)),c),join(b,join(a,meet(b,c)))),
inference(symmetry,[status(thm)],[391]) ).
tff(393,plain,
join(a,b) = join(join(meet(join(a,join(a,b)),c),b),join(a,meet(b,c))),
inference(transitivity,[status(thm)],[64,63,59,343,342,68,392,381]) ).
tff(394,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(join(a,join(a,b)),c),join(meet(join(a,join(a,b)),c),join(a,b))) = meet(join(a,join(a,b)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(395,plain,
meet(meet(join(a,join(a,b)),c),join(meet(join(a,join(a,b)),c),join(a,b))) = meet(join(a,join(a,b)),c),
inference(unit_resolution,[status(thm)],[394,52]) ).
tff(396,plain,
join(a,b) = join(meet(join(a,join(a,b)),c),join(a,b)),
inference(transitivity,[status(thm)],[64,63,59,343,342,68]) ).
tff(397,plain,
meet(meet(join(a,join(a,b)),c),join(a,b)) = meet(meet(join(a,join(a,b)),c),join(meet(join(a,join(a,b)),c),join(a,b))),
inference(monotonicity,[status(thm)],[396]) ).
tff(398,plain,
meet(meet(join(a,join(a,b)),c),join(a,b)) = meet(join(a,join(a,b)),c),
inference(transitivity,[status(thm)],[397,395]) ).
tff(399,plain,
join(meet(meet(join(a,join(a,b)),c),join(a,b)),b) = join(meet(join(a,join(a,b)),c),b),
inference(monotonicity,[status(thm)],[398]) ).
tff(400,plain,
meet(join(meet(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)) = meet(join(meet(join(a,join(a,b)),c),b),join(join(meet(join(a,join(a,b)),c),b),join(a,meet(b,c)))),
inference(monotonicity,[status(thm)],[399,393]) ).
tff(401,plain,
meet(join(meet(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)) = join(meet(join(a,join(a,b)),c),b),
inference(transitivity,[status(thm)],[400,378]) ).
tff(402,plain,
join(meet(join(meet(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),meet(b,meet(join(a,join(a,b)),c))) = join(join(meet(join(a,join(a,b)),c),b),meet(b,c)),
inference(monotonicity,[status(thm)],[401,376]) ).
tff(403,plain,
join(join(meet(join(a,join(a,b)),c),b),meet(b,c)) = join(meet(join(meet(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),meet(b,meet(join(a,join(a,b)),c))),
inference(symmetry,[status(thm)],[402]) ).
tff(404,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,join(a,b)),c),b),meet(b,c)) = join(meet(join(a,join(a,b)),c),join(b,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(405,plain,
join(join(meet(join(a,join(a,b)),c),b),meet(b,c)) = join(meet(join(a,join(a,b)),c),join(b,meet(b,c))),
inference(unit_resolution,[status(thm)],[404,36]) ).
tff(406,plain,
join(meet(join(a,join(a,b)),c),join(b,meet(b,c))) = join(join(meet(join(a,join(a,b)),c),b),meet(b,c)),
inference(symmetry,[status(thm)],[405]) ).
tff(407,plain,
join(meet(join(a,join(a,b)),c),join(b,meet(b,c))) = join(meet(join(a,join(a,b)),c),b),
inference(monotonicity,[status(thm)],[353]) ).
tff(408,plain,
join(meet(join(a,join(a,b)),c),b) = join(meet(join(a,join(a,b)),c),join(b,meet(b,c))),
inference(symmetry,[status(thm)],[407]) ).
tff(409,plain,
join(meet(join(a,join(a,b)),c),b) = meet(join(a,b),join(meet(join(a,join(a,b)),c),b)),
inference(transitivity,[status(thm)],[408,406,403,369,367]) ).
tff(410,plain,
meet(c,join(meet(join(a,join(a,b)),c),b)) = meet(c,meet(join(a,b),join(meet(join(a,join(a,b)),c),b))),
inference(monotonicity,[status(thm)],[409]) ).
tff(411,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(join(a,join(a,b)),c),b),c) = meet(c,join(meet(join(a,join(a,b)),c),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(412,plain,
meet(join(meet(join(a,join(a,b)),c),b),c) = meet(c,join(meet(join(a,join(a,b)),c),b)),
inference(unit_resolution,[status(thm)],[411,16]) ).
tff(413,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,c),c) = meet(c,join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(414,plain,
meet(join(a,c),c) = meet(c,join(a,c)),
inference(unit_resolution,[status(thm)],[413,16]) ).
tff(415,plain,
meet(join(a,c),c) = c,
inference(transitivity,[status(thm)],[414,128,126]) ).
tff(416,plain,
meet(join(a,b),meet(join(a,c),c)) = meet(join(a,b),c),
inference(monotonicity,[status(thm)],[415]) ).
tff(417,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,b),join(a,c)),c) = meet(join(a,b),meet(join(a,c),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(418,plain,
meet(meet(join(a,b),join(a,c)),c) = meet(join(a,b),meet(join(a,c),c)),
inference(unit_resolution,[status(thm)],[417,105]) ).
tff(419,plain,
meet(join(meet(join(a,join(a,c)),b),a),c) = meet(meet(join(a,b),join(a,c)),c),
inference(monotonicity,[status(thm)],[291]) ).
tff(420,plain,
meet(join(meet(join(a,join(a,c)),b),a),c) = meet(join(a,join(a,b)),c),
inference(transitivity,[status(thm)],[419,418,416,70]) ).
tff(421,plain,
join(meet(join(meet(join(a,join(a,c)),b),a),c),b) = join(meet(join(a,join(a,b)),c),b),
inference(monotonicity,[status(thm)],[420]) ).
tff(422,plain,
meet(join(meet(join(meet(join(a,join(a,c)),b),a),c),b),c) = meet(join(meet(join(a,join(a,b)),c),b),c),
inference(monotonicity,[status(thm)],[421]) ).
tff(423,plain,
meet(join(meet(join(meet(join(a,join(a,c)),b),a),c),b),c) = meet(join(a,join(a,b)),c),
inference(transitivity,[status(thm)],[422,412,410,327,324,322]) ).
tff(424,plain,
join(meet(join(meet(join(meet(join(a,join(a,c)),b),a),c),b),c),meet(b,join(meet(join(a,join(a,c)),b),a))) = join(meet(join(a,join(a,b)),c),meet(join(a,meet(join(a,b),join(a,c))),b)),
inference(monotonicity,[status(thm)],[423,320]) ).
tff(425,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(join(meet(join(a,join(a,c)),b),a),c),b),c),meet(b,join(meet(join(a,join(a,c)),b),a))) = meet(join(meet(join(join(meet(join(a,join(a,c)),b),a),c),b),c),join(b,join(meet(join(a,join(a,c)),b),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(426,plain,
join(meet(join(meet(join(meet(join(a,join(a,c)),b),a),c),b),c),meet(b,join(meet(join(a,join(a,c)),b),a))) = meet(join(meet(join(join(meet(join(a,join(a,c)),b),a),c),b),c),join(b,join(meet(join(a,join(a,c)),b),a))),
inference(unit_resolution,[status(thm)],[425,91]) ).
tff(427,plain,
meet(join(meet(join(join(meet(join(a,join(a,c)),b),a),c),b),c),join(b,join(meet(join(a,join(a,c)),b),a))) = join(meet(join(meet(join(meet(join(a,join(a,c)),b),a),c),b),c),meet(b,join(meet(join(a,join(a,c)),b),a))),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
join(b,join(meet(join(a,join(a,c)),b),a)) = join(b,meet(join(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[291]) ).
tff(429,plain,
join(b,meet(join(a,b),join(a,c))) = join(b,join(meet(join(a,join(a,c)),b),a)),
inference(symmetry,[status(thm)],[428]) ).
tff(430,plain,
join(meet(join(a,b),join(a,c)),meet(meet(join(a,b),join(a,c)),a)) = join(meet(join(a,b),join(a,c)),a),
inference(symmetry,[status(thm)],[114]) ).
tff(431,plain,
meet(join(a,b),join(a,c)) = join(meet(join(a,b),join(a,c)),meet(meet(join(a,b),join(a,c)),a)),
inference(symmetry,[status(thm)],[95]) ).
tff(432,plain,
meet(join(a,b),join(a,c)) = join(a,meet(join(a,b),join(a,c))),
inference(transitivity,[status(thm)],[431,430,116]) ).
tff(433,plain,
join(b,meet(join(a,b),join(a,c))) = join(b,join(a,meet(join(a,b),join(a,c)))),
inference(monotonicity,[status(thm)],[432]) ).
tff(434,plain,
join(b,join(a,meet(join(a,b),join(a,c)))) = join(b,meet(join(a,b),join(a,c))),
inference(symmetry,[status(thm)],[433]) ).
tff(435,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(b,a),meet(join(a,b),join(a,c))) = join(b,join(a,meet(join(a,b),join(a,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(436,plain,
join(join(b,a),meet(join(a,b),join(a,c))) = join(b,join(a,meet(join(a,b),join(a,c)))),
inference(unit_resolution,[status(thm)],[435,36]) ).
tff(437,plain,
join(join(b,a),meet(join(a,b),join(a,c))) = join(join(a,b),meet(join(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[231]) ).
tff(438,plain,
join(join(a,b),meet(join(a,b),join(a,c))) = join(join(b,a),meet(join(a,b),join(a,c))),
inference(symmetry,[status(thm)],[437]) ).
tff(439,plain,
join(b,a) = join(b,join(meet(join(a,join(a,c)),b),a)),
inference(transitivity,[status(thm)],[231,174,438,436,434,429]) ).
tff(440,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,join(a,c)),b),a),c) = join(meet(join(a,join(a,c)),b),join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(441,plain,
join(join(meet(join(a,join(a,c)),b),a),c) = join(meet(join(a,join(a,c)),b),join(a,c)),
inference(unit_resolution,[status(thm)],[440,36]) ).
tff(442,plain,
join(join(meet(join(a,join(a,c)),b),a),c) = join(a,c),
inference(transitivity,[status(thm)],[441,253,250,249,247,209,212]) ).
tff(443,plain,
meet(join(join(meet(join(a,join(a,c)),b),a),c),b) = meet(join(a,c),b),
inference(monotonicity,[status(thm)],[442]) ).
tff(444,plain,
meet(join(join(meet(join(a,join(a,c)),b),a),c),b) = meet(join(a,join(a,c)),b),
inference(transitivity,[status(thm)],[443,241]) ).
tff(445,plain,
join(meet(join(join(meet(join(a,join(a,c)),b),a),c),b),c) = join(meet(join(a,join(a,c)),b),c),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
join(meet(join(a,join(a,c)),b),c) = join(meet(join(join(meet(join(a,join(a,c)),b),a),c),b),c),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
join(meet(join(a,c),b),c) = join(meet(join(a,join(a,c)),b),c),
inference(monotonicity,[status(thm)],[241]) ).
tff(448,plain,
join(meet(join(a,c),b),c) = join(meet(join(join(meet(join(a,join(a,c)),b),a),c),b),c),
inference(transitivity,[status(thm)],[447,446]) ).
tff(449,plain,
meet(join(meet(join(a,c),b),c),join(b,a)) = meet(join(meet(join(join(meet(join(a,join(a,c)),b),a),c),b),c),join(b,join(meet(join(a,join(a,c)),b),a))),
inference(monotonicity,[status(thm)],[448,439]) ).
tff(450,plain,
join(meet(join(a,join(a,c)),b),c) = join(meet(join(a,c),b),c),
inference(symmetry,[status(thm)],[447]) ).
tff(451,plain,
meet(join(meet(join(a,join(a,c)),b),c),join(a,b)) = meet(join(meet(join(a,c),b),c),join(b,a)),
inference(monotonicity,[status(thm)],[450,297]) ).
tff(452,plain,
meet(join(meet(join(a,join(a,c)),b),c),join(a,b)) = join(meet(join(a,join(a,b)),c),meet(join(a,meet(join(a,b),join(a,c))),b)),
inference(transitivity,[status(thm)],[451,449,427,424]) ).
tff(453,plain,
join(meet(join(meet(join(a,join(a,c)),b),c),join(a,b)),a) = join(join(meet(join(a,join(a,b)),c),meet(join(a,meet(join(a,b),join(a,c))),b)),a),
inference(monotonicity,[status(thm)],[452]) ).
tff(454,plain,
meet(join(meet(join(a,c),b),c),join(b,a)) = meet(join(meet(join(a,join(a,c)),b),c),join(a,b)),
inference(symmetry,[status(thm)],[451]) ).
tff(455,plain,
meet(join(meet(join(join(meet(join(a,join(a,c)),b),a),c),b),c),join(b,join(meet(join(a,join(a,c)),b),a))) = meet(join(meet(join(a,c),b),c),join(b,a)),
inference(symmetry,[status(thm)],[449]) ).
tff(456,plain,
join(meet(join(a,join(a,b)),c),meet(join(a,meet(join(a,b),join(a,c))),b)) = join(meet(join(meet(join(meet(join(a,join(a,c)),b),a),c),b),c),meet(b,join(meet(join(a,join(a,c)),b),a))),
inference(symmetry,[status(thm)],[424]) ).
tff(457,plain,
join(meet(join(a,join(a,b)),c),meet(join(a,join(a,c)),b)) = join(meet(join(a,join(a,b)),c),meet(join(a,meet(join(a,b),join(a,c))),b)),
inference(symmetry,[status(thm)],[308]) ).
tff(458,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,join(a,c)),b),meet(join(a,join(a,b)),c)) = join(meet(join(a,join(a,b)),c),meet(join(a,join(a,c)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(459,plain,
join(meet(join(a,join(a,c)),b),meet(join(a,join(a,b)),c)) = join(meet(join(a,join(a,b)),c),meet(join(a,join(a,c)),b)),
inference(unit_resolution,[status(thm)],[458,26]) ).
tff(460,plain,
join(meet(join(a,meet(join(a,b),join(a,c))),b),c) = join(meet(join(a,join(a,c)),b),c),
inference(monotonicity,[status(thm)],[307]) ).
tff(461,plain,
meet(join(meet(join(a,meet(join(a,b),join(a,c))),b),c),b) = meet(join(meet(join(a,join(a,c)),b),c),b),
inference(monotonicity,[status(thm)],[460]) ).
tff(462,plain,
meet(join(meet(join(a,join(a,c)),b),c),b) = meet(join(meet(join(a,meet(join(a,b),join(a,c))),b),c),b),
inference(symmetry,[status(thm)],[461]) ).
tff(463,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,join(meet(join(a,join(a,c)),b),c)) = meet(join(meet(join(a,join(a,c)),b),c),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(464,plain,
meet(b,join(meet(join(a,join(a,c)),b),c)) = meet(join(meet(join(a,join(a,c)),b),c),b),
inference(unit_resolution,[status(thm)],[463,16]) ).
tff(465,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,meet(join(a,join(a,c)),b)) = join(meet(join(a,join(a,c)),b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(466,plain,
join(c,meet(join(a,join(a,c)),b)) = join(meet(join(a,join(a,c)),b),c),
inference(unit_resolution,[status(thm)],[465,26]) ).
tff(467,plain,
join(meet(join(a,join(a,c)),b),c) = join(c,meet(join(a,join(a,c)),b)),
inference(symmetry,[status(thm)],[466]) ).
tff(468,plain,
meet(join(meet(join(a,join(a,c)),b),join(a,c)),c) = meet(join(a,c),c),
inference(monotonicity,[status(thm)],[254]) ).
tff(469,plain,
meet(join(meet(join(a,join(a,c)),b),join(a,c)),c) = c,
inference(transitivity,[status(thm)],[468,414,128,126]) ).
tff(470,plain,
join(meet(join(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)) = join(c,join(a,c)),
inference(monotonicity,[status(thm)],[469]) ).
tff(471,plain,
join(c,join(a,c)) = join(meet(join(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)),
inference(symmetry,[status(thm)],[470]) ).
tff(472,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,join(a,c)) = join(join(a,c),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(473,plain,
join(c,join(a,c)) = join(join(a,c),c),
inference(unit_resolution,[status(thm)],[472,26]) ).
tff(474,plain,
join(join(a,c),c) = join(c,join(a,c)),
inference(symmetry,[status(thm)],[473]) ).
tff(475,plain,
join(join(a,c),c) = join(join(join(a,c),a),c),
inference(monotonicity,[status(thm)],[214]) ).
tff(476,plain,
join(join(join(a,c),a),c) = join(join(a,c),c),
inference(symmetry,[status(thm)],[475]) ).
tff(477,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(a,c),a),c) = join(join(a,c),join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(478,plain,
join(join(join(a,c),a),c) = join(join(a,c),join(a,c)),
inference(unit_resolution,[status(thm)],[477,36]) ).
tff(479,plain,
join(join(a,c),join(a,c)) = join(join(join(a,c),a),c),
inference(symmetry,[status(thm)],[478]) ).
tff(480,plain,
^ [X: $i] :
refl(
( ( meet(X,X) = X )
<=> ( meet(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(481,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(quant_intro,[status(thm)],[480]) ).
tff(482,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(483,axiom,
! [X: $i] : ( meet(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
tff(484,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[483,482]) ).
tff(485,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(skolemize,[status(sab)],[484]) ).
tff(486,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[485,481]) ).
tff(487,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(join(a,c),join(a,c)) = join(a,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(488,plain,
meet(join(a,c),join(a,c)) = join(a,c),
inference(unit_resolution,[status(thm)],[487,486]) ).
tff(489,plain,
join(a,c) = meet(join(a,c),join(a,c)),
inference(symmetry,[status(thm)],[488]) ).
tff(490,plain,
join(join(a,c),join(a,c)) = join(join(a,c),meet(join(a,c),join(a,c))),
inference(monotonicity,[status(thm)],[489]) ).
tff(491,plain,
join(join(a,c),meet(join(a,c),join(a,c))) = join(join(a,c),join(a,c)),
inference(symmetry,[status(thm)],[490]) ).
tff(492,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(a,c),meet(join(a,c),join(a,c))) = join(a,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(493,plain,
join(join(a,c),meet(join(a,c),join(a,c))) = join(a,c),
inference(unit_resolution,[status(thm)],[492,7]) ).
tff(494,plain,
join(a,c) = join(join(a,c),meet(join(a,c),join(a,c))),
inference(symmetry,[status(thm)],[493]) ).
tff(495,plain,
join(a,c) = join(meet(join(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)),
inference(transitivity,[status(thm)],[494,491,479,476,474,471]) ).
tff(496,plain,
meet(join(a,c),join(meet(join(a,join(a,c)),b),c)) = meet(join(meet(join(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)),join(c,meet(join(a,join(a,c)),b))),
inference(monotonicity,[status(thm)],[495,467]) ).
tff(497,plain,
meet(join(meet(join(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)),join(c,meet(join(a,join(a,c)),b))) = meet(join(a,c),join(meet(join(a,join(a,c)),b),c)),
inference(symmetry,[status(thm)],[496]) ).
tff(498,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)),meet(c,meet(join(a,join(a,c)),b))) = meet(join(meet(join(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)),join(c,meet(join(a,join(a,c)),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(499,plain,
join(meet(join(meet(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)),meet(c,meet(join(a,join(a,c)),b))) = meet(join(meet(join(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)),join(c,meet(join(a,join(a,c)),b))),
inference(unit_resolution,[status(thm)],[498,91]) ).
tff(500,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,b) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(501,plain,
meet(c,b) = meet(b,c),
inference(unit_resolution,[status(thm)],[500,16]) ).
tff(502,plain,
meet(meet(c,join(a,c)),b) = meet(c,b),
inference(monotonicity,[status(thm)],[129]) ).
tff(503,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(c,join(a,c)),b) = meet(c,meet(join(a,c),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(504,plain,
meet(meet(c,join(a,c)),b) = meet(c,meet(join(a,c),b)),
inference(unit_resolution,[status(thm)],[503,105]) ).
tff(505,plain,
meet(c,meet(join(a,c),b)) = meet(meet(c,join(a,c)),b),
inference(symmetry,[status(thm)],[504]) ).
tff(506,plain,
meet(c,meet(join(a,join(a,c)),b)) = meet(c,meet(join(a,c),b)),
inference(monotonicity,[status(thm)],[242]) ).
tff(507,plain,
meet(c,meet(join(a,join(a,c)),b)) = meet(b,c),
inference(transitivity,[status(thm)],[506,505,502,501]) ).
tff(508,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(join(meet(join(a,join(a,c)),b),c),join(join(meet(join(a,join(a,c)),b),c),a)) = join(meet(join(a,join(a,c)),b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(509,plain,
meet(join(meet(join(a,join(a,c)),b),c),join(join(meet(join(a,join(a,c)),b),c),a)) = join(meet(join(a,join(a,c)),b),c),
inference(unit_resolution,[status(thm)],[508,52]) ).
tff(510,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,join(a,c)),b),c),a) = join(meet(join(a,join(a,c)),b),join(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(511,plain,
join(join(meet(join(a,join(a,c)),b),c),a) = join(meet(join(a,join(a,c)),b),join(c,a)),
inference(unit_resolution,[status(thm)],[510,36]) ).
tff(512,plain,
join(meet(join(a,join(a,c)),b),join(c,a)) = join(join(meet(join(a,join(a,c)),b),c),a),
inference(symmetry,[status(thm)],[511]) ).
tff(513,plain,
join(meet(join(a,join(a,c)),b),join(c,a)) = join(meet(join(a,join(a,c)),b),join(a,c)),
inference(monotonicity,[status(thm)],[28]) ).
tff(514,plain,
join(meet(join(a,join(a,c)),b),join(a,c)) = join(meet(join(a,join(a,c)),b),join(c,a)),
inference(symmetry,[status(thm)],[513]) ).
tff(515,plain,
join(join(a,join(a,c)),meet(join(a,join(a,c)),b)) = join(join(a,c),meet(join(a,join(a,c)),b)),
inference(symmetry,[status(thm)],[250]) ).
tff(516,plain,
join(a,join(a,c)) = join(join(a,join(a,c)),meet(join(a,join(a,c)),b)),
inference(symmetry,[status(thm)],[249]) ).
tff(517,plain,
join(a,c) = join(join(meet(join(a,join(a,c)),b),c),a),
inference(transitivity,[status(thm)],[213,210,239,516,515,252,514,512]) ).
tff(518,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(join(a,join(a,c)),b),join(meet(join(a,join(a,c)),b),join(a,c))) = meet(join(a,join(a,c)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(519,plain,
meet(meet(join(a,join(a,c)),b),join(meet(join(a,join(a,c)),b),join(a,c))) = meet(join(a,join(a,c)),b),
inference(unit_resolution,[status(thm)],[518,52]) ).
tff(520,plain,
join(a,c) = join(meet(join(a,join(a,c)),b),join(a,c)),
inference(transitivity,[status(thm)],[213,210,239,516,515,252]) ).
tff(521,plain,
meet(meet(join(a,join(a,c)),b),join(a,c)) = meet(meet(join(a,join(a,c)),b),join(meet(join(a,join(a,c)),b),join(a,c))),
inference(monotonicity,[status(thm)],[520]) ).
tff(522,plain,
meet(meet(join(a,join(a,c)),b),join(a,c)) = meet(join(a,join(a,c)),b),
inference(transitivity,[status(thm)],[521,519]) ).
tff(523,plain,
join(meet(meet(join(a,join(a,c)),b),join(a,c)),c) = join(meet(join(a,join(a,c)),b),c),
inference(monotonicity,[status(thm)],[522]) ).
tff(524,plain,
meet(join(meet(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)) = meet(join(meet(join(a,join(a,c)),b),c),join(join(meet(join(a,join(a,c)),b),c),a)),
inference(monotonicity,[status(thm)],[523,517]) ).
tff(525,plain,
meet(join(meet(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)) = join(meet(join(a,join(a,c)),b),c),
inference(transitivity,[status(thm)],[524,509]) ).
tff(526,plain,
join(meet(join(meet(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)),meet(c,meet(join(a,join(a,c)),b))) = join(join(meet(join(a,join(a,c)),b),c),meet(b,c)),
inference(monotonicity,[status(thm)],[525,507]) ).
tff(527,plain,
join(join(meet(join(a,join(a,c)),b),c),meet(b,c)) = join(meet(join(meet(meet(join(a,join(a,c)),b),join(a,c)),c),join(a,c)),meet(c,meet(join(a,join(a,c)),b))),
inference(symmetry,[status(thm)],[526]) ).
tff(528,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,join(a,c)),b),c),meet(b,c)) = join(meet(join(a,join(a,c)),b),join(c,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(529,plain,
join(join(meet(join(a,join(a,c)),b),c),meet(b,c)) = join(meet(join(a,join(a,c)),b),join(c,meet(b,c))),
inference(unit_resolution,[status(thm)],[528,36]) ).
tff(530,plain,
join(meet(join(a,join(a,c)),b),join(c,meet(b,c))) = join(join(meet(join(a,join(a,c)),b),c),meet(b,c)),
inference(symmetry,[status(thm)],[529]) ).
tff(531,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(c,meet(c,b)) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(532,plain,
join(c,meet(c,b)) = c,
inference(unit_resolution,[status(thm)],[531,7]) ).
tff(533,plain,
meet(b,c) = meet(c,b),
inference(symmetry,[status(thm)],[501]) ).
tff(534,plain,
join(c,meet(b,c)) = join(c,meet(c,b)),
inference(monotonicity,[status(thm)],[533]) ).
tff(535,plain,
join(c,meet(b,c)) = c,
inference(transitivity,[status(thm)],[534,532]) ).
tff(536,plain,
join(meet(join(a,join(a,c)),b),join(c,meet(b,c))) = join(meet(join(a,join(a,c)),b),c),
inference(monotonicity,[status(thm)],[535]) ).
tff(537,plain,
join(meet(join(a,join(a,c)),b),c) = join(meet(join(a,join(a,c)),b),join(c,meet(b,c))),
inference(symmetry,[status(thm)],[536]) ).
tff(538,plain,
join(meet(join(a,join(a,c)),b),c) = meet(join(a,c),join(meet(join(a,join(a,c)),b),c)),
inference(transitivity,[status(thm)],[537,530,527,499,497]) ).
tff(539,plain,
meet(b,join(meet(join(a,join(a,c)),b),c)) = meet(b,meet(join(a,c),join(meet(join(a,join(a,c)),b),c))),
inference(monotonicity,[status(thm)],[538]) ).
tff(540,plain,
meet(b,meet(join(a,c),join(meet(join(a,join(a,c)),b),c))) = meet(b,join(meet(join(a,join(a,c)),b),c)),
inference(symmetry,[status(thm)],[539]) ).
tff(541,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(b,join(a,c)),join(meet(join(a,join(a,c)),b),c)) = meet(b,meet(join(a,c),join(meet(join(a,join(a,c)),b),c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(542,plain,
meet(meet(b,join(a,c)),join(meet(join(a,join(a,c)),b),c)) = meet(b,meet(join(a,c),join(meet(join(a,join(a,c)),b),c))),
inference(unit_resolution,[status(thm)],[541,105]) ).
tff(543,plain,
meet(b,join(a,c)) = meet(join(a,join(a,c)),b),
inference(transitivity,[status(thm)],[245,244]) ).
tff(544,plain,
meet(meet(b,join(a,c)),join(meet(join(a,join(a,c)),b),c)) = meet(meet(join(a,join(a,c)),b),join(meet(join(a,join(a,c)),b),c)),
inference(monotonicity,[status(thm)],[543]) ).
tff(545,plain,
meet(meet(join(a,join(a,c)),b),join(meet(join(a,join(a,c)),b),c)) = meet(meet(b,join(a,c)),join(meet(join(a,join(a,c)),b),c)),
inference(symmetry,[status(thm)],[544]) ).
tff(546,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(join(a,join(a,c)),b),join(meet(join(a,join(a,c)),b),c)) = meet(join(a,join(a,c)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(547,plain,
meet(meet(join(a,join(a,c)),b),join(meet(join(a,join(a,c)),b),c)) = meet(join(a,join(a,c)),b),
inference(unit_resolution,[status(thm)],[546,52]) ).
tff(548,plain,
meet(join(a,join(a,c)),b) = meet(meet(join(a,join(a,c)),b),join(meet(join(a,join(a,c)),b),c)),
inference(symmetry,[status(thm)],[547]) ).
tff(549,plain,
meet(join(a,join(a,c)),b) = meet(join(meet(join(a,meet(join(a,b),join(a,c))),b),c),b),
inference(transitivity,[status(thm)],[548,545,542,540,464,462]) ).
tff(550,plain,
join(meet(join(a,join(a,c)),b),meet(join(a,join(a,b)),c)) = join(meet(join(meet(join(a,meet(join(a,b),join(a,c))),b),c),b),meet(c,join(a,meet(join(a,b),join(a,c))))),
inference(monotonicity,[status(thm)],[549,137]) ).
tff(551,plain,
join(meet(join(meet(join(a,meet(join(a,b),join(a,c))),b),c),b),meet(c,join(a,meet(join(a,b),join(a,c))))) = join(meet(join(a,join(a,c)),b),meet(join(a,join(a,b)),c)),
inference(symmetry,[status(thm)],[550]) ).
tff(552,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(join(a,meet(join(a,b),join(a,c))),b),c),b),meet(c,join(a,meet(join(a,b),join(a,c))))) = meet(join(meet(join(join(a,meet(join(a,b),join(a,c))),b),c),b),join(c,join(a,meet(join(a,b),join(a,c))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(553,plain,
join(meet(join(meet(join(a,meet(join(a,b),join(a,c))),b),c),b),meet(c,join(a,meet(join(a,b),join(a,c))))) = meet(join(meet(join(join(a,meet(join(a,b),join(a,c))),b),c),b),join(c,join(a,meet(join(a,b),join(a,c))))),
inference(unit_resolution,[status(thm)],[552,91]) ).
tff(554,plain,
meet(join(meet(join(join(a,meet(join(a,b),join(a,c))),b),c),b),join(c,join(a,meet(join(a,b),join(a,c))))) = join(meet(join(meet(join(a,meet(join(a,b),join(a,c))),b),c),b),meet(c,join(a,meet(join(a,b),join(a,c))))),
inference(symmetry,[status(thm)],[553]) ).
tff(555,plain,
join(c,join(a,meet(join(a,b),join(a,c)))) = join(c,a),
inference(transitivity,[status(thm)],[39,29,9,127]) ).
tff(556,plain,
join(meet(join(a,b),c),b) = join(meet(join(a,join(a,b)),c),b),
inference(monotonicity,[status(thm)],[70]) ).
tff(557,plain,
join(meet(join(a,join(a,b)),c),b) = join(meet(join(a,b),c),b),
inference(symmetry,[status(thm)],[556]) ).
tff(558,plain,
join(b,join(a,meet(join(a,b),join(a,c)))) = join(join(b,a),meet(join(a,b),join(a,c))),
inference(symmetry,[status(thm)],[436]) ).
tff(559,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(a,meet(join(a,b),join(a,c))),b) = join(b,join(a,meet(join(a,b),join(a,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(560,plain,
join(join(a,meet(join(a,b),join(a,c))),b) = join(b,join(a,meet(join(a,b),join(a,c)))),
inference(unit_resolution,[status(thm)],[559,26]) ).
tff(561,plain,
join(join(a,meet(join(a,b),join(a,c))),b) = join(a,b),
inference(transitivity,[status(thm)],[560,558,437,72]) ).
tff(562,plain,
meet(join(join(a,meet(join(a,b),join(a,c))),b),c) = meet(join(a,b),c),
inference(monotonicity,[status(thm)],[561]) ).
tff(563,plain,
meet(join(join(a,meet(join(a,b),join(a,c))),b),c) = meet(join(a,join(a,b)),c),
inference(transitivity,[status(thm)],[562,70]) ).
tff(564,plain,
join(meet(join(join(a,meet(join(a,b),join(a,c))),b),c),b) = join(meet(join(a,join(a,b)),c),b),
inference(monotonicity,[status(thm)],[563]) ).
tff(565,plain,
join(meet(join(join(a,meet(join(a,b),join(a,c))),b),c),b) = join(meet(join(a,b),c),b),
inference(transitivity,[status(thm)],[564,557]) ).
tff(566,plain,
meet(join(meet(join(join(a,meet(join(a,b),join(a,c))),b),c),b),join(c,join(a,meet(join(a,b),join(a,c))))) = meet(join(meet(join(a,b),c),b),join(c,a)),
inference(monotonicity,[status(thm)],[565,555]) ).
tff(567,plain,
meet(join(meet(join(a,b),c),b),join(c,a)) = meet(join(meet(join(join(a,meet(join(a,b),join(a,c))),b),c),b),join(c,join(a,meet(join(a,b),join(a,c))))),
inference(symmetry,[status(thm)],[566]) ).
tff(568,plain,
meet(join(meet(join(a,join(a,b)),c),b),join(a,c)) = meet(join(meet(join(a,b),c),b),join(c,a)),
inference(monotonicity,[status(thm)],[557,127]) ).
tff(569,plain,
meet(join(meet(join(a,join(a,b)),c),b),join(a,c)) = meet(join(meet(join(a,join(a,c)),b),c),join(a,b)),
inference(transitivity,[status(thm)],[568,567,554,551,459,457,456,426,455,454]) ).
tff(570,plain,
join(meet(join(meet(join(a,join(a,b)),c),b),join(a,c)),a) = join(meet(join(meet(join(a,join(a,c)),b),c),join(a,b)),a),
inference(monotonicity,[status(thm)],[569]) ).
tff(571,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,c),join(meet(join(a,join(a,b)),c),b)) = meet(join(meet(join(a,join(a,b)),c),b),join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(572,plain,
meet(join(a,c),join(meet(join(a,join(a,b)),c),b)) = meet(join(meet(join(a,join(a,b)),c),b),join(a,c)),
inference(unit_resolution,[status(thm)],[571,16]) ).
tff(573,plain,
meet(join(meet(join(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),join(b,meet(join(a,join(a,b)),c))) = join(meet(join(meet(meet(join(a,join(a,b)),c),join(a,b)),b),join(a,b)),meet(b,meet(join(a,join(a,b)),c))),
inference(symmetry,[status(thm)],[369]) ).
tff(574,plain,
meet(join(a,b),join(meet(join(a,join(a,b)),c),b)) = join(meet(join(a,join(a,b)),c),b),
inference(transitivity,[status(thm)],[366,573,402,405,407]) ).
tff(575,plain,
meet(join(a,c),meet(join(a,b),join(meet(join(a,join(a,b)),c),b))) = meet(join(a,c),join(meet(join(a,join(a,b)),c),b)),
inference(monotonicity,[status(thm)],[574]) ).
tff(576,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,c),join(a,b)),join(meet(join(a,join(a,b)),c),b)) = meet(join(a,c),meet(join(a,b),join(meet(join(a,join(a,b)),c),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(577,plain,
meet(meet(join(a,c),join(a,b)),join(meet(join(a,join(a,b)),c),b)) = meet(join(a,c),meet(join(a,b),join(meet(join(a,join(a,b)),c),b))),
inference(unit_resolution,[status(thm)],[576,105]) ).
tff(578,plain,
meet(meet(join(a,b),join(a,c)),join(meet(join(a,join(a,b)),c),b)) = meet(meet(join(a,c),join(a,b)),join(meet(join(a,join(a,b)),c),b)),
inference(monotonicity,[status(thm)],[19]) ).
tff(579,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(join(a,b),join(a,c)),join(meet(join(a,join(a,b)),c),b)) = meet(join(meet(join(a,join(a,b)),c),b),meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(580,plain,
meet(meet(join(a,b),join(a,c)),join(meet(join(a,join(a,b)),c),b)) = meet(join(meet(join(a,join(a,b)),c),b),meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[579,16]) ).
tff(581,plain,
meet(join(meet(join(a,join(a,b)),c),b),meet(join(a,b),join(a,c))) = meet(meet(join(a,b),join(a,c)),join(meet(join(a,join(a,b)),c),b)),
inference(symmetry,[status(thm)],[580]) ).
tff(582,plain,
meet(join(meet(join(a,join(a,b)),c),b),join(a,meet(join(a,b),join(a,c)))) = meet(join(meet(join(a,join(a,b)),c),b),meet(join(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[118]) ).
tff(583,plain,
meet(join(a,b),meet(join(a,c),join(a,c))) = meet(join(a,b),join(a,c)),
inference(monotonicity,[status(thm)],[488]) ).
tff(584,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,b),join(a,c)),join(a,c)) = meet(join(a,b),meet(join(a,c),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(585,plain,
meet(meet(join(a,b),join(a,c)),join(a,c)) = meet(join(a,b),meet(join(a,c),join(a,c))),
inference(unit_resolution,[status(thm)],[584,105]) ).
tff(586,plain,
join(c,meet(join(a,b),join(a,c))) = join(c,join(a,meet(join(a,b),join(a,c)))),
inference(monotonicity,[status(thm)],[432]) ).
tff(587,plain,
join(c,meet(join(a,b),join(a,c))) = join(a,c),
inference(transitivity,[status(thm)],[586,39,29,9]) ).
tff(588,plain,
meet(join(a,meet(join(a,b),join(a,c))),join(c,meet(join(a,b),join(a,c)))) = meet(meet(join(a,b),join(a,c)),join(a,c)),
inference(monotonicity,[status(thm)],[118,587]) ).
tff(589,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,b),join(a,c)),c) = join(c,meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(590,plain,
join(meet(join(a,b),join(a,c)),c) = join(c,meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[589,26]) ).
tff(591,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(join(a,b),join(a,c)),join(a,c)) = meet(join(a,c),meet(join(a,b),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(592,plain,
meet(meet(join(a,b),join(a,c)),join(a,c)) = meet(join(a,c),meet(join(a,b),join(a,c))),
inference(unit_resolution,[status(thm)],[591,16]) ).
tff(593,plain,
meet(join(a,c),meet(join(a,b),join(a,c))) = meet(meet(join(a,b),join(a,c)),join(a,c)),
inference(symmetry,[status(thm)],[592]) ).
tff(594,plain,
meet(join(c,a),meet(join(a,b),join(a,c))) = meet(join(a,c),meet(join(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[28]) ).
tff(595,plain,
meet(join(c,a),meet(join(a,b),join(a,c))) = meet(join(a,b),join(a,c)),
inference(transitivity,[status(thm)],[594,593,585,583]) ).
tff(596,plain,
join(meet(join(c,a),meet(join(a,b),join(a,c))),a) = join(meet(join(a,b),join(a,c)),a),
inference(monotonicity,[status(thm)],[595]) ).
tff(597,plain,
join(meet(join(c,a),meet(join(a,b),join(a,c))),a) = join(a,meet(join(a,b),join(a,c))),
inference(transitivity,[status(thm)],[596,116]) ).
tff(598,plain,
meet(join(meet(join(c,a),meet(join(a,b),join(a,c))),a),join(meet(join(a,b),join(a,c)),c)) = meet(join(a,meet(join(a,b),join(a,c))),join(c,meet(join(a,b),join(a,c)))),
inference(monotonicity,[status(thm)],[597,590]) ).
tff(599,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(c,a),meet(join(a,b),join(a,c))),a),meet(meet(join(a,b),join(a,c)),c)) = meet(join(meet(join(c,a),meet(join(a,b),join(a,c))),a),join(meet(join(a,b),join(a,c)),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(600,plain,
join(meet(join(meet(c,a),meet(join(a,b),join(a,c))),a),meet(meet(join(a,b),join(a,c)),c)) = meet(join(meet(join(c,a),meet(join(a,b),join(a,c))),a),join(meet(join(a,b),join(a,c)),c)),
inference(unit_resolution,[status(thm)],[599,91]) ).
tff(601,plain,
meet(join(a,b),meet(join(a,c),c)) = meet(meet(join(a,b),join(a,c)),c),
inference(symmetry,[status(thm)],[418]) ).
tff(602,plain,
meet(join(a,b),c) = meet(join(a,b),meet(join(a,c),c)),
inference(symmetry,[status(thm)],[416]) ).
tff(603,plain,
meet(c,join(a,b)) = meet(meet(join(a,b),join(a,c)),c),
inference(transitivity,[status(thm)],[132,135,374,602,601]) ).
tff(604,plain,
meet(join(meet(join(a,join(a,b)),c),join(a,b)),join(c,a)) = meet(join(a,b),join(a,c)),
inference(monotonicity,[status(thm)],[331,28]) ).
tff(605,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(a,join(a,b)),c),join(a,b)),meet(c,a)) = meet(join(meet(join(a,join(a,b)),c),join(a,b)),join(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(606,plain,
join(meet(join(meet(a,join(a,b)),c),join(a,b)),meet(c,a)) = meet(join(meet(join(a,join(a,b)),c),join(a,b)),join(c,a)),
inference(unit_resolution,[status(thm)],[605,91]) ).
tff(607,plain,
join(meet(a,join(a,b)),c) = join(a,c),
inference(monotonicity,[status(thm)],[54]) ).
tff(608,plain,
meet(join(meet(a,join(a,b)),c),join(a,b)) = meet(join(a,c),join(a,b)),
inference(monotonicity,[status(thm)],[607]) ).
tff(609,plain,
meet(join(a,c),join(a,b)) = meet(join(meet(a,join(a,b)),c),join(a,b)),
inference(symmetry,[status(thm)],[608]) ).
tff(610,plain,
meet(join(a,b),join(a,c)) = meet(join(meet(a,join(a,b)),c),join(a,b)),
inference(transitivity,[status(thm)],[19,609]) ).
tff(611,plain,
join(meet(join(a,b),join(a,c)),meet(c,a)) = join(meet(join(meet(a,join(a,b)),c),join(a,b)),meet(c,a)),
inference(monotonicity,[status(thm)],[610]) ).
tff(612,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(c,a),meet(join(a,b),join(a,c))) = join(meet(join(a,b),join(a,c)),meet(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(613,plain,
join(meet(c,a),meet(join(a,b),join(a,c))) = join(meet(join(a,b),join(a,c)),meet(c,a)),
inference(unit_resolution,[status(thm)],[612,26]) ).
tff(614,plain,
join(meet(c,a),meet(join(a,b),join(a,c))) = meet(join(a,b),join(a,c)),
inference(transitivity,[status(thm)],[613,611,606,604]) ).
tff(615,plain,
meet(join(meet(c,a),meet(join(a,b),join(a,c))),a) = meet(meet(join(a,b),join(a,c)),a),
inference(monotonicity,[status(thm)],[614]) ).
tff(616,plain,
meet(meet(join(a,b),join(a,c)),a) = meet(join(meet(c,a),meet(join(a,b),join(a,c))),a),
inference(symmetry,[status(thm)],[615]) ).
tff(617,plain,
meet(join(a,b),a) = a,
inference(transitivity,[status(thm)],[44,54]) ).
tff(618,plain,
join(meet(join(a,b),a),c) = join(a,c),
inference(monotonicity,[status(thm)],[617]) ).
tff(619,plain,
meet(join(meet(join(a,b),a),c),a) = meet(join(a,c),a),
inference(monotonicity,[status(thm)],[618]) ).
tff(620,plain,
meet(join(meet(join(a,b),a),c),a) = meet(join(meet(c,a),meet(join(a,b),join(a,c))),a),
inference(transitivity,[status(thm)],[619,206,109,107,98,616]) ).
tff(621,plain,
join(meet(join(meet(join(a,b),a),c),a),meet(c,join(a,b))) = join(meet(join(meet(c,a),meet(join(a,b),join(a,c))),a),meet(meet(join(a,b),join(a,c)),c)),
inference(monotonicity,[status(thm)],[620,603]) ).
tff(622,plain,
meet(join(a,join(a,b)),c) = meet(c,join(a,b)),
inference(transitivity,[status(thm)],[136,133]) ).
tff(623,plain,
meet(join(a,c),a) = meet(join(meet(join(a,b),a),c),a),
inference(symmetry,[status(thm)],[619]) ).
tff(624,plain,
a = meet(join(meet(join(a,b),a),c),a),
inference(transitivity,[status(thm)],[112,207,623]) ).
tff(625,plain,
join(a,meet(join(a,join(a,b)),c)) = join(meet(join(meet(join(a,b),a),c),a),meet(c,join(a,b))),
inference(monotonicity,[status(thm)],[624,622]) ).
tff(626,plain,
join(a,meet(join(a,join(a,b)),c)) = join(a,meet(join(a,b),join(a,c))),
inference(transitivity,[status(thm)],[625,621,600,598,588,585,583,431,430,116]) ).
tff(627,plain,
join(meet(join(a,join(a,b)),c),join(b,a)) = join(meet(join(a,join(a,b)),c),join(a,b)),
inference(monotonicity,[status(thm)],[231]) ).
tff(628,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,join(a,b)),c),b),a) = join(meet(join(a,join(a,b)),c),join(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(629,plain,
join(join(meet(join(a,join(a,b)),c),b),a) = join(meet(join(a,join(a,b)),c),join(b,a)),
inference(unit_resolution,[status(thm)],[628,36]) ).
tff(630,plain,
join(join(meet(join(a,join(a,b)),c),b),a) = join(join(meet(join(a,join(a,b)),c),b),join(a,meet(b,c))),
inference(transitivity,[status(thm)],[629,627,392,381]) ).
tff(631,plain,
join(meet(join(a,join(a,b)),c),join(b,b)) = join(meet(join(a,join(a,b)),c),b),
inference(monotonicity,[status(thm)],[362]) ).
tff(632,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,join(a,b)),c),b),b) = join(meet(join(a,join(a,b)),c),join(b,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(633,plain,
join(join(meet(join(a,join(a,b)),c),b),b) = join(meet(join(a,join(a,b)),c),join(b,b)),
inference(unit_resolution,[status(thm)],[632,36]) ).
tff(634,plain,
join(meet(join(a,b),join(meet(join(a,join(a,b)),c),b)),b) = join(join(meet(join(a,join(a,b)),c),b),b),
inference(monotonicity,[status(thm)],[574]) ).
tff(635,plain,
join(meet(join(a,b),join(meet(join(a,join(a,b)),c),b)),b) = join(meet(join(a,join(a,b)),c),b),
inference(transitivity,[status(thm)],[634,633,631]) ).
tff(636,plain,
meet(join(meet(join(a,b),join(meet(join(a,join(a,b)),c),b)),b),join(join(meet(join(a,join(a,b)),c),b),a)) = meet(join(meet(join(a,join(a,b)),c),b),join(join(meet(join(a,join(a,b)),c),b),join(a,meet(b,c)))),
inference(monotonicity,[status(thm)],[635,630]) ).
tff(637,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(a,b),join(meet(join(a,join(a,b)),c),b)),b),meet(join(meet(join(a,join(a,b)),c),b),a)) = meet(join(meet(join(a,b),join(meet(join(a,join(a,b)),c),b)),b),join(join(meet(join(a,join(a,b)),c),b),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(638,plain,
join(meet(join(meet(a,b),join(meet(join(a,join(a,b)),c),b)),b),meet(join(meet(join(a,join(a,b)),c),b),a)) = meet(join(meet(join(a,b),join(meet(join(a,join(a,b)),c),b)),b),join(join(meet(join(a,join(a,b)),c),b),a)),
inference(unit_resolution,[status(thm)],[637,91]) ).
tff(639,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(b,meet(b,a)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(640,plain,
join(b,meet(b,a)) = b,
inference(unit_resolution,[status(thm)],[639,7]) ).
tff(641,plain,
join(meet(join(a,join(a,b)),c),join(b,meet(b,a))) = join(meet(join(a,join(a,b)),c),b),
inference(monotonicity,[status(thm)],[640]) ).
tff(642,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,join(a,b)),c),b),meet(b,a)) = join(meet(join(a,join(a,b)),c),join(b,meet(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(643,plain,
join(join(meet(join(a,join(a,b)),c),b),meet(b,a)) = join(meet(join(a,join(a,b)),c),join(b,meet(b,a))),
inference(unit_resolution,[status(thm)],[642,36]) ).
tff(644,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,a),join(meet(join(a,join(a,b)),c),b)) = join(join(meet(join(a,join(a,b)),c),b),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(645,plain,
join(meet(b,a),join(meet(join(a,join(a,b)),c),b)) = join(join(meet(join(a,join(a,b)),c),b),meet(b,a)),
inference(unit_resolution,[status(thm)],[644,26]) ).
tff(646,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,b) = meet(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(647,plain,
meet(a,b) = meet(b,a),
inference(unit_resolution,[status(thm)],[646,16]) ).
tff(648,plain,
join(meet(a,b),join(meet(join(a,join(a,b)),c),b)) = join(meet(b,a),join(meet(join(a,join(a,b)),c),b)),
inference(monotonicity,[status(thm)],[647]) ).
tff(649,plain,
join(meet(a,b),join(meet(join(a,join(a,b)),c),b)) = join(b,meet(join(a,join(a,b)),c)),
inference(transitivity,[status(thm)],[648,645,643,641,330]) ).
tff(650,plain,
meet(join(meet(a,b),join(meet(join(a,join(a,b)),c),b)),b) = meet(join(b,meet(join(a,join(a,b)),c)),b),
inference(monotonicity,[status(thm)],[649]) ).
tff(651,plain,
meet(join(b,meet(join(a,join(a,b)),c)),b) = meet(join(meet(a,b),join(meet(join(a,join(a,b)),c),b)),b),
inference(symmetry,[status(thm)],[650]) ).
tff(652,plain,
meet(join(b,meet(join(a,join(a,b)),c)),b) = meet(join(meet(join(a,join(a,b)),c),b),b),
inference(monotonicity,[status(thm)],[329]) ).
tff(653,plain,
meet(join(meet(join(a,join(a,b)),c),b),b) = meet(join(b,meet(join(a,join(a,b)),c)),b),
inference(symmetry,[status(thm)],[652]) ).
tff(654,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,join(meet(join(a,join(a,b)),c),b)) = meet(join(meet(join(a,join(a,b)),c),b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(655,plain,
meet(b,join(meet(join(a,join(a,b)),c),b)) = meet(join(meet(join(a,join(a,b)),c),b),b),
inference(unit_resolution,[status(thm)],[654,16]) ).
tff(656,plain,
meet(b,join(meet(join(a,join(a,b)),c),b)) = meet(b,join(b,meet(join(a,join(a,b)),c))),
inference(monotonicity,[status(thm)],[330]) ).
tff(657,plain,
meet(b,join(b,meet(join(a,join(a,b)),c))) = meet(b,join(meet(join(a,join(a,b)),c),b)),
inference(symmetry,[status(thm)],[656]) ).
tff(658,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(b,join(b,meet(join(a,join(a,b)),c))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(659,plain,
meet(b,join(b,meet(join(a,join(a,b)),c))) = b,
inference(unit_resolution,[status(thm)],[658,52]) ).
tff(660,plain,
b = meet(b,join(b,meet(join(a,join(a,b)),c))),
inference(symmetry,[status(thm)],[659]) ).
tff(661,plain,
b = meet(join(meet(a,b),join(meet(join(a,join(a,b)),c),b)),b),
inference(transitivity,[status(thm)],[660,657,655,653,651]) ).
tff(662,plain,
join(b,meet(join(meet(join(a,join(a,b)),c),b),a)) = join(meet(join(meet(a,b),join(meet(join(a,join(a,b)),c),b)),b),meet(join(meet(join(a,join(a,b)),c),b),a)),
inference(monotonicity,[status(thm)],[661]) ).
tff(663,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,meet(join(meet(join(a,join(a,b)),c),b),a)) = join(meet(join(meet(join(a,join(a,b)),c),b),a),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(664,plain,
join(b,meet(join(meet(join(a,join(a,b)),c),b),a)) = join(meet(join(meet(join(a,join(a,b)),c),b),a),b),
inference(unit_resolution,[status(thm)],[663,26]) ).
tff(665,plain,
join(meet(join(meet(join(a,join(a,b)),c),b),a),b) = join(b,meet(join(meet(join(a,join(a,b)),c),b),a)),
inference(symmetry,[status(thm)],[664]) ).
tff(666,plain,
join(meet(join(meet(join(a,join(a,b)),c),b),a),b) = join(meet(join(a,join(a,b)),c),b),
inference(transitivity,[status(thm)],[665,662,638,636,378]) ).
tff(667,plain,
meet(join(meet(join(meet(join(a,join(a,b)),c),b),a),b),join(a,meet(join(a,join(a,b)),c))) = meet(join(meet(join(a,join(a,b)),c),b),join(a,meet(join(a,b),join(a,c)))),
inference(monotonicity,[status(thm)],[666,626]) ).
tff(668,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(meet(join(a,join(a,b)),c),b),a),b),meet(a,meet(join(a,join(a,b)),c))) = meet(join(meet(join(meet(join(a,join(a,b)),c),b),a),b),join(a,meet(join(a,join(a,b)),c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(669,plain,
join(meet(join(meet(meet(join(a,join(a,b)),c),b),a),b),meet(a,meet(join(a,join(a,b)),c))) = meet(join(meet(join(meet(join(a,join(a,b)),c),b),a),b),join(a,meet(join(a,join(a,b)),c))),
inference(unit_resolution,[status(thm)],[668,91]) ).
tff(670,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,meet(join(a,join(a,b)),c)) = meet(meet(join(a,join(a,b)),c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(671,plain,
meet(a,meet(join(a,join(a,b)),c)) = meet(meet(join(a,join(a,b)),c),a),
inference(unit_resolution,[status(thm)],[670,16]) ).
tff(672,plain,
meet(meet(join(a,join(a,b)),c),a) = meet(a,meet(join(a,join(a,b)),c)),
inference(symmetry,[status(thm)],[671]) ).
tff(673,plain,
meet(meet(join(a,join(a,b)),c),a) = meet(meet(c,join(a,b)),a),
inference(monotonicity,[status(thm)],[622]) ).
tff(674,plain,
meet(meet(c,join(a,b)),a) = meet(meet(join(a,join(a,b)),c),a),
inference(symmetry,[status(thm)],[673]) ).
tff(675,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(c,join(a,b)),a) = meet(c,meet(join(a,b),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(676,plain,
meet(meet(c,join(a,b)),a) = meet(c,meet(join(a,b),a)),
inference(unit_resolution,[status(thm)],[675,105]) ).
tff(677,plain,
meet(c,meet(join(a,b),a)) = meet(meet(c,join(a,b)),a),
inference(symmetry,[status(thm)],[676]) ).
tff(678,plain,
meet(c,meet(join(a,b),a)) = meet(c,a),
inference(monotonicity,[status(thm)],[617]) ).
tff(679,plain,
meet(c,a) = meet(c,meet(join(a,b),a)),
inference(symmetry,[status(thm)],[678]) ).
tff(680,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,c) = meet(c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(681,plain,
meet(a,c) = meet(c,a),
inference(unit_resolution,[status(thm)],[680,16]) ).
tff(682,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(a,meet(a,c)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(683,plain,
join(a,meet(a,c)) = a,
inference(unit_resolution,[status(thm)],[682,7]) ).
tff(684,plain,
meet(c,a) = meet(a,c),
inference(symmetry,[status(thm)],[681]) ).
tff(685,plain,
join(a,meet(c,a)) = join(a,meet(a,c)),
inference(monotonicity,[status(thm)],[684]) ).
tff(686,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,meet(c,a)) = join(meet(c,a),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(687,plain,
join(a,meet(c,a)) = join(meet(c,a),a),
inference(unit_resolution,[status(thm)],[686,26]) ).
tff(688,plain,
join(meet(c,a),a) = join(a,meet(c,a)),
inference(symmetry,[status(thm)],[687]) ).
tff(689,plain,
join(meet(a,c),a) = join(meet(c,a),a),
inference(monotonicity,[status(thm)],[681]) ).
tff(690,plain,
join(meet(a,c),a) = a,
inference(transitivity,[status(thm)],[689,688,685,683]) ).
tff(691,plain,
meet(join(meet(a,c),a),c) = meet(a,c),
inference(monotonicity,[status(thm)],[690]) ).
tff(692,plain,
meet(join(meet(a,c),a),c) = meet(a,meet(join(a,join(a,b)),c)),
inference(transitivity,[status(thm)],[691,681,679,677,674,672]) ).
tff(693,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(join(a,join(a,b)),c),b) = meet(b,meet(join(a,join(a,b)),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(694,plain,
meet(meet(join(a,join(a,b)),c),b) = meet(b,meet(join(a,join(a,b)),c)),
inference(unit_resolution,[status(thm)],[693,16]) ).
tff(695,plain,
meet(meet(join(a,join(a,b)),c),b) = meet(b,c),
inference(transitivity,[status(thm)],[694,375,373,370]) ).
tff(696,plain,
join(meet(meet(join(a,join(a,b)),c),b),a) = join(meet(b,c),a),
inference(monotonicity,[status(thm)],[695]) ).
tff(697,plain,
join(meet(meet(join(a,join(a,b)),c),b),a) = join(a,meet(b,c)),
inference(transitivity,[status(thm)],[696,387]) ).
tff(698,plain,
meet(join(meet(meet(join(a,join(a,b)),c),b),a),b) = meet(join(a,meet(b,c)),b),
inference(monotonicity,[status(thm)],[697]) ).
tff(699,plain,
meet(join(a,meet(b,c)),b) = meet(join(meet(meet(join(a,join(a,b)),c),b),a),b),
inference(symmetry,[status(thm)],[698]) ).
tff(700,plain,
join(meet(join(a,meet(b,c)),b),meet(join(meet(a,c),a),c)) = join(meet(join(meet(meet(join(a,join(a,b)),c),b),a),b),meet(a,meet(join(a,join(a,b)),c))),
inference(monotonicity,[status(thm)],[699,692]) ).
tff(701,plain,
join(meet(join(a,meet(b,c)),b),meet(join(meet(a,c),a),c)) = meet(join(meet(join(a,join(a,b)),c),b),join(a,c)),
inference(transitivity,[status(thm)],[700,669,667,582,581,578,577,575,572]) ).
tff(702,plain,
join(join(meet(join(a,meet(b,c)),b),meet(join(meet(a,c),a),c)),a) = join(meet(join(meet(join(a,join(a,b)),c),b),join(a,c)),a),
inference(monotonicity,[status(thm)],[701]) ).
tff(703,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,meet(b,c)),b),meet(join(meet(a,c),a),c)),a) = join(meet(join(a,meet(b,c)),b),join(meet(join(meet(a,c),a),c),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(704,plain,
join(join(meet(join(a,meet(b,c)),b),meet(join(meet(a,c),a),c)),a) = join(meet(join(a,meet(b,c)),b),join(meet(join(meet(a,c),a),c),a)),
inference(unit_resolution,[status(thm)],[703,36]) ).
tff(705,plain,
join(meet(join(a,meet(b,c)),b),join(meet(join(meet(a,c),a),c),a)) = join(join(meet(join(a,meet(b,c)),b),meet(join(meet(a,c),a),c)),a),
inference(symmetry,[status(thm)],[704]) ).
tff(706,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,meet(b,c))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(707,plain,
meet(a,join(a,meet(b,c))) = a,
inference(unit_resolution,[status(thm)],[706,52]) ).
tff(708,plain,
a = meet(a,join(a,meet(b,c))),
inference(symmetry,[status(thm)],[707]) ).
tff(709,plain,
join(a,a) = join(a,meet(a,join(a,meet(b,c)))),
inference(monotonicity,[status(thm)],[708]) ).
tff(710,plain,
join(a,meet(a,join(a,meet(b,c)))) = join(a,a),
inference(symmetry,[status(thm)],[709]) ).
tff(711,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(a,meet(a,join(a,meet(b,c)))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(712,plain,
join(a,meet(a,join(a,meet(b,c)))) = a,
inference(unit_resolution,[status(thm)],[711,7]) ).
tff(713,plain,
a = join(a,meet(a,join(a,meet(b,c)))),
inference(symmetry,[status(thm)],[712]) ).
tff(714,plain,
a = join(a,a),
inference(transitivity,[status(thm)],[713,710]) ).
tff(715,plain,
meet(a,a) = meet(a,join(a,a)),
inference(monotonicity,[status(thm)],[714]) ).
tff(716,plain,
meet(a,join(a,a)) = meet(a,a),
inference(symmetry,[status(thm)],[715]) ).
tff(717,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,a)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(718,plain,
meet(a,join(a,a)) = a,
inference(unit_resolution,[status(thm)],[717,52]) ).
tff(719,plain,
a = meet(a,join(a,a)),
inference(symmetry,[status(thm)],[718]) ).
tff(720,plain,
a = meet(a,a),
inference(transitivity,[status(thm)],[719,716]) ).
tff(721,plain,
join(meet(join(meet(a,c),a),c),a) = join(meet(join(meet(a,c),a),c),meet(a,a)),
inference(monotonicity,[status(thm)],[720]) ).
tff(722,plain,
join(meet(join(meet(a,c),a),c),meet(a,a)) = join(meet(join(meet(a,c),a),c),a),
inference(symmetry,[status(thm)],[721]) ).
tff(723,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(a,c),a),c),meet(a,a)) = meet(join(meet(join(a,c),a),c),join(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(724,plain,
join(meet(join(meet(a,c),a),c),meet(a,a)) = meet(join(meet(join(a,c),a),c),join(a,a)),
inference(unit_resolution,[status(thm)],[723,91]) ).
tff(725,plain,
meet(join(meet(join(a,c),a),c),join(a,a)) = join(meet(join(meet(a,c),a),c),meet(a,a)),
inference(symmetry,[status(thm)],[724]) ).
tff(726,plain,
join(a,a) = a,
inference(transitivity,[status(thm)],[709,712]) ).
tff(727,plain,
meet(join(meet(join(a,c),a),c),join(a,a)) = meet(join(meet(join(a,c),a),c),a),
inference(monotonicity,[status(thm)],[726]) ).
tff(728,plain,
meet(join(meet(join(a,c),a),c),a) = meet(join(meet(join(a,c),a),c),join(a,a)),
inference(symmetry,[status(thm)],[727]) ).
tff(729,plain,
join(meet(join(a,c),a),c) = join(a,c),
inference(monotonicity,[status(thm)],[277]) ).
tff(730,plain,
meet(join(meet(join(a,c),a),c),a) = meet(join(a,c),a),
inference(monotonicity,[status(thm)],[729]) ).
tff(731,plain,
meet(join(a,c),a) = meet(join(meet(join(a,c),a),c),a),
inference(symmetry,[status(thm)],[730]) ).
tff(732,plain,
a = join(meet(join(meet(a,c),a),c),a),
inference(transitivity,[status(thm)],[112,207,731,728,725,722]) ).
tff(733,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(a,meet(b,c)),meet(join(a,meet(b,c)),a)) = join(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(734,plain,
join(join(a,meet(b,c)),meet(join(a,meet(b,c)),a)) = join(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[733,7]) ).
tff(735,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,meet(b,c)),a) = meet(a,join(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(736,plain,
meet(join(a,meet(b,c)),a) = meet(a,join(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[735,16]) ).
tff(737,plain,
meet(a,join(a,meet(b,c))) = meet(join(a,meet(b,c)),a),
inference(symmetry,[status(thm)],[736]) ).
tff(738,plain,
a = meet(join(a,meet(b,c)),a),
inference(transitivity,[status(thm)],[708,737]) ).
tff(739,plain,
join(join(a,meet(b,c)),a) = join(join(a,meet(b,c)),meet(join(a,meet(b,c)),a)),
inference(monotonicity,[status(thm)],[738]) ).
tff(740,plain,
join(join(a,meet(b,c)),a) = join(a,meet(b,c)),
inference(transitivity,[status(thm)],[739,734]) ).
tff(741,plain,
meet(join(join(a,meet(b,c)),a),b) = meet(join(a,meet(b,c)),b),
inference(monotonicity,[status(thm)],[740]) ).
tff(742,plain,
join(meet(join(join(a,meet(b,c)),a),b),a) = join(meet(join(a,meet(b,c)),b),join(meet(join(meet(a,c),a),c),a)),
inference(monotonicity,[status(thm)],[741,732]) ).
tff(743,plain,
meet(join(a,meet(b,c)),b) = meet(join(join(a,meet(b,c)),a),b),
inference(symmetry,[status(thm)],[741]) ).
tff(744,plain,
join(meet(join(a,meet(b,c)),b),a) = join(meet(join(join(a,meet(b,c)),a),b),a),
inference(monotonicity,[status(thm)],[743]) ).
tff(745,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,meet(join(a,meet(b,c)),b)) = join(meet(join(a,meet(b,c)),b),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(746,plain,
join(a,meet(join(a,meet(b,c)),b)) = join(meet(join(a,meet(b,c)),b),a),
inference(unit_resolution,[status(thm)],[745,26]) ).
tff(747,plain,
meet(join(a,meet(b,c)),meet(join(a,b),b)) = meet(join(a,meet(b,c)),b),
inference(monotonicity,[status(thm)],[301]) ).
tff(748,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,meet(b,c)),join(a,b)),b) = meet(join(a,meet(b,c)),meet(join(a,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(749,plain,
meet(meet(join(a,meet(b,c)),join(a,b)),b) = meet(join(a,meet(b,c)),meet(join(a,b),b)),
inference(unit_resolution,[status(thm)],[748,105]) ).
tff(750,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,meet(b,c)),join(a,b)) = meet(join(a,b),join(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(751,plain,
meet(join(a,meet(b,c)),join(a,b)) = meet(join(a,b),join(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[750,16]) ).
tff(752,plain,
meet(join(a,b),join(a,meet(b,c))) = meet(join(a,meet(b,c)),join(a,b)),
inference(symmetry,[status(thm)],[751]) ).
tff(753,plain,
meet(meet(join(a,b),join(a,meet(b,c))),b) = meet(meet(join(a,meet(b,c)),join(a,b)),b),
inference(monotonicity,[status(thm)],[752]) ).
tff(754,plain,
meet(meet(join(a,b),join(a,meet(b,c))),b) = meet(join(a,meet(b,c)),b),
inference(transitivity,[status(thm)],[753,749,747]) ).
tff(755,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(join(a,meet(b,c)),join(join(a,meet(b,c)),b)) = join(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(756,plain,
meet(join(a,meet(b,c)),join(join(a,meet(b,c)),b)) = join(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[755,52]) ).
tff(757,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(a,meet(b,c)),b) = join(b,join(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(758,plain,
join(join(a,meet(b,c)),b) = join(b,join(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[757,26]) ).
tff(759,plain,
join(join(a,meet(b,c)),b) = join(a,b),
inference(transitivity,[status(thm)],[758,389,385,382,231]) ).
tff(760,plain,
meet(join(a,meet(b,c)),join(join(a,meet(b,c)),b)) = meet(join(a,meet(b,c)),join(a,b)),
inference(monotonicity,[status(thm)],[759]) ).
tff(761,plain,
meet(join(a,meet(b,c)),join(a,b)) = meet(join(a,meet(b,c)),join(join(a,meet(b,c)),b)),
inference(symmetry,[status(thm)],[760]) ).
tff(762,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(a,meet(b,c)),meet(join(a,meet(b,c)),b)) = join(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(763,plain,
join(join(a,meet(b,c)),meet(join(a,meet(b,c)),b)) = join(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[762,7]) ).
tff(764,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(a,meet(b,c)),meet(join(a,meet(b,c)),b)) = join(meet(join(a,meet(b,c)),b),join(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(765,plain,
join(join(a,meet(b,c)),meet(join(a,meet(b,c)),b)) = join(meet(join(a,meet(b,c)),b),join(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[764,26]) ).
tff(766,plain,
join(meet(join(a,meet(b,c)),b),join(a,meet(b,c))) = join(join(a,meet(b,c)),meet(join(a,meet(b,c)),b)),
inference(symmetry,[status(thm)],[765]) ).
tff(767,plain,
join(join(a,a),meet(b,c)) = join(a,meet(b,c)),
inference(monotonicity,[status(thm)],[726]) ).
tff(768,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(a,a),meet(b,c)) = join(a,join(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(769,plain,
join(join(a,a),meet(b,c)) = join(a,join(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[768,36]) ).
tff(770,plain,
join(a,join(a,meet(b,c))) = join(join(a,a),meet(b,c)),
inference(symmetry,[status(thm)],[769]) ).
tff(771,plain,
join(a,join(a,meet(b,c))) = join(a,meet(b,c)),
inference(transitivity,[status(thm)],[770,767]) ).
tff(772,plain,
meet(join(a,join(a,meet(b,c))),b) = meet(join(a,meet(b,c)),b),
inference(monotonicity,[status(thm)],[771]) ).
tff(773,plain,
join(meet(join(a,join(a,meet(b,c))),b),join(a,meet(b,c))) = join(meet(join(a,meet(b,c)),b),join(a,meet(b,c))),
inference(monotonicity,[status(thm)],[772]) ).
tff(774,plain,
join(meet(join(a,join(a,meet(b,c))),b),join(a,meet(b,c))) = join(a,meet(b,c)),
inference(transitivity,[status(thm)],[773,766,763]) ).
tff(775,plain,
meet(join(meet(join(a,join(a,meet(b,c))),b),join(a,meet(b,c))),join(b,a)) = meet(join(a,meet(b,c)),join(a,b)),
inference(monotonicity,[status(thm)],[774,231]) ).
tff(776,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(a,join(a,meet(b,c))),b),join(a,meet(b,c))),meet(b,a)) = meet(join(meet(join(a,join(a,meet(b,c))),b),join(a,meet(b,c))),join(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(777,plain,
join(meet(join(meet(a,join(a,meet(b,c))),b),join(a,meet(b,c))),meet(b,a)) = meet(join(meet(join(a,join(a,meet(b,c))),b),join(a,meet(b,c))),join(b,a)),
inference(unit_resolution,[status(thm)],[776,91]) ).
tff(778,plain,
join(meet(a,join(a,meet(b,c))),b) = join(a,b),
inference(monotonicity,[status(thm)],[707]) ).
tff(779,plain,
meet(join(meet(a,join(a,meet(b,c))),b),join(a,meet(b,c))) = meet(join(a,b),join(a,meet(b,c))),
inference(monotonicity,[status(thm)],[778]) ).
tff(780,plain,
meet(join(a,b),join(a,meet(b,c))) = meet(join(meet(a,join(a,meet(b,c))),b),join(a,meet(b,c))),
inference(symmetry,[status(thm)],[779]) ).
tff(781,plain,
join(meet(join(a,b),join(a,meet(b,c))),meet(b,a)) = join(meet(join(meet(a,join(a,meet(b,c))),b),join(a,meet(b,c))),meet(b,a)),
inference(monotonicity,[status(thm)],[780]) ).
tff(782,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,a),meet(join(a,b),join(a,meet(b,c)))) = join(meet(join(a,b),join(a,meet(b,c))),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(783,plain,
join(meet(b,a),meet(join(a,b),join(a,meet(b,c)))) = join(meet(join(a,b),join(a,meet(b,c))),meet(b,a)),
inference(unit_resolution,[status(thm)],[782,26]) ).
tff(784,plain,
join(meet(b,a),meet(join(a,b),join(a,meet(b,c)))) = join(a,meet(b,c)),
inference(transitivity,[status(thm)],[783,781,777,775,761,756]) ).
tff(785,plain,
meet(join(meet(b,a),meet(join(a,b),join(a,meet(b,c)))),a) = meet(join(a,meet(b,c)),a),
inference(monotonicity,[status(thm)],[784]) ).
tff(786,plain,
meet(join(meet(b,a),meet(join(a,b),join(a,meet(b,c)))),a) = a,
inference(transitivity,[status(thm)],[785,736,707]) ).
tff(787,plain,
join(meet(join(meet(b,a),meet(join(a,b),join(a,meet(b,c)))),a),meet(meet(join(a,b),join(a,meet(b,c))),b)) = join(a,meet(join(a,meet(b,c)),b)),
inference(monotonicity,[status(thm)],[786,754]) ).
tff(788,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)) )
| ( join(meet(join(meet(b,a),meet(join(a,b),join(a,meet(b,c)))),a),meet(meet(join(a,b),join(a,meet(b,c))),b)) = meet(join(meet(join(b,a),meet(join(a,b),join(a,meet(b,c)))),a),join(meet(join(a,b),join(a,meet(b,c))),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(789,plain,
join(meet(join(meet(b,a),meet(join(a,b),join(a,meet(b,c)))),a),meet(meet(join(a,b),join(a,meet(b,c))),b)) = meet(join(meet(join(b,a),meet(join(a,b),join(a,meet(b,c)))),a),join(meet(join(a,b),join(a,meet(b,c))),b)),
inference(unit_resolution,[status(thm)],[788,91]) ).
tff(790,plain,
meet(join(meet(join(b,a),meet(join(a,b),join(a,meet(b,c)))),a),join(meet(join(a,b),join(a,meet(b,c))),b)) = join(meet(join(meet(b,a),meet(join(a,b),join(a,meet(b,c)))),a),meet(meet(join(a,b),join(a,meet(b,c))),b)),
inference(symmetry,[status(thm)],[789]) ).
tff(791,plain,
meet(join(a,b),join(a,meet(b,c))) = join(a,meet(b,c)),
inference(transitivity,[status(thm)],[752,761,756]) ).
tff(792,plain,
join(meet(join(a,b),join(a,meet(b,c))),b) = join(join(a,meet(b,c)),b),
inference(monotonicity,[status(thm)],[791]) ).
tff(793,plain,
join(join(a,meet(b,c)),b) = join(meet(join(a,b),join(a,meet(b,c))),b),
inference(symmetry,[status(thm)],[792]) ).
tff(794,plain,
join(b,join(a,meet(b,c))) = join(join(a,meet(b,c)),b),
inference(symmetry,[status(thm)],[758]) ).
tff(795,plain,
join(b,join(meet(b,c),a)) = join(b,join(a,meet(b,c))),
inference(symmetry,[status(thm)],[389]) ).
tff(796,plain,
join(b,a) = join(join(b,meet(b,c)),a),
inference(symmetry,[status(thm)],[382]) ).
tff(797,plain,
join(a,b) = join(meet(join(a,b),join(a,meet(b,c))),b),
inference(transitivity,[status(thm)],[297,796,384,795,794,793]) ).
tff(798,plain,
meet(meet(join(a,b),join(a,b)),join(a,meet(b,c))) = meet(join(a,b),join(a,meet(b,c))),
inference(monotonicity,[status(thm)],[190]) ).
tff(799,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,b),join(a,b)),join(a,meet(b,c))) = meet(join(a,b),meet(join(a,b),join(a,meet(b,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(800,plain,
meet(meet(join(a,b),join(a,b)),join(a,meet(b,c))) = meet(join(a,b),meet(join(a,b),join(a,meet(b,c)))),
inference(unit_resolution,[status(thm)],[799,105]) ).
tff(801,plain,
meet(join(a,b),meet(join(a,b),join(a,meet(b,c)))) = meet(meet(join(a,b),join(a,b)),join(a,meet(b,c))),
inference(symmetry,[status(thm)],[800]) ).
tff(802,plain,
meet(join(b,a),meet(join(a,b),join(a,meet(b,c)))) = meet(join(a,b),meet(join(a,b),join(a,meet(b,c)))),
inference(monotonicity,[status(thm)],[231]) ).
tff(803,plain,
meet(join(b,a),meet(join(a,b),join(a,meet(b,c)))) = meet(join(a,b),join(a,meet(b,c))),
inference(transitivity,[status(thm)],[802,801,798]) ).
tff(804,plain,
join(meet(join(b,a),meet(join(a,b),join(a,meet(b,c)))),a) = join(meet(join(a,b),join(a,meet(b,c))),a),
inference(monotonicity,[status(thm)],[803]) ).
tff(805,plain,
join(meet(join(a,b),join(a,meet(b,c))),a) = join(meet(join(b,a),meet(join(a,b),join(a,meet(b,c)))),a),
inference(symmetry,[status(thm)],[804]) ).
tff(806,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(join(a,b),join(a,meet(b,c))),a) = meet(a,meet(join(a,b),join(a,meet(b,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(807,plain,
meet(meet(join(a,b),join(a,meet(b,c))),a) = meet(a,meet(join(a,b),join(a,meet(b,c)))),
inference(unit_resolution,[status(thm)],[806,16]) ).
tff(808,plain,
meet(a,meet(join(a,b),join(a,meet(b,c)))) = meet(meet(join(a,b),join(a,meet(b,c))),a),
inference(symmetry,[status(thm)],[807]) ).
tff(809,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,join(a,b)),join(a,meet(b,c))) = meet(a,meet(join(a,b),join(a,meet(b,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(810,plain,
meet(meet(a,join(a,b)),join(a,meet(b,c))) = meet(a,meet(join(a,b),join(a,meet(b,c)))),
inference(unit_resolution,[status(thm)],[809,105]) ).
tff(811,plain,
meet(meet(a,join(a,b)),join(a,meet(b,c))) = meet(a,join(a,meet(b,c))),
inference(monotonicity,[status(thm)],[54]) ).
tff(812,plain,
meet(a,join(a,meet(b,c))) = meet(meet(a,join(a,b)),join(a,meet(b,c))),
inference(symmetry,[status(thm)],[811]) ).
tff(813,plain,
a = meet(meet(join(a,b),join(a,meet(b,c))),a),
inference(transitivity,[status(thm)],[708,812,810,808]) ).
tff(814,plain,
join(meet(join(a,b),join(a,meet(b,c))),a) = join(meet(join(a,b),join(a,meet(b,c))),meet(meet(join(a,b),join(a,meet(b,c))),a)),
inference(monotonicity,[status(thm)],[813]) ).
tff(815,plain,
join(meet(join(a,b),join(a,meet(b,c))),meet(meet(join(a,b),join(a,meet(b,c))),a)) = join(meet(join(a,b),join(a,meet(b,c))),a),
inference(symmetry,[status(thm)],[814]) ).
tff(816,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(join(a,b),join(a,meet(b,c))),meet(meet(join(a,b),join(a,meet(b,c))),a)) = meet(join(a,b),join(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(817,plain,
join(meet(join(a,b),join(a,meet(b,c))),meet(meet(join(a,b),join(a,meet(b,c))),a)) = meet(join(a,b),join(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[816,7]) ).
tff(818,plain,
meet(join(a,b),join(a,meet(b,c))) = join(meet(join(a,b),join(a,meet(b,c))),meet(meet(join(a,b),join(a,meet(b,c))),a)),
inference(symmetry,[status(thm)],[817]) ).
tff(819,plain,
join(a,meet(b,c)) = meet(join(a,meet(b,c)),join(join(a,meet(b,c)),b)),
inference(symmetry,[status(thm)],[756]) ).
tff(820,plain,
join(a,meet(b,c)) = join(meet(join(b,a),meet(join(a,b),join(a,meet(b,c)))),a),
inference(transitivity,[status(thm)],[819,760,751,818,815,805]) ).
tff(821,plain,
meet(join(a,meet(b,c)),join(a,b)) = meet(join(meet(join(b,a),meet(join(a,b),join(a,meet(b,c)))),a),join(meet(join(a,b),join(a,meet(b,c))),b)),
inference(monotonicity,[status(thm)],[820,797]) ).
tff(822,plain,
join(a,meet(b,c)) = meet(join(a,b),join(a,c)),
inference(transitivity,[status(thm)],[819,760,821,790,787,746,744,742,705,702,570,453,309,294,292,160,157,93,84]) ).
tff(823,plain,
( ( join(a,meet(b,c)) != meet(join(a,b),join(a,c)) )
<=> ( join(a,meet(b,c)) != meet(join(a,b),join(a,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(824,axiom,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
tff(825,plain,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
inference(modus_ponens,[status(thm)],[824,823]) ).
tff(826,plain,
$false,
inference(unit_resolution,[status(thm)],[825,822]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT009-1 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 10:37:32 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 71.35/46.15 % SZS status Unsatisfiable
% 71.35/46.15 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------