TSTP Solution File: LAT026-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT026-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 18:31:46 EDT 2022
% Result : Unsatisfiable 8.50s 5.72s
% Output : Proof 8.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 101
% Number of leaves : 190
% Syntax : Number of formulae : 861 ( 679 unt; 5 typ; 0 def)
% Number of atoms : 1047 (1039 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 350 ( 166 ~; 162 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 7 ( 7 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 : 548 ( 533 !; 0 ?; 548 :)
% Comments :
%------------------------------------------------------------------------------
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
<=> ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',wal_1) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(meet(a,b),meet(a,meet(b,c))),join(c,meet(a,meet(b,c)))),meet(a,meet(b,c))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
meet(meet(join(meet(a,b),meet(a,meet(b,c))),join(c,meet(a,meet(b,c)))),meet(a,meet(b,c))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(c,a),meet(a,b))),join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) = meet(meet(c,a),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(11,plain,
meet(meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(c,a),meet(a,b))),join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) = meet(meet(c,a),meet(a,b)),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
<=> ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',wal_2) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) = meet(meet(c,a),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) = meet(meet(c,a),meet(a,b)),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b)))) = join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) = join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b)))),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) = meet(meet(c,a),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) = meet(meet(c,a),meet(a,b)),
inference(unit_resolution,[status(thm)],[23,18]) ).
tff(25,plain,
meet(meet(c,a),meet(a,b)) = join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
meet(meet(c,a),meet(a,b)) = join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b)))),
inference(transitivity,[status(thm)],[25,22]) ).
tff(27,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(X,join(Y,join(X,Z))) = X )
<=> ( meet(X,join(Y,join(X,Z))) = X ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))) = join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))) = join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b)))) = join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),meet(meet(c,a),meet(a,b))),
inference(monotonicity,[status(thm)],[20]) ).
tff(37,plain,
join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),meet(meet(c,a),meet(a,b))) = join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b)))),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(39,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)],[38]) ).
tff(40,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(41,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',commutativity_of_meet) ).
tff(42,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(a,b),meet(meet(c,a),meet(a,b))) = meet(meet(meet(c,a),meet(a,b)),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
meet(meet(a,b),meet(meet(c,a),meet(a,b))) = meet(meet(meet(c,a),meet(a,b)),meet(a,b)),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
meet(meet(meet(c,a),meet(a,b)),meet(a,b)) = meet(meet(a,b),meet(meet(c,a),meet(a,b))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,meet(a,b)) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
meet(c,meet(a,b)) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[48,44]) ).
tff(50,plain,
meet(meet(a,b),c) = meet(c,meet(a,b)),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)) = join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c))) = join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))) = join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(55,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)],[54]) ).
tff(56,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(57,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',commutativity_of_join) ).
tff(58,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))) = join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))) = join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b)),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b)) = join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[64,18]) ).
tff(66,plain,
meet(a,b) = join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b)),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
meet(a,b) = join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c))),
inference(transitivity,[status(thm)],[66,63,53]) ).
tff(68,plain,
meet(meet(meet(c,a),meet(a,b)),meet(a,b)) = meet(meet(meet(c,a),meet(a,b)),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)))),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
meet(meet(meet(c,a),meet(a,b)),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)))) = meet(meet(meet(c,a),meet(a,b)),meet(a,b)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(meet(c,a),meet(a,b)),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)))) = meet(meet(c,a),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
meet(meet(meet(c,a),meet(a,b)),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)))) = meet(meet(c,a),meet(a,b)),
inference(unit_resolution,[status(thm)],[70,33]) ).
tff(72,plain,
meet(meet(c,a),meet(a,b)) = meet(meet(meet(c,a),meet(a,b)),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
meet(meet(c,a),meet(a,b)) = meet(meet(a,b),meet(meet(c,a),meet(a,b))),
inference(transitivity,[status(thm)],[72,69,47]) ).
tff(74,plain,
join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(c,a),meet(a,b))) = join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(c,a),meet(a,b))),join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),meet(meet(c,a),meet(a,b)))) = meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))),
inference(monotonicity,[status(thm)],[74,37]) ).
tff(76,plain,
meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(c,a),meet(a,b))),join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),meet(meet(c,a),meet(a,b)))) = join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),
inference(transitivity,[status(thm)],[75,35]) ).
tff(77,plain,
meet(meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(c,a),meet(a,b))),join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) = meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))),
inference(monotonicity,[status(thm)],[76,26]) ).
tff(78,plain,
meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))) = meet(meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(c,a),meet(a,b))),join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))) = join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))) = join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),
inference(unit_resolution,[status(thm)],[79,33]) ).
tff(81,plain,
join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) = meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(meet(meet(c,a),meet(a,b)),meet(a,meet(b,c))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))) = join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(meet(meet(c,a),meet(a,b)),meet(a,meet(b,c))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))) = join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),
inference(unit_resolution,[status(thm)],[82,33]) ).
tff(84,plain,
join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) = meet(meet(a,b),meet(meet(c,a),meet(a,b))),
inference(transitivity,[status(thm)],[20,72,69,47]) ).
tff(85,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))) = meet(meet(meet(c,a),meet(a,b)),meet(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))) = meet(meet(meet(c,a),meet(a,b)),meet(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[85,44]) ).
tff(87,plain,
meet(meet(meet(c,a),meet(a,b)),meet(a,meet(b,c))) = meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
join(meet(meet(meet(c,a),meet(a,b)),meet(a,meet(b,c))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b)))) = join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),
inference(monotonicity,[status(thm)],[87,84]) ).
tff(89,plain,
meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(meet(meet(c,a),meet(a,b)),meet(a,meet(b,c))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))) = meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(meet(meet(c,a),meet(a,b)),meet(a,meet(b,c))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),
inference(unit_resolution,[status(thm)],[91,44]) ).
tff(93,plain,
join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) = meet(meet(a,b),meet(meet(c,a),meet(a,b))),
inference(transitivity,[status(thm)],[24,72,69,47]) ).
tff(94,plain,
join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b)))) = join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) = join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b)))),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))) = meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))) = join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))) = join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),
inference(unit_resolution,[status(thm)],[98,33]) ).
tff(100,plain,
join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) = meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(meet(a,b),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),join(c,join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))))),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
meet(meet(join(meet(a,b),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),join(c,join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))))),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),
inference(unit_resolution,[status(thm)],[101,7]) ).
tff(103,plain,
meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),
inference(symmetry,[status(thm)],[92]) ).
tff(104,plain,
join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) = meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),join(meet(meet(meet(c,a),meet(a,b)),meet(a,meet(b,c))),join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))))),
inference(symmetry,[status(thm)],[83]) ).
tff(105,plain,
meet(meet(c,a),meet(a,b)) = meet(meet(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(c,a),meet(a,b))),join(meet(join(meet(a,b),meet(c,a)),meet(b,c)),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))),
inference(symmetry,[status(thm)],[11]) ).
tff(106,plain,
meet(meet(c,a),meet(a,b)) = join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),
inference(transitivity,[status(thm)],[105,77,80,104,89,103,96,99]) ).
tff(107,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),c),meet(meet(a,b),c)),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
join(join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),c),meet(meet(a,b),c)),c) = c,
inference(unit_resolution,[status(thm)],[107,18]) ).
tff(109,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(meet(c,a),meet(a,b)),join(meet(meet(a,b),c),join(meet(meet(c,a),meet(a,b)),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))))) = meet(meet(c,a),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
meet(meet(meet(c,a),meet(a,b)),join(meet(meet(a,b),c),join(meet(meet(c,a),meet(a,b)),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))))) = meet(meet(c,a),meet(a,b)),
inference(unit_resolution,[status(thm)],[109,33]) ).
tff(111,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(meet(c,a),meet(a,b)),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
join(meet(meet(c,a),meet(a,b)),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = join(join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))),
inference(unit_resolution,[status(thm)],[111,60]) ).
tff(113,plain,
join(meet(meet(c,a),meet(a,b)),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = meet(meet(c,a),meet(a,b)),
inference(transitivity,[status(thm)],[112,20]) ).
tff(114,plain,
join(meet(meet(a,b),c),join(meet(meet(c,a),meet(a,b)),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))))) = join(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
join(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))) = join(meet(meet(a,b),c),join(meet(meet(c,a),meet(a,b)),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))) = join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
join(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))) = join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[116,60]) ).
tff(118,plain,
join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)) = join(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))) = join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[51]) ).
tff(120,plain,
join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))) = join(meet(meet(a,b),c),join(meet(meet(c,a),meet(a,b)),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))))),
inference(transitivity,[status(thm)],[119,118,115]) ).
tff(121,plain,
join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))) = meet(a,b),
inference(transitivity,[status(thm)],[62,65]) ).
tff(122,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(meet(a,b),c),meet(c,a)),meet(meet(a,b),meet(c,a))),meet(c,a)) = meet(c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
join(join(meet(meet(meet(a,b),c),meet(c,a)),meet(meet(a,b),meet(c,a))),meet(c,a)) = meet(c,a),
inference(unit_resolution,[status(thm)],[122,18]) ).
tff(124,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(a,b),meet(c,a)) = meet(meet(c,a),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
meet(meet(a,b),meet(c,a)) = meet(meet(c,a),meet(a,b)),
inference(unit_resolution,[status(thm)],[124,44]) ).
tff(126,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(c,meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
meet(meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(c,meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[126,7]) ).
tff(128,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,b),c),meet(join(meet(a,b),c),c)),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
join(join(meet(meet(a,b),c),meet(join(meet(a,b),c),c)),c) = c,
inference(unit_resolution,[status(thm)],[128,18]) ).
tff(130,plain,
^ [X: $i] :
refl(
( ( join(X,X) = X )
<=> ( join(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(131,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,axiom,
! [X: $i] : ( join(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',idempotence_of_join) ).
tff(134,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [X: $i] : ( join(X,X) = X ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(c,a),meet(c,a)) = meet(c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
join(meet(c,a),meet(c,a)) = meet(c,a),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,c) = meet(c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
meet(a,c) = meet(c,a),
inference(unit_resolution,[status(thm)],[139,44]) ).
tff(141,plain,
join(meet(a,c),meet(a,c)) = join(meet(c,a),meet(c,a)),
inference(monotonicity,[status(thm)],[140,140]) ).
tff(142,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(a,c),meet(a,c)),join(join(meet(a,c),meet(a,c)),join(join(meet(a,c),meet(a,c)),c))) = join(meet(a,c),meet(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
meet(join(meet(a,c),meet(a,c)),join(join(meet(a,c),meet(a,c)),join(join(meet(a,c),meet(a,c)),c))) = join(meet(a,c),meet(a,c)),
inference(unit_resolution,[status(thm)],[142,33]) ).
tff(144,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(a,c),meet(a,c)),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
join(join(meet(a,c),meet(a,c)),c) = c,
inference(unit_resolution,[status(thm)],[144,18]) ).
tff(146,plain,
join(join(meet(a,c),meet(a,c)),join(join(meet(a,c),meet(a,c)),c)) = join(join(meet(a,c),meet(a,c)),c),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
join(join(meet(a,c),meet(a,c)),c) = join(join(meet(a,c),meet(a,c)),join(join(meet(a,c),meet(a,c)),c)),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
c = join(join(meet(a,c),meet(a,c)),c),
inference(symmetry,[status(thm)],[145]) ).
tff(149,plain,
c = join(join(meet(a,c),meet(a,c)),join(join(meet(a,c),meet(a,c)),c)),
inference(transitivity,[status(thm)],[148,147]) ).
tff(150,plain,
join(meet(c,a),meet(c,a)) = join(meet(a,c),meet(a,c)),
inference(symmetry,[status(thm)],[141]) ).
tff(151,plain,
meet(c,a) = join(meet(c,a),meet(c,a)),
inference(symmetry,[status(thm)],[138]) ).
tff(152,plain,
meet(c,a) = join(meet(a,c),meet(a,c)),
inference(transitivity,[status(thm)],[151,150]) ).
tff(153,plain,
meet(meet(c,a),c) = meet(join(meet(a,c),meet(a,c)),join(join(meet(a,c),meet(a,c)),join(join(meet(a,c),meet(a,c)),c))),
inference(monotonicity,[status(thm)],[152,149]) ).
tff(154,plain,
meet(meet(c,a),c) = meet(c,a),
inference(transitivity,[status(thm)],[153,143,141,138]) ).
tff(155,plain,
join(meet(b,c),meet(meet(c,a),c)) = join(meet(b,c),meet(c,a)),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
join(meet(b,c),meet(c,a)) = join(meet(b,c),meet(meet(c,a),c)),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
join(join(meet(b,c),meet(c,a)),c) = join(join(meet(b,c),meet(meet(c,a),c)),c),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
join(join(meet(b,c),meet(meet(c,a),c)),c) = join(join(meet(b,c),meet(c,a)),c),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(b,c),meet(meet(c,a),c)),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
join(join(meet(b,c),meet(meet(c,a),c)),c) = c,
inference(unit_resolution,[status(thm)],[159,18]) ).
tff(161,plain,
c = join(join(meet(b,c),meet(meet(c,a),c)),c),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(c,join(meet(a,b),join(c,meet(b,c)))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
meet(c,join(meet(a,b),join(c,meet(b,c)))) = c,
inference(unit_resolution,[status(thm)],[162,33]) ).
tff(164,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(b,c),meet(join(meet(a,b),join(c,a)),c)),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
join(join(meet(b,c),meet(join(meet(a,b),join(c,a)),c)),c) = c,
inference(unit_resolution,[status(thm)],[164,18]) ).
tff(166,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(c,join(meet(a,b),join(c,a))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
meet(c,join(meet(a,b),join(c,a))) = c,
inference(unit_resolution,[status(thm)],[166,33]) ).
tff(168,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,b),join(c,a)),c) = meet(c,join(meet(a,b),join(c,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(169,plain,
meet(join(meet(a,b),join(c,a)),c) = meet(c,join(meet(a,b),join(c,a))),
inference(unit_resolution,[status(thm)],[168,44]) ).
tff(170,plain,
meet(join(meet(a,b),join(c,a)),c) = c,
inference(transitivity,[status(thm)],[169,167]) ).
tff(171,plain,
join(meet(b,c),meet(join(meet(a,b),join(c,a)),c)) = join(meet(b,c),c),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
join(meet(b,c),c) = join(meet(b,c),meet(join(meet(a,b),join(c,a)),c)),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,c),c) = join(c,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
join(meet(b,c),c) = join(c,meet(b,c)),
inference(unit_resolution,[status(thm)],[173,60]) ).
tff(175,plain,
join(c,meet(b,c)) = join(meet(b,c),c),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
join(c,meet(b,c)) = join(meet(b,c),meet(join(meet(a,b),join(c,a)),c)),
inference(transitivity,[status(thm)],[175,172]) ).
tff(177,plain,
join(join(c,meet(b,c)),c) = join(join(meet(b,c),meet(join(meet(a,b),join(c,a)),c)),c),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,join(c,meet(b,c))) = join(join(c,meet(b,c)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(179,plain,
join(c,join(c,meet(b,c))) = join(join(c,meet(b,c)),c),
inference(unit_resolution,[status(thm)],[178,60]) ).
tff(180,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(c,join(meet(b,c),join(c,meet(c,a)))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
meet(c,join(meet(b,c),join(c,meet(c,a)))) = c,
inference(unit_resolution,[status(thm)],[180,33]) ).
tff(182,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,join(meet(a,c),meet(a,c))) = join(join(meet(a,c),meet(a,c)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
join(c,join(meet(a,c),meet(a,c))) = join(join(meet(a,c),meet(a,c)),c),
inference(unit_resolution,[status(thm)],[182,60]) ).
tff(184,plain,
join(c,meet(c,a)) = join(c,join(meet(a,c),meet(a,c))),
inference(monotonicity,[status(thm)],[152]) ).
tff(185,plain,
join(c,meet(c,a)) = c,
inference(transitivity,[status(thm)],[184,183,145]) ).
tff(186,plain,
join(meet(b,c),join(c,meet(c,a))) = join(meet(b,c),c),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
join(meet(b,c),c) = join(meet(b,c),join(c,meet(c,a))),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
join(c,meet(b,c)) = join(meet(b,c),join(c,meet(c,a))),
inference(transitivity,[status(thm)],[175,187]) ).
tff(189,plain,
meet(c,join(c,meet(b,c))) = meet(c,join(meet(b,c),join(c,meet(c,a)))),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
meet(c,join(c,meet(b,c))) = c,
inference(transitivity,[status(thm)],[189,181]) ).
tff(191,plain,
^ [X: $i] :
refl(
( ( meet(X,X) = X )
<=> ( meet(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(192,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(quant_intro,[status(thm)],[191]) ).
tff(193,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,axiom,
! [X: $i] : ( meet(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',idempotence_of_meet) ).
tff(195,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[194,193]) ).
tff(196,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(skolemize,[status(sab)],[195]) ).
tff(197,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[196,192]) ).
tff(198,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(join(c,meet(b,c)),join(c,meet(b,c))) = join(c,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(199,plain,
meet(join(c,meet(b,c)),join(c,meet(b,c))) = join(c,meet(b,c)),
inference(unit_resolution,[status(thm)],[198,197]) ).
tff(200,plain,
meet(join(c,meet(b,c)),join(c,meet(b,c))) = join(meet(b,c),meet(join(meet(a,b),join(c,a)),c)),
inference(transitivity,[status(thm)],[199,175,172]) ).
tff(201,plain,
join(meet(join(c,meet(b,c)),join(c,meet(b,c))),meet(c,join(c,meet(b,c)))) = join(join(meet(b,c),meet(join(meet(a,b),join(c,a)),c)),c),
inference(monotonicity,[status(thm)],[200,190]) ).
tff(202,plain,
join(meet(join(c,meet(b,c)),join(c,meet(b,c))),meet(c,join(c,meet(b,c)))) = c,
inference(transitivity,[status(thm)],[201,165]) ).
tff(203,plain,
join(join(meet(join(c,meet(b,c)),join(c,meet(b,c))),meet(c,join(c,meet(b,c)))),join(c,meet(b,c))) = join(c,join(c,meet(b,c))),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(c,meet(b,c)),join(c,meet(b,c))),meet(c,join(c,meet(b,c)))),join(c,meet(b,c))) = join(c,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
join(join(meet(join(c,meet(b,c)),join(c,meet(b,c))),meet(c,join(c,meet(b,c)))),join(c,meet(b,c))) = join(c,meet(b,c)),
inference(unit_resolution,[status(thm)],[204,18]) ).
tff(206,plain,
join(c,meet(b,c)) = join(join(meet(join(c,meet(b,c)),join(c,meet(b,c))),meet(c,join(c,meet(b,c)))),join(c,meet(b,c))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
join(c,meet(b,c)) = c,
inference(transitivity,[status(thm)],[206,203,179,177,165]) ).
tff(208,plain,
join(meet(a,b),join(c,meet(b,c))) = join(meet(a,b),c),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
join(meet(a,b),c) = join(meet(a,b),join(c,meet(b,c))),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
meet(c,join(meet(a,b),c)) = meet(c,join(meet(a,b),join(c,meet(b,c)))),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,b),c),c) = meet(c,join(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(212,plain,
meet(join(meet(a,b),c),c) = meet(c,join(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[211,44]) ).
tff(213,plain,
meet(join(meet(a,b),c),c) = join(join(meet(b,c),meet(c,a)),c),
inference(transitivity,[status(thm)],[212,210,163,161,158]) ).
tff(214,plain,
join(meet(meet(a,b),c),meet(join(meet(a,b),c),c)) = join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)) = join(meet(meet(a,b),c),meet(join(meet(a,b),c),c)),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
join(join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)),c) = join(join(meet(meet(a,b),c),meet(join(meet(a,b),c),c)),c),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))) = join(join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(218,plain,
join(c,join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))) = join(join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)),c),
inference(unit_resolution,[status(thm)],[217,60]) ).
tff(219,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(c,join(meet(meet(a,b),c),join(c,meet(b,c)))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(220,plain,
meet(c,join(meet(meet(a,b),c),join(c,meet(b,c)))) = c,
inference(unit_resolution,[status(thm)],[219,33]) ).
tff(221,plain,
join(c,meet(b,c)) = join(join(meet(b,c),meet(c,a)),c),
inference(transitivity,[status(thm)],[206,203,179,177,165,161,158]) ).
tff(222,plain,
join(meet(meet(a,b),c),join(c,meet(b,c))) = join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)) = join(meet(meet(a,b),c),join(c,meet(b,c))),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
meet(c,join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))) = meet(c,join(meet(meet(a,b),c),join(c,meet(b,c)))),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
meet(c,join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))) = c,
inference(transitivity,[status(thm)],[224,220]) ).
tff(226,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,c),join(meet(meet(a,b),c),join(meet(b,c),c))) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(227,plain,
meet(meet(b,c),join(meet(meet(a,b),c),join(meet(b,c),c))) = meet(b,c),
inference(unit_resolution,[status(thm)],[226,33]) ).
tff(228,plain,
join(meet(b,c),c) = join(join(meet(b,c),meet(c,a)),c),
inference(transitivity,[status(thm)],[174,206,203,179,177,165,161,158]) ).
tff(229,plain,
join(meet(meet(a,b),c),join(meet(b,c),c)) = join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)) = join(meet(meet(a,b),c),join(meet(b,c),c)),
inference(symmetry,[status(thm)],[229]) ).
tff(231,plain,
meet(meet(b,c),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))) = meet(meet(b,c),join(meet(meet(a,b),c),join(meet(b,c),c))),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
meet(meet(b,c),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))) = meet(b,c),
inference(transitivity,[status(thm)],[231,227]) ).
tff(233,plain,
join(meet(meet(b,c),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))),meet(c,join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)))) = join(meet(b,c),c),
inference(monotonicity,[status(thm)],[232,225]) ).
tff(234,plain,
join(meet(meet(b,c),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))),meet(c,join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)))) = c,
inference(transitivity,[status(thm)],[233,174,206,203,179,177,165]) ).
tff(235,plain,
join(join(meet(meet(b,c),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))),meet(c,join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)))),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))) = join(c,join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(b,c),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))),meet(c,join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)))),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))) = join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(237,plain,
join(join(meet(meet(b,c),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))),meet(c,join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)))),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))) = join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)),
inference(unit_resolution,[status(thm)],[236,18]) ).
tff(238,plain,
join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)) = join(join(meet(meet(b,c),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))),meet(c,join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)))),join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c))),
inference(symmetry,[status(thm)],[237]) ).
tff(239,plain,
c = join(join(meet(b,c),meet(c,a)),c),
inference(transitivity,[status(thm)],[161,158]) ).
tff(240,plain,
join(meet(meet(a,b),c),c) = join(meet(meet(a,b),c),join(join(meet(b,c),meet(c,a)),c)),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,meet(meet(a,b),c)) = join(meet(meet(a,b),c),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(242,plain,
join(c,meet(meet(a,b),c)) = join(meet(meet(a,b),c),c),
inference(unit_resolution,[status(thm)],[241,60]) ).
tff(243,plain,
join(c,meet(meet(a,b),c)) = c,
inference(transitivity,[status(thm)],[242,240,238,235,218,216,129]) ).
tff(244,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(meet(a,b),c),a),meet(join(b,join(c,join(meet(a,b),join(c,a)))),a)),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(245,plain,
join(join(meet(meet(meet(a,b),c),a),meet(join(b,join(c,join(meet(a,b),join(c,a)))),a)),a) = a,
inference(unit_resolution,[status(thm)],[244,18]) ).
tff(246,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(b,join(a,join(meet(a,b),join(c,a))))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(247,plain,
meet(a,join(b,join(a,join(meet(a,b),join(c,a))))) = a,
inference(unit_resolution,[status(thm)],[246,33]) ).
tff(248,plain,
meet(a,c) = join(meet(a,c),meet(a,c)),
inference(transitivity,[status(thm)],[140,151,150]) ).
tff(249,plain,
join(meet(join(meet(a,b),join(c,a)),c),meet(a,c)) = join(c,join(meet(a,c),meet(a,c))),
inference(monotonicity,[status(thm)],[170,248]) ).
tff(250,plain,
join(c,join(meet(a,c),meet(a,c))) = join(meet(join(meet(a,b),join(c,a)),c),meet(a,c)),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
join(join(meet(a,c),meet(a,c)),c) = join(c,join(meet(a,c),meet(a,c))),
inference(symmetry,[status(thm)],[183]) ).
tff(252,plain,
meet(c,join(meet(a,b),join(c,a))) = join(meet(join(meet(a,b),join(c,a)),c),meet(a,c)),
inference(transitivity,[status(thm)],[167,148,251,250]) ).
tff(253,plain,
join(meet(c,join(meet(a,b),join(c,a))),meet(c,join(meet(a,b),join(c,a)))) = join(join(meet(join(meet(a,b),join(c,a)),c),meet(a,c)),c),
inference(monotonicity,[status(thm)],[252,167]) ).
tff(254,plain,
join(join(meet(join(meet(a,b),join(c,a)),c),meet(a,c)),c) = join(meet(c,join(meet(a,b),join(c,a))),meet(c,join(meet(a,b),join(c,a)))),
inference(symmetry,[status(thm)],[253]) ).
tff(255,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(a,b),join(c,a)),c),meet(a,c)),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(256,plain,
join(join(meet(join(meet(a,b),join(c,a)),c),meet(a,c)),c) = c,
inference(unit_resolution,[status(thm)],[255,18]) ).
tff(257,plain,
c = join(join(meet(join(meet(a,b),join(c,a)),c),meet(a,c)),c),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
c = join(meet(c,join(meet(a,b),join(c,a))),meet(c,join(meet(a,b),join(c,a)))),
inference(transitivity,[status(thm)],[257,254]) ).
tff(259,plain,
join(c,join(meet(a,b),join(c,a))) = join(join(meet(c,join(meet(a,b),join(c,a))),meet(c,join(meet(a,b),join(c,a)))),join(meet(a,b),join(c,a))),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
join(join(meet(c,join(meet(a,b),join(c,a))),meet(c,join(meet(a,b),join(c,a)))),join(meet(a,b),join(c,a))) = join(c,join(meet(a,b),join(c,a))),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(c,join(meet(a,b),join(c,a))),meet(c,join(meet(a,b),join(c,a)))),join(meet(a,b),join(c,a))) = join(meet(a,b),join(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(262,plain,
join(join(meet(c,join(meet(a,b),join(c,a))),meet(c,join(meet(a,b),join(c,a)))),join(meet(a,b),join(c,a))) = join(meet(a,b),join(c,a)),
inference(unit_resolution,[status(thm)],[261,18]) ).
tff(263,plain,
join(meet(a,b),join(c,a)) = join(join(meet(c,join(meet(a,b),join(c,a))),meet(c,join(meet(a,b),join(c,a)))),join(meet(a,b),join(c,a))),
inference(symmetry,[status(thm)],[262]) ).
tff(264,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(a,join(meet(a,b),join(c,a))),meet(a,join(meet(a,b),join(c,a)))),join(meet(a,b),join(c,a))) = join(meet(a,b),join(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(265,plain,
join(join(meet(a,join(meet(a,b),join(c,a))),meet(a,join(meet(a,b),join(c,a)))),join(meet(a,b),join(c,a))) = join(meet(a,b),join(c,a)),
inference(unit_resolution,[status(thm)],[264,18]) ).
tff(266,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(meet(a,b),join(a,c))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(267,plain,
meet(a,join(meet(a,b),join(a,c))) = a,
inference(unit_resolution,[status(thm)],[266,33]) ).
tff(268,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,c) = join(c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(269,plain,
join(a,c) = join(c,a),
inference(unit_resolution,[status(thm)],[268,60]) ).
tff(270,plain,
join(meet(a,b),join(a,c)) = join(meet(a,b),join(c,a)),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
join(meet(a,b),join(c,a)) = join(meet(a,b),join(a,c)),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
meet(a,join(meet(a,b),join(c,a))) = meet(a,join(meet(a,b),join(a,c))),
inference(monotonicity,[status(thm)],[271]) ).
tff(273,plain,
meet(a,join(meet(a,b),join(c,a))) = a,
inference(transitivity,[status(thm)],[272,267]) ).
tff(274,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,b),join(c,a)),a) = meet(a,join(meet(a,b),join(c,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(275,plain,
meet(join(meet(a,b),join(c,a)),a) = meet(a,join(meet(a,b),join(c,a))),
inference(unit_resolution,[status(thm)],[274,44]) ).
tff(276,plain,
meet(join(meet(a,b),join(c,a)),a) = a,
inference(transitivity,[status(thm)],[275,272,267]) ).
tff(277,plain,
join(meet(join(meet(a,b),join(c,a)),a),meet(c,a)) = join(a,meet(c,a)),
inference(monotonicity,[status(thm)],[276]) ).
tff(278,plain,
join(a,meet(c,a)) = join(meet(join(meet(a,b),join(c,a)),a),meet(c,a)),
inference(symmetry,[status(thm)],[277]) ).
tff(279,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(280,plain,
join(a,meet(c,a)) = join(meet(c,a),a),
inference(unit_resolution,[status(thm)],[279,60]) ).
tff(281,plain,
join(meet(c,a),a) = join(a,meet(c,a)),
inference(symmetry,[status(thm)],[280]) ).
tff(282,plain,
join(meet(c,a),a) = join(join(meet(c,a),meet(c,a)),a),
inference(monotonicity,[status(thm)],[151]) ).
tff(283,plain,
join(join(meet(c,a),meet(c,a)),a) = join(meet(c,a),a),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(c,a),meet(c,a)),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(285,plain,
join(join(meet(c,a),meet(c,a)),a) = a,
inference(unit_resolution,[status(thm)],[284,18]) ).
tff(286,plain,
a = join(join(meet(c,a),meet(c,a)),a),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
meet(a,join(meet(a,b),join(c,a))) = join(meet(join(meet(a,b),join(c,a)),a),meet(c,a)),
inference(transitivity,[status(thm)],[272,267,286,283,281,278]) ).
tff(288,plain,
join(meet(a,join(meet(a,b),join(c,a))),meet(a,join(meet(a,b),join(c,a)))) = join(join(meet(join(meet(a,b),join(c,a)),a),meet(c,a)),a),
inference(monotonicity,[status(thm)],[287,273]) ).
tff(289,plain,
join(join(meet(join(meet(a,b),join(c,a)),a),meet(c,a)),a) = join(meet(a,join(meet(a,b),join(c,a))),meet(a,join(meet(a,b),join(c,a)))),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(a,b),join(c,a)),a),meet(c,a)),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(291,plain,
join(join(meet(join(meet(a,b),join(c,a)),a),meet(c,a)),a) = a,
inference(unit_resolution,[status(thm)],[290,18]) ).
tff(292,plain,
a = join(join(meet(join(meet(a,b),join(c,a)),a),meet(c,a)),a),
inference(symmetry,[status(thm)],[291]) ).
tff(293,plain,
a = join(meet(a,join(meet(a,b),join(c,a))),meet(a,join(meet(a,b),join(c,a)))),
inference(transitivity,[status(thm)],[292,289]) ).
tff(294,plain,
join(a,join(meet(a,b),join(c,a))) = join(join(meet(a,join(meet(a,b),join(c,a))),meet(a,join(meet(a,b),join(c,a)))),join(meet(a,b),join(c,a))),
inference(monotonicity,[status(thm)],[293]) ).
tff(295,plain,
join(a,join(meet(a,b),join(c,a))) = join(c,join(meet(a,b),join(c,a))),
inference(transitivity,[status(thm)],[294,265,263,260]) ).
tff(296,plain,
join(b,join(a,join(meet(a,b),join(c,a)))) = join(b,join(c,join(meet(a,b),join(c,a)))),
inference(monotonicity,[status(thm)],[295]) ).
tff(297,plain,
join(b,join(c,join(meet(a,b),join(c,a)))) = join(b,join(a,join(meet(a,b),join(c,a)))),
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
meet(a,join(b,join(c,join(meet(a,b),join(c,a))))) = meet(a,join(b,join(a,join(meet(a,b),join(c,a))))),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,join(c,join(meet(a,b),join(c,a)))),a) = meet(a,join(b,join(c,join(meet(a,b),join(c,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(300,plain,
meet(join(b,join(c,join(meet(a,b),join(c,a)))),a) = meet(a,join(b,join(c,join(meet(a,b),join(c,a))))),
inference(unit_resolution,[status(thm)],[299,44]) ).
tff(301,plain,
meet(join(b,join(c,join(meet(a,b),join(c,a)))),a) = a,
inference(transitivity,[status(thm)],[300,298,247]) ).
tff(302,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(meet(a,b),c),join(a,join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(303,plain,
meet(meet(meet(a,b),c),join(a,join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[302,33]) ).
tff(304,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(meet(meet(a,b),c),meet(a,b)),join(meet(c,a),meet(a,b))),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(305,plain,
meet(meet(join(meet(meet(a,b),c),meet(a,b)),join(meet(c,a),meet(a,b))),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[304,7]) ).
tff(306,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(307,plain,
join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[306,18]) ).
tff(308,plain,
join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b))) = join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b))) = meet(a,b),
inference(transitivity,[status(thm)],[308,307]) ).
tff(310,plain,
join(meet(c,a),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b))) = join(meet(c,a),meet(a,b)),
inference(monotonicity,[status(thm)],[307]) ).
tff(311,plain,
join(meet(c,a),meet(a,b)) = join(meet(c,a),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b))),
inference(symmetry,[status(thm)],[310]) ).
tff(312,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,join(a,meet(b,c))),meet(a,b)) = meet(meet(a,b),join(b,join(a,meet(b,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(313,plain,
meet(join(b,join(a,meet(b,c))),meet(a,b)) = meet(meet(a,b),join(b,join(a,meet(b,c)))),
inference(unit_resolution,[status(thm)],[312,44]) ).
tff(314,plain,
meet(meet(a,b),join(b,join(a,meet(b,c)))) = meet(join(b,join(a,meet(b,c))),meet(a,b)),
inference(symmetry,[status(thm)],[313]) ).
tff(315,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(b,join(a,meet(b,c))),join(meet(a,b),meet(b,c))) = join(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(316,plain,
join(join(b,join(a,meet(b,c))),join(meet(a,b),meet(b,c))) = join(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c)))),
inference(unit_resolution,[status(thm)],[315,60]) ).
tff(317,plain,
join(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c)))) = join(join(b,join(a,meet(b,c))),join(meet(a,b),meet(b,c))),
inference(symmetry,[status(thm)],[316]) ).
tff(318,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(a,b),meet(b,c)),join(join(a,meet(b,c)),join(join(meet(a,b),meet(b,c)),b))) = join(meet(a,b),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(319,plain,
meet(join(meet(a,b),meet(b,c)),join(join(a,meet(b,c)),join(join(meet(a,b),meet(b,c)),b))) = join(meet(a,b),meet(b,c)),
inference(unit_resolution,[status(thm)],[318,33]) ).
tff(320,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(a,b),meet(c,b)),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(321,plain,
join(join(meet(a,b),meet(c,b)),b) = b,
inference(unit_resolution,[status(thm)],[320,18]) ).
tff(322,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,b) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(323,plain,
meet(c,b) = meet(b,c),
inference(unit_resolution,[status(thm)],[322,44]) ).
tff(324,plain,
join(meet(a,b),meet(c,b)) = join(meet(a,b),meet(b,c)),
inference(monotonicity,[status(thm)],[323]) ).
tff(325,plain,
join(meet(a,b),meet(b,c)) = join(meet(a,b),meet(c,b)),
inference(symmetry,[status(thm)],[324]) ).
tff(326,plain,
join(join(meet(a,b),meet(b,c)),b) = join(join(meet(a,b),meet(c,b)),b),
inference(monotonicity,[status(thm)],[325]) ).
tff(327,plain,
join(join(meet(a,b),meet(b,c)),b) = b,
inference(transitivity,[status(thm)],[326,321]) ).
tff(328,plain,
join(join(a,meet(b,c)),join(join(meet(a,b),meet(b,c)),b)) = join(join(a,meet(b,c)),b),
inference(monotonicity,[status(thm)],[327]) ).
tff(329,plain,
join(join(a,meet(b,c)),b) = join(join(a,meet(b,c)),join(join(meet(a,b),meet(b,c)),b)),
inference(symmetry,[status(thm)],[328]) ).
tff(330,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(331,plain,
join(join(a,meet(b,c)),b) = join(b,join(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[330,60]) ).
tff(332,plain,
join(b,join(a,meet(b,c))) = join(join(a,meet(b,c)),b),
inference(symmetry,[status(thm)],[331]) ).
tff(333,plain,
join(b,join(a,meet(b,c))) = join(join(a,meet(b,c)),join(join(meet(a,b),meet(b,c)),b)),
inference(transitivity,[status(thm)],[332,329]) ).
tff(334,plain,
meet(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c)))) = meet(join(meet(a,b),meet(b,c)),join(join(a,meet(b,c)),join(join(meet(a,b),meet(b,c)),b))),
inference(monotonicity,[status(thm)],[333]) ).
tff(335,plain,
meet(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c)))) = join(meet(a,b),meet(b,c)),
inference(transitivity,[status(thm)],[334,319]) ).
tff(336,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(b,meet(b,c)),meet(b,meet(b,c))) = meet(b,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(337,plain,
join(meet(b,meet(b,c)),meet(b,meet(b,c))) = meet(b,meet(b,c)),
inference(unit_resolution,[status(thm)],[336,136]) ).
tff(338,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),join(join(meet(b,meet(b,c)),meet(b,meet(b,c))),meet(b,c)))) = join(meet(b,meet(b,c)),meet(b,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(339,plain,
meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),join(join(meet(b,meet(b,c)),meet(b,meet(b,c))),meet(b,c)))) = join(meet(b,meet(b,c)),meet(b,meet(b,c))),
inference(unit_resolution,[status(thm)],[338,33]) ).
tff(340,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(b,meet(b,c)),meet(b,meet(b,c))),meet(b,c)) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(341,plain,
join(join(meet(b,meet(b,c)),meet(b,meet(b,c))),meet(b,c)) = meet(b,c),
inference(unit_resolution,[status(thm)],[340,18]) ).
tff(342,plain,
join(meet(a,b),join(join(meet(b,meet(b,c)),meet(b,meet(b,c))),meet(b,c))) = join(meet(a,b),meet(b,c)),
inference(monotonicity,[status(thm)],[341]) ).
tff(343,plain,
join(meet(a,b),meet(b,c)) = join(meet(a,b),join(join(meet(b,meet(b,c)),meet(b,meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[342]) ).
tff(344,plain,
meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c))) = meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),join(join(meet(b,meet(b,c)),meet(b,meet(b,c))),meet(b,c)))),
inference(monotonicity,[status(thm)],[343]) ).
tff(345,plain,
meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c))) = meet(b,meet(b,c)),
inference(transitivity,[status(thm)],[344,339,337]) ).
tff(346,plain,
join(meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c))),meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c)))) = join(meet(b,meet(b,c)),meet(b,meet(b,c))),
inference(monotonicity,[status(thm)],[345,345]) ).
tff(347,plain,
join(meet(b,meet(b,c)),meet(b,meet(b,c))) = join(meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c))),meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c)))),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
meet(b,meet(b,c)) = join(meet(b,meet(b,c)),meet(b,meet(b,c))),
inference(symmetry,[status(thm)],[337]) ).
tff(349,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(b,c),b) = meet(b,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(350,plain,
meet(meet(b,c),b) = meet(b,meet(b,c)),
inference(unit_resolution,[status(thm)],[349,44]) ).
tff(351,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))) = join(join(meet(b,meet(b,c)),meet(b,meet(b,c))),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(352,plain,
join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))) = join(join(meet(b,meet(b,c)),meet(b,meet(b,c))),meet(b,c)),
inference(unit_resolution,[status(thm)],[351,60]) ).
tff(353,plain,
join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))) = meet(b,c),
inference(transitivity,[status(thm)],[352,341]) ).
tff(354,plain,
join(b,join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c))))) = join(b,meet(b,c)),
inference(monotonicity,[status(thm)],[353]) ).
tff(355,plain,
join(b,meet(b,c)) = join(b,join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c))))),
inference(symmetry,[status(thm)],[354]) ).
tff(356,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,c),b) = join(b,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(357,plain,
join(meet(b,c),b) = join(b,meet(b,c)),
inference(unit_resolution,[status(thm)],[356,60]) ).
tff(358,plain,
meet(meet(b,c),b) = join(meet(b,meet(b,c)),meet(b,meet(b,c))),
inference(transitivity,[status(thm)],[350,348]) ).
tff(359,plain,
join(meet(c,b),meet(meet(b,c),b)) = join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))),
inference(monotonicity,[status(thm)],[323,358]) ).
tff(360,plain,
join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))) = join(meet(c,b),meet(meet(b,c),b)),
inference(symmetry,[status(thm)],[359]) ).
tff(361,plain,
join(join(meet(b,meet(b,c)),meet(b,meet(b,c))),meet(b,c)) = join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))),
inference(symmetry,[status(thm)],[352]) ).
tff(362,plain,
meet(b,c) = join(join(meet(b,meet(b,c)),meet(b,meet(b,c))),meet(b,c)),
inference(symmetry,[status(thm)],[341]) ).
tff(363,plain,
meet(b,c) = join(meet(c,b),meet(meet(b,c),b)),
inference(transitivity,[status(thm)],[362,361,360]) ).
tff(364,plain,
join(meet(b,c),b) = join(join(meet(c,b),meet(meet(b,c),b)),b),
inference(monotonicity,[status(thm)],[363]) ).
tff(365,plain,
join(join(meet(c,b),meet(meet(b,c),b)),b) = join(meet(b,c),b),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(c,b),meet(meet(b,c),b)),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(367,plain,
join(join(meet(c,b),meet(meet(b,c),b)),b) = b,
inference(unit_resolution,[status(thm)],[366,18]) ).
tff(368,plain,
b = join(join(meet(c,b),meet(meet(b,c),b)),b),
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
b = join(b,join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c))))),
inference(transitivity,[status(thm)],[368,365,357,355]) ).
tff(370,plain,
meet(meet(b,c),b) = meet(meet(b,c),join(b,join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))))),
inference(monotonicity,[status(thm)],[369]) ).
tff(371,plain,
meet(meet(b,c),join(b,join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))))) = meet(meet(b,c),b),
inference(symmetry,[status(thm)],[370]) ).
tff(372,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,c),join(b,join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))))) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(373,plain,
meet(meet(b,c),join(b,join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))))) = meet(b,c),
inference(unit_resolution,[status(thm)],[372,33]) ).
tff(374,plain,
meet(b,c) = meet(meet(b,c),join(b,join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))))),
inference(symmetry,[status(thm)],[373]) ).
tff(375,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,c),join(b,join(meet(b,c),a))) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(376,plain,
meet(meet(b,c),join(b,join(meet(b,c),a))) = meet(b,c),
inference(unit_resolution,[status(thm)],[375,33]) ).
tff(377,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(378,plain,
join(meet(b,c),a) = join(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[377,60]) ).
tff(379,plain,
join(b,join(meet(b,c),a)) = join(b,join(a,meet(b,c))),
inference(monotonicity,[status(thm)],[378]) ).
tff(380,plain,
join(b,join(a,meet(b,c))) = join(b,join(meet(b,c),a)),
inference(symmetry,[status(thm)],[379]) ).
tff(381,plain,
meet(meet(b,c),join(b,join(a,meet(b,c)))) = meet(meet(b,c),join(b,join(meet(b,c),a))),
inference(monotonicity,[status(thm)],[380]) ).
tff(382,plain,
meet(meet(b,c),join(b,join(a,meet(b,c)))) = join(meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c))),meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c)))),
inference(transitivity,[status(thm)],[381,376,374,371,350,348,347]) ).
tff(383,plain,
join(meet(meet(b,c),join(b,join(a,meet(b,c)))),meet(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c))))) = join(join(meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c))),meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c)))),join(meet(a,b),meet(b,c))),
inference(monotonicity,[status(thm)],[382,335]) ).
tff(384,plain,
join(join(meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c))),meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c)))),join(meet(a,b),meet(b,c))) = join(meet(meet(b,c),join(b,join(a,meet(b,c)))),meet(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c))))),
inference(symmetry,[status(thm)],[383]) ).
tff(385,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c))),meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c)))),join(meet(a,b),meet(b,c))) = join(meet(a,b),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(386,plain,
join(join(meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c))),meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c)))),join(meet(a,b),meet(b,c))) = join(meet(a,b),meet(b,c)),
inference(unit_resolution,[status(thm)],[385,18]) ).
tff(387,plain,
join(meet(a,b),meet(b,c)) = join(join(meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c))),meet(join(meet(b,meet(b,c)),meet(b,meet(b,c))),join(meet(a,b),meet(b,c)))),join(meet(a,b),meet(b,c))),
inference(symmetry,[status(thm)],[386]) ).
tff(388,plain,
join(meet(a,b),meet(b,c)) = join(meet(meet(b,c),join(b,join(a,meet(b,c)))),meet(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c))))),
inference(transitivity,[status(thm)],[387,384]) ).
tff(389,plain,
join(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c)))) = join(join(meet(meet(b,c),join(b,join(a,meet(b,c)))),meet(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c))))),join(b,join(a,meet(b,c)))),
inference(monotonicity,[status(thm)],[388]) ).
tff(390,plain,
join(join(meet(meet(b,c),join(b,join(a,meet(b,c)))),meet(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c))))),join(b,join(a,meet(b,c)))) = join(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c)))),
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(b,c),join(b,join(a,meet(b,c)))),meet(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c))))),join(b,join(a,meet(b,c)))) = join(b,join(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(392,plain,
join(join(meet(meet(b,c),join(b,join(a,meet(b,c)))),meet(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c))))),join(b,join(a,meet(b,c)))) = join(b,join(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[391,18]) ).
tff(393,plain,
join(b,join(a,meet(b,c))) = join(join(meet(meet(b,c),join(b,join(a,meet(b,c)))),meet(join(meet(a,b),meet(b,c)),join(b,join(a,meet(b,c))))),join(b,join(a,meet(b,c)))),
inference(symmetry,[status(thm)],[392]) ).
tff(394,plain,
join(b,join(a,meet(b,c))) = join(join(b,join(a,meet(b,c))),join(meet(a,b),meet(b,c))),
inference(transitivity,[status(thm)],[393,390,317]) ).
tff(395,plain,
meet(meet(a,b),join(b,join(a,meet(b,c)))) = meet(meet(a,b),join(join(b,join(a,meet(b,c))),join(meet(a,b),meet(b,c)))),
inference(monotonicity,[status(thm)],[394]) ).
tff(396,plain,
meet(meet(a,b),join(join(b,join(a,meet(b,c))),join(meet(a,b),meet(b,c)))) = meet(meet(a,b),join(b,join(a,meet(b,c)))),
inference(symmetry,[status(thm)],[395]) ).
tff(397,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,b),join(join(b,join(a,meet(b,c))),join(meet(a,b),meet(b,c)))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(398,plain,
meet(meet(a,b),join(join(b,join(a,meet(b,c))),join(meet(a,b),meet(b,c)))) = meet(a,b),
inference(unit_resolution,[status(thm)],[397,33]) ).
tff(399,plain,
meet(a,b) = meet(meet(a,b),join(join(b,join(a,meet(b,c))),join(meet(a,b),meet(b,c)))),
inference(symmetry,[status(thm)],[398]) ).
tff(400,plain,
meet(a,b) = meet(join(b,join(a,meet(b,c))),meet(a,b)),
inference(transitivity,[status(thm)],[399,396,314]) ).
tff(401,plain,
join(meet(meet(a,b),c),meet(a,b)) = join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),
inference(monotonicity,[status(thm)],[50,400]) ).
tff(402,plain,
meet(join(meet(meet(a,b),c),meet(a,b)),join(meet(c,a),meet(a,b))) = meet(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(meet(c,a),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)))),
inference(monotonicity,[status(thm)],[401,311]) ).
tff(403,plain,
meet(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(meet(c,a),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)))) = meet(join(meet(meet(a,b),c),meet(a,b)),join(meet(c,a),meet(a,b))),
inference(symmetry,[status(thm)],[402]) ).
tff(404,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(meet(c,a),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)))) = join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(405,plain,
meet(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(meet(c,a),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)))) = join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),
inference(unit_resolution,[status(thm)],[404,33]) ).
tff(406,plain,
join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))) = meet(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(meet(c,a),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)))),
inference(symmetry,[status(thm)],[405]) ).
tff(407,plain,
join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))) = meet(join(meet(meet(a,b),c),meet(a,b)),join(meet(c,a),meet(a,b))),
inference(transitivity,[status(thm)],[406,403]) ).
tff(408,plain,
meet(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)))) = meet(meet(join(meet(meet(a,b),c),meet(a,b)),join(meet(c,a),meet(a,b))),meet(a,b)),
inference(monotonicity,[status(thm)],[407,309]) ).
tff(409,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)))) = join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(410,plain,
meet(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)))) = join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),
inference(unit_resolution,[status(thm)],[409,33]) ).
tff(411,plain,
join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))) = meet(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),join(join(meet(c,meet(a,b)),meet(join(b,join(a,meet(b,c))),meet(a,b))),meet(a,b)))),
inference(symmetry,[status(thm)],[410]) ).
tff(412,plain,
join(meet(meet(a,b),c),meet(a,b)) = meet(a,b),
inference(transitivity,[status(thm)],[401,411,408,305]) ).
tff(413,plain,
join(a,join(meet(meet(a,b),c),meet(a,b))) = join(a,meet(a,b)),
inference(monotonicity,[status(thm)],[412]) ).
tff(414,plain,
join(a,meet(a,b)) = join(a,join(meet(meet(a,b),c),meet(a,b))),
inference(symmetry,[status(thm)],[413]) ).
tff(415,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,meet(a,b)) = join(meet(a,b),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(416,plain,
join(a,meet(a,b)) = join(meet(a,b),a),
inference(unit_resolution,[status(thm)],[415,60]) ).
tff(417,plain,
join(meet(a,b),a) = join(a,meet(a,b)),
inference(symmetry,[status(thm)],[416]) ).
tff(418,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,a) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(419,plain,
meet(b,a) = meet(a,b),
inference(unit_resolution,[status(thm)],[418,44]) ).
tff(420,plain,
join(meet(b,a),meet(b,a)) = join(meet(a,b),meet(a,b)),
inference(monotonicity,[status(thm)],[419,419]) ).
tff(421,plain,
join(meet(a,b),meet(a,b)) = join(meet(b,a),meet(b,a)),
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(a,b),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(423,plain,
join(meet(a,b),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[422,136]) ).
tff(424,plain,
meet(a,b) = join(meet(a,b),meet(a,b)),
inference(symmetry,[status(thm)],[423]) ).
tff(425,plain,
meet(a,b) = join(meet(b,a),meet(b,a)),
inference(transitivity,[status(thm)],[424,421]) ).
tff(426,plain,
join(meet(a,b),a) = join(join(meet(b,a),meet(b,a)),a),
inference(monotonicity,[status(thm)],[425]) ).
tff(427,plain,
join(join(meet(b,a),meet(b,a)),a) = join(meet(a,b),a),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(b,a),meet(b,a)),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(429,plain,
join(join(meet(b,a),meet(b,a)),a) = a,
inference(unit_resolution,[status(thm)],[428,18]) ).
tff(430,plain,
a = join(join(meet(b,a),meet(b,a)),a),
inference(symmetry,[status(thm)],[429]) ).
tff(431,plain,
a = join(a,join(meet(meet(a,b),c),meet(a,b))),
inference(transitivity,[status(thm)],[430,427,417,414]) ).
tff(432,plain,
meet(meet(meet(a,b),c),a) = meet(meet(meet(a,b),c),join(a,join(meet(meet(a,b),c),meet(a,b)))),
inference(monotonicity,[status(thm)],[431]) ).
tff(433,plain,
meet(meet(meet(a,b),c),a) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[432,303]) ).
tff(434,plain,
join(meet(meet(meet(a,b),c),a),meet(join(b,join(c,join(meet(a,b),join(c,a)))),a)) = join(meet(meet(a,b),c),a),
inference(monotonicity,[status(thm)],[433,301]) ).
tff(435,plain,
join(join(meet(meet(meet(a,b),c),a),meet(join(b,join(c,join(meet(a,b),join(c,a)))),a)),a) = join(join(meet(meet(a,b),c),a),a),
inference(monotonicity,[status(thm)],[434]) ).
tff(436,plain,
join(join(meet(meet(a,b),c),a),a) = join(join(meet(meet(meet(a,b),c),a),meet(join(b,join(c,join(meet(a,b),join(c,a)))),a)),a),
inference(symmetry,[status(thm)],[435]) ).
tff(437,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,join(meet(meet(a,b),c),a)) = join(join(meet(meet(a,b),c),a),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(438,plain,
join(a,join(meet(meet(a,b),c),a)) = join(join(meet(meet(a,b),c),a),a),
inference(unit_resolution,[status(thm)],[437,60]) ).
tff(439,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(meet(meet(a,b),c),join(a,meet(join(meet(a,b),a),join(meet(a,b),c))))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(440,plain,
meet(a,join(meet(meet(a,b),c),join(a,meet(join(meet(a,b),a),join(meet(a,b),c))))) = a,
inference(unit_resolution,[status(thm)],[439,33]) ).
tff(441,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,b),a),meet(join(meet(a,b),c),a)),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(442,plain,
join(join(meet(meet(a,b),a),meet(join(meet(a,b),c),a)),a) = a,
inference(unit_resolution,[status(thm)],[441,18]) ).
tff(443,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,b),c),join(meet(a,b),a)) = meet(join(meet(a,b),a),join(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(444,plain,
meet(join(meet(a,b),c),join(meet(a,b),a)) = meet(join(meet(a,b),a),join(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[443,44]) ).
tff(445,plain,
a = join(meet(a,b),a),
inference(transitivity,[status(thm)],[430,427]) ).
tff(446,plain,
meet(join(meet(a,b),c),a) = meet(join(meet(a,b),c),join(meet(a,b),a)),
inference(monotonicity,[status(thm)],[445]) ).
tff(447,plain,
meet(join(meet(a,b),c),a) = meet(join(meet(a,b),a),join(meet(a,b),c)),
inference(transitivity,[status(thm)],[446,444]) ).
tff(448,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(a,meet(a,b)),join(c,meet(a,b))),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(449,plain,
meet(meet(join(a,meet(a,b)),join(c,meet(a,b))),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[448,7]) ).
tff(450,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(a,b),meet(join(a,meet(a,b)),join(c,meet(a,b)))) = meet(meet(join(a,meet(a,b)),join(c,meet(a,b))),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(451,plain,
meet(meet(a,b),meet(join(a,meet(a,b)),join(c,meet(a,b)))) = meet(meet(join(a,meet(a,b)),join(c,meet(a,b))),meet(a,b)),
inference(unit_resolution,[status(thm)],[450,44]) ).
tff(452,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,meet(a,b)) = join(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(453,plain,
join(c,meet(a,b)) = join(meet(a,b),c),
inference(unit_resolution,[status(thm)],[452,60]) ).
tff(454,plain,
meet(join(a,meet(a,b)),join(c,meet(a,b))) = meet(join(meet(a,b),a),join(meet(a,b),c)),
inference(monotonicity,[status(thm)],[416,453]) ).
tff(455,plain,
meet(join(meet(a,b),a),join(meet(a,b),c)) = meet(join(a,meet(a,b)),join(c,meet(a,b))),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c))) = meet(meet(a,b),meet(join(a,meet(a,b)),join(c,meet(a,b)))),
inference(monotonicity,[status(thm)],[455]) ).
tff(457,plain,
meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c))) = meet(a,b),
inference(transitivity,[status(thm)],[456,451,449]) ).
tff(458,plain,
join(meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c))),meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c)))) = join(meet(a,b),meet(a,b)),
inference(monotonicity,[status(thm)],[457,457]) ).
tff(459,plain,
join(meet(a,b),meet(a,b)) = join(meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c))),meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c)))),
inference(symmetry,[status(thm)],[458]) ).
tff(460,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,b),join(join(meet(a,b),meet(c,a)),join(meet(a,b),a))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(461,plain,
meet(meet(a,b),join(join(meet(a,b),meet(c,a)),join(meet(a,b),a))) = meet(a,b),
inference(unit_resolution,[status(thm)],[460,33]) ).
tff(462,plain,
join(meet(a,b),a) = a,
inference(transitivity,[status(thm)],[426,429]) ).
tff(463,plain,
join(meet(b,a),meet(c,a)) = join(meet(a,b),meet(c,a)),
inference(monotonicity,[status(thm)],[419]) ).
tff(464,plain,
join(meet(a,b),meet(c,a)) = join(meet(b,a),meet(c,a)),
inference(symmetry,[status(thm)],[463]) ).
tff(465,plain,
join(join(meet(a,b),meet(c,a)),join(meet(a,b),a)) = join(join(meet(b,a),meet(c,a)),a),
inference(monotonicity,[status(thm)],[464,462]) ).
tff(466,plain,
join(join(meet(b,a),meet(c,a)),a) = join(join(meet(a,b),meet(c,a)),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[465]) ).
tff(467,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(b,a),meet(c,a)),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(468,plain,
join(join(meet(b,a),meet(c,a)),a) = a,
inference(unit_resolution,[status(thm)],[467,18]) ).
tff(469,plain,
a = join(join(meet(b,a),meet(c,a)),a),
inference(symmetry,[status(thm)],[468]) ).
tff(470,plain,
a = join(join(meet(a,b),meet(c,a)),join(meet(a,b),a)),
inference(transitivity,[status(thm)],[469,466]) ).
tff(471,plain,
meet(meet(a,b),a) = meet(meet(a,b),join(join(meet(a,b),meet(c,a)),join(meet(a,b),a))),
inference(monotonicity,[status(thm)],[470]) ).
tff(472,plain,
meet(meet(a,b),a) = join(meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c))),meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c)))),
inference(transitivity,[status(thm)],[471,461,424,459]) ).
tff(473,plain,
join(meet(meet(a,b),a),meet(join(meet(a,b),c),a)) = join(join(meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c))),meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c)))),meet(join(meet(a,b),a),join(meet(a,b),c))),
inference(monotonicity,[status(thm)],[472,447]) ).
tff(474,plain,
join(join(meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c))),meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c)))),meet(join(meet(a,b),a),join(meet(a,b),c))) = join(meet(meet(a,b),a),meet(join(meet(a,b),c),a)),
inference(symmetry,[status(thm)],[473]) ).
tff(475,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c))),meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c)))),meet(join(meet(a,b),a),join(meet(a,b),c))) = meet(join(meet(a,b),a),join(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(476,plain,
join(join(meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c))),meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c)))),meet(join(meet(a,b),a),join(meet(a,b),c))) = meet(join(meet(a,b),a),join(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[475,18]) ).
tff(477,plain,
meet(join(meet(a,b),a),join(meet(a,b),c)) = join(join(meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c))),meet(meet(a,b),meet(join(meet(a,b),a),join(meet(a,b),c)))),meet(join(meet(a,b),a),join(meet(a,b),c))),
inference(symmetry,[status(thm)],[476]) ).
tff(478,plain,
meet(join(meet(a,b),a),join(meet(a,b),c)) = join(meet(meet(a,b),a),meet(join(meet(a,b),c),a)),
inference(transitivity,[status(thm)],[477,474]) ).
tff(479,plain,
join(meet(join(meet(a,b),a),join(meet(a,b),c)),a) = join(join(meet(meet(a,b),a),meet(join(meet(a,b),c),a)),a),
inference(monotonicity,[status(thm)],[478]) ).
tff(480,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,meet(join(meet(a,b),a),join(meet(a,b),c))) = join(meet(join(meet(a,b),a),join(meet(a,b),c)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(481,plain,
join(a,meet(join(meet(a,b),a),join(meet(a,b),c))) = join(meet(join(meet(a,b),a),join(meet(a,b),c)),a),
inference(unit_resolution,[status(thm)],[480,60]) ).
tff(482,plain,
join(a,meet(join(meet(a,b),a),join(meet(a,b),c))) = a,
inference(transitivity,[status(thm)],[481,479,442]) ).
tff(483,plain,
join(meet(meet(a,b),c),join(a,meet(join(meet(a,b),a),join(meet(a,b),c)))) = join(meet(meet(a,b),c),a),
inference(monotonicity,[status(thm)],[482]) ).
tff(484,plain,
join(meet(meet(a,b),c),a) = join(meet(meet(a,b),c),join(a,meet(join(meet(a,b),a),join(meet(a,b),c)))),
inference(symmetry,[status(thm)],[483]) ).
tff(485,plain,
meet(a,join(meet(meet(a,b),c),a)) = meet(a,join(meet(meet(a,b),c),join(a,meet(join(meet(a,b),a),join(meet(a,b),c))))),
inference(monotonicity,[status(thm)],[484]) ).
tff(486,plain,
meet(a,join(meet(meet(a,b),c),a)) = a,
inference(transitivity,[status(thm)],[485,440]) ).
tff(487,plain,
meet(a,join(meet(meet(a,b),c),a)) = join(meet(join(meet(a,b),join(c,a)),a),meet(c,a)),
inference(transitivity,[status(thm)],[485,440,286,283,281,278]) ).
tff(488,plain,
join(meet(a,join(meet(meet(a,b),c),a)),meet(a,join(meet(meet(a,b),c),a))) = join(join(meet(join(meet(a,b),join(c,a)),a),meet(c,a)),a),
inference(monotonicity,[status(thm)],[487,486]) ).
tff(489,plain,
join(join(meet(join(meet(a,b),join(c,a)),a),meet(c,a)),a) = join(meet(a,join(meet(meet(a,b),c),a)),meet(a,join(meet(meet(a,b),c),a))),
inference(symmetry,[status(thm)],[488]) ).
tff(490,plain,
a = join(meet(a,join(meet(meet(a,b),c),a)),meet(a,join(meet(meet(a,b),c),a))),
inference(transitivity,[status(thm)],[292,489]) ).
tff(491,plain,
join(a,join(meet(meet(a,b),c),a)) = join(join(meet(a,join(meet(meet(a,b),c),a)),meet(a,join(meet(meet(a,b),c),a))),join(meet(meet(a,b),c),a)),
inference(monotonicity,[status(thm)],[490]) ).
tff(492,plain,
join(join(meet(a,join(meet(meet(a,b),c),a)),meet(a,join(meet(meet(a,b),c),a))),join(meet(meet(a,b),c),a)) = join(a,join(meet(meet(a,b),c),a)),
inference(symmetry,[status(thm)],[491]) ).
tff(493,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(a,join(meet(meet(a,b),c),a)),meet(a,join(meet(meet(a,b),c),a))),join(meet(meet(a,b),c),a)) = join(meet(meet(a,b),c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(494,plain,
join(join(meet(a,join(meet(meet(a,b),c),a)),meet(a,join(meet(meet(a,b),c),a))),join(meet(meet(a,b),c),a)) = join(meet(meet(a,b),c),a),
inference(unit_resolution,[status(thm)],[493,18]) ).
tff(495,plain,
join(meet(meet(a,b),c),a) = join(join(meet(a,join(meet(meet(a,b),c),a)),meet(a,join(meet(meet(a,b),c),a))),join(meet(meet(a,b),c),a)),
inference(symmetry,[status(thm)],[494]) ).
tff(496,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,meet(meet(a,b),c)) = join(meet(meet(a,b),c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(497,plain,
join(a,meet(meet(a,b),c)) = join(meet(meet(a,b),c),a),
inference(unit_resolution,[status(thm)],[496,60]) ).
tff(498,plain,
join(meet(meet(a,b),c),a) = a,
inference(transitivity,[status(thm)],[495,492,438,436,245]) ).
tff(499,plain,
join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)) = join(a,meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[498]) ).
tff(500,plain,
join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)) = a,
inference(transitivity,[status(thm)],[499,497,495,492,438,436,245]) ).
tff(501,plain,
meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(c,meet(meet(a,b),c))) = meet(a,c),
inference(monotonicity,[status(thm)],[500,243]) ).
tff(502,plain,
meet(a,c) = meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(c,meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[501]) ).
tff(503,plain,
meet(c,a) = meet(a,c),
inference(symmetry,[status(thm)],[140]) ).
tff(504,plain,
meet(c,a) = meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(c,meet(meet(a,b),c))),
inference(transitivity,[status(thm)],[503,502]) ).
tff(505,plain,
meet(meet(c,a),meet(meet(a,b),c)) = meet(meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(c,meet(meet(a,b),c))),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[504]) ).
tff(506,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(meet(a,b),c),meet(c,a)) = meet(meet(c,a),meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(507,plain,
meet(meet(meet(a,b),c),meet(c,a)) = meet(meet(c,a),meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[506,44]) ).
tff(508,plain,
meet(meet(meet(a,b),c),meet(c,a)) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[507,505,127]) ).
tff(509,plain,
join(meet(meet(meet(a,b),c),meet(c,a)),meet(meet(a,b),meet(c,a))) = join(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))),
inference(monotonicity,[status(thm)],[508,125]) ).
tff(510,plain,
join(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))) = join(meet(meet(meet(a,b),c),meet(c,a)),meet(meet(a,b),meet(c,a))),
inference(symmetry,[status(thm)],[509]) ).
tff(511,plain,
join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))) = join(meet(meet(meet(a,b),c),meet(c,a)),meet(meet(a,b),meet(c,a))),
inference(transitivity,[status(thm)],[119,118,510]) ).
tff(512,plain,
join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(c,a)) = join(join(meet(meet(meet(a,b),c),meet(c,a)),meet(meet(a,b),meet(c,a))),meet(c,a)),
inference(monotonicity,[status(thm)],[511]) ).
tff(513,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(c,a),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))) = join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(514,plain,
join(meet(c,a),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))) = join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(c,a)),
inference(unit_resolution,[status(thm)],[513,60]) ).
tff(515,plain,
join(meet(c,a),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))) = meet(c,a),
inference(transitivity,[status(thm)],[514,512,123]) ).
tff(516,plain,
meet(join(meet(c,a),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))))) = meet(meet(c,a),meet(a,b)),
inference(monotonicity,[status(thm)],[515,121]) ).
tff(517,plain,
meet(meet(join(meet(c,a),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))))),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))) = meet(meet(meet(c,a),meet(a,b)),join(meet(meet(a,b),c),join(meet(meet(c,a),meet(a,b)),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))))),
inference(monotonicity,[status(thm)],[516,120]) ).
tff(518,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(meet(c,a),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))))),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))) = join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(519,plain,
meet(meet(join(meet(c,a),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))))),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))) = join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),
inference(unit_resolution,[status(thm)],[518,7]) ).
tff(520,plain,
join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))) = meet(meet(join(meet(c,a),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))))),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))),
inference(symmetry,[status(thm)],[519]) ).
tff(521,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(c,join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(c,a)))) = join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(522,plain,
meet(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(c,join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(c,a)))) = join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),
inference(unit_resolution,[status(thm)],[521,33]) ).
tff(523,plain,
join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(c,a)) = join(meet(a,c),meet(a,c)),
inference(transitivity,[status(thm)],[512,123,151,150]) ).
tff(524,plain,
join(c,join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(c,a))) = join(c,join(meet(a,c),meet(a,c))),
inference(monotonicity,[status(thm)],[523]) ).
tff(525,plain,
join(c,join(meet(a,c),meet(a,c))) = join(c,join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(c,a))),
inference(symmetry,[status(thm)],[524]) ).
tff(526,plain,
c = join(c,join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(c,a))),
inference(transitivity,[status(thm)],[148,251,525]) ).
tff(527,plain,
meet(meet(meet(c,a),meet(a,b)),join(meet(meet(a,b),c),join(meet(meet(c,a),meet(a,b)),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))))) = meet(meet(join(meet(c,a),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))))),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))),
inference(symmetry,[status(thm)],[517]) ).
tff(528,plain,
meet(meet(c,a),meet(a,b)) = meet(meet(meet(c,a),meet(a,b)),join(meet(meet(a,b),c),join(meet(meet(c,a),meet(a,b)),join(meet(join(meet(meet(a,b),c),a),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))))),
inference(symmetry,[status(thm)],[110]) ).
tff(529,plain,
meet(meet(c,a),meet(a,b)) = join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),
inference(transitivity,[status(thm)],[528,527,519]) ).
tff(530,plain,
meet(meet(meet(c,a),meet(a,b)),c) = meet(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(c,join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(c,a)))),
inference(monotonicity,[status(thm)],[529,526]) ).
tff(531,plain,
join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) = meet(meet(c,a),meet(a,b)),
inference(transitivity,[status(thm)],[100,97,92,90,83,81,78,11]) ).
tff(532,plain,
meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),c) = meet(meet(meet(c,a),meet(a,b)),c),
inference(monotonicity,[status(thm)],[531]) ).
tff(533,plain,
meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),c) = meet(meet(c,a),meet(a,b)),
inference(transitivity,[status(thm)],[532,530,522,520,517,110]) ).
tff(534,plain,
join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),c),meet(meet(a,b),c)) = join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),
inference(monotonicity,[status(thm)],[533,50]) ).
tff(535,plain,
join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))) = join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),c),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[534]) ).
tff(536,plain,
join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) = join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),c),meet(meet(a,b),c)),
inference(transitivity,[status(thm)],[100,97,92,90,83,81,78,11,528,527,519,535]) ).
tff(537,plain,
join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),c) = join(join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),c),meet(meet(a,b),c)),c),
inference(monotonicity,[status(thm)],[536]) ).
tff(538,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(539,plain,
join(c,join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),c),
inference(unit_resolution,[status(thm)],[538,60]) ).
tff(540,plain,
join(c,join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = c,
inference(transitivity,[status(thm)],[539,537,108]) ).
tff(541,plain,
join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) = join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),
inference(transitivity,[status(thm)],[100,97,92,90,83,81,78,11,528,527,519]) ).
tff(542,plain,
join(meet(a,b),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b)))),
inference(monotonicity,[status(thm)],[541]) ).
tff(543,plain,
join(meet(a,b),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = meet(a,b),
inference(transitivity,[status(thm)],[542,62,65]) ).
tff(544,plain,
meet(join(meet(a,b),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),join(c,join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))))) = meet(meet(a,b),c),
inference(monotonicity,[status(thm)],[543,540]) ).
tff(545,plain,
meet(meet(a,b),c) = meet(join(meet(a,b),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),join(c,join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))))),
inference(symmetry,[status(thm)],[544]) ).
tff(546,plain,
meet(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))) = meet(meet(join(meet(a,b),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),join(c,join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))))),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),
inference(monotonicity,[status(thm)],[545,106]) ).
tff(547,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)) = meet(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(548,plain,
meet(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)) = meet(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))),
inference(unit_resolution,[status(thm)],[547,44]) ).
tff(549,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b)))) = join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(550,plain,
meet(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b)))) = join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),
inference(unit_resolution,[status(thm)],[549,33]) ).
tff(551,plain,
join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b))) = join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b)),
inference(monotonicity,[status(thm)],[65]) ).
tff(552,plain,
join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b)) = join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b))),
inference(symmetry,[status(thm)],[551]) ).
tff(553,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),meet(meet(a,b),c)) = join(meet(meet(a,b),c),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(554,plain,
join(meet(a,b),meet(meet(a,b),c)) = join(meet(meet(a,b),c),meet(a,b)),
inference(unit_resolution,[status(thm)],[553,60]) ).
tff(555,plain,
join(meet(a,b),meet(meet(a,b),c)) = join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b))),
inference(transitivity,[status(thm)],[554,401,411,408,305,66,552]) ).
tff(556,plain,
meet(join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)),join(meet(a,b),meet(meet(a,b),c))) = meet(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),join(join(meet(meet(c,a),meet(a,b)),meet(c,meet(a,b))),meet(a,b)))),
inference(monotonicity,[status(thm)],[51,555]) ).
tff(557,plain,
meet(join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)),join(meet(a,b),meet(meet(a,b),c))) = meet(meet(c,a),meet(a,b)),
inference(transitivity,[status(thm)],[556,550,520,517,110]) ).
tff(558,plain,
meet(meet(join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)),join(meet(a,b),meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[557]) ).
tff(559,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)),join(meet(a,b),meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(560,plain,
meet(meet(join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)),join(meet(a,b),meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[559,7]) ).
tff(561,plain,
meet(meet(a,b),c) = meet(meet(join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)),join(meet(a,b),meet(meet(a,b),c))),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[560]) ).
tff(562,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,meet(b,c)),c),meet(meet(a,b),c)),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(563,plain,
join(join(meet(meet(a,meet(b,c)),c),meet(meet(a,b),c)),c) = c,
inference(unit_resolution,[status(thm)],[562,18]) ).
tff(564,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,meet(b,c)),join(c,join(meet(a,meet(b,c)),meet(b,c)))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(565,plain,
meet(meet(a,meet(b,c)),join(c,join(meet(a,meet(b,c)),meet(b,c)))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[564,33]) ).
tff(566,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(meet(a,b),c),a),meet(b,c)),meet(join(meet(meet(a,b),c),a),meet(b,c))),meet(b,c)) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(567,plain,
join(join(meet(join(meet(meet(a,b),c),a),meet(b,c)),meet(join(meet(meet(a,b),c),a),meet(b,c))),meet(b,c)) = meet(b,c),
inference(unit_resolution,[status(thm)],[566,18]) ).
tff(568,plain,
meet(join(meet(meet(a,b),c),a),meet(b,c)) = meet(a,meet(b,c)),
inference(monotonicity,[status(thm)],[498]) ).
tff(569,plain,
join(meet(join(meet(meet(a,b),c),a),meet(b,c)),meet(join(meet(meet(a,b),c),a),meet(b,c))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[568,568]) ).
tff(570,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = join(meet(join(meet(meet(a,b),c),a),meet(b,c)),meet(join(meet(meet(a,b),c),a),meet(b,c))),
inference(symmetry,[status(thm)],[569]) ).
tff(571,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(a,meet(b,c)),meet(a,meet(b,c))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(572,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[571,136]) ).
tff(573,plain,
meet(a,meet(b,c)) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(symmetry,[status(thm)],[572]) ).
tff(574,plain,
meet(a,meet(b,c)) = join(meet(join(meet(meet(a,b),c),a),meet(b,c)),meet(join(meet(meet(a,b),c),a),meet(b,c))),
inference(transitivity,[status(thm)],[573,570]) ).
tff(575,plain,
join(meet(a,meet(b,c)),meet(b,c)) = join(join(meet(join(meet(meet(a,b),c),a),meet(b,c)),meet(join(meet(meet(a,b),c),a),meet(b,c))),meet(b,c)),
inference(monotonicity,[status(thm)],[574]) ).
tff(576,plain,
join(meet(a,meet(b,c)),meet(b,c)) = meet(b,c),
inference(transitivity,[status(thm)],[575,567]) ).
tff(577,plain,
join(c,join(meet(a,meet(b,c)),meet(b,c))) = join(c,meet(b,c)),
inference(monotonicity,[status(thm)],[576]) ).
tff(578,plain,
join(c,meet(b,c)) = join(c,join(meet(a,meet(b,c)),meet(b,c))),
inference(symmetry,[status(thm)],[577]) ).
tff(579,plain,
join(c,join(c,meet(b,c))) = join(join(meet(join(c,meet(b,c)),join(c,meet(b,c))),meet(c,join(c,meet(b,c)))),join(c,meet(b,c))),
inference(symmetry,[status(thm)],[203]) ).
tff(580,plain,
join(join(c,meet(b,c)),c) = join(c,join(c,meet(b,c))),
inference(symmetry,[status(thm)],[179]) ).
tff(581,plain,
join(join(meet(b,c),meet(join(meet(a,b),join(c,a)),c)),c) = join(join(c,meet(b,c)),c),
inference(symmetry,[status(thm)],[177]) ).
tff(582,plain,
c = join(join(meet(b,c),meet(join(meet(a,b),join(c,a)),c)),c),
inference(symmetry,[status(thm)],[165]) ).
tff(583,plain,
c = join(c,join(meet(a,meet(b,c)),meet(b,c))),
inference(transitivity,[status(thm)],[582,581,580,579,205,578]) ).
tff(584,plain,
meet(meet(a,meet(b,c)),c) = meet(meet(a,meet(b,c)),join(c,join(meet(a,meet(b,c)),meet(b,c)))),
inference(monotonicity,[status(thm)],[583]) ).
tff(585,plain,
meet(meet(a,meet(b,c)),c) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[584,565]) ).
tff(586,plain,
join(meet(meet(a,meet(b,c)),c),meet(meet(a,b),c)) = join(meet(a,meet(b,c)),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[585]) ).
tff(587,plain,
join(meet(a,meet(b,c)),meet(meet(a,b),c)) = join(meet(meet(a,meet(b,c)),c),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[586]) ).
tff(588,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,meet(b,c)),meet(meet(a,b),c)) = join(meet(meet(a,b),c),meet(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(589,plain,
join(meet(a,meet(b,c)),meet(meet(a,b),c)) = join(meet(meet(a,b),c),meet(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[588,60]) ).
tff(590,plain,
join(meet(meet(a,b),c),meet(a,meet(b,c))) = join(meet(a,meet(b,c)),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[589]) ).
tff(591,plain,
join(meet(meet(a,b),c),meet(a,meet(b,c))) = join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(monotonicity,[status(thm)],[573]) ).
tff(592,plain,
join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(meet(meet(a,b),c),meet(a,meet(b,c))),
inference(symmetry,[status(thm)],[591]) ).
tff(593,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))))),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(594,plain,
join(join(meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))))),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(unit_resolution,[status(thm)],[593,18]) ).
tff(595,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(596,plain,
meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[595,33]) ).
tff(597,plain,
join(meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[596,596]) ).
tff(598,plain,
join(meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))))) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[597,572]) ).
tff(599,plain,
join(join(meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))))),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = join(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(monotonicity,[status(thm)],[598]) ).
tff(600,plain,
join(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = join(join(meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))))),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(symmetry,[status(thm)],[599]) ).
tff(601,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))) = join(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(602,plain,
join(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))) = join(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(unit_resolution,[status(thm)],[601,60]) ).
tff(603,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(604,plain,
meet(meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[603,7]) ).
tff(605,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,c),join(meet(meet(a,b),c),join(meet(b,c),meet(b,c)))) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(606,plain,
meet(meet(b,c),join(meet(meet(a,b),c),join(meet(b,c),meet(b,c)))) = meet(b,c),
inference(unit_resolution,[status(thm)],[605,33]) ).
tff(607,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(a,b),join(c,a)),meet(b,c)),meet(b,meet(b,c))),meet(b,c)) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(608,plain,
join(join(meet(join(meet(a,b),join(c,a)),meet(b,c)),meet(b,meet(b,c))),meet(b,c)) = meet(b,c),
inference(unit_resolution,[status(thm)],[607,18]) ).
tff(609,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(b,c),join(join(meet(a,b),join(c,a)),join(meet(b,c),c))) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(610,plain,
meet(meet(b,c),join(join(meet(a,b),join(c,a)),join(meet(b,c),c))) = meet(b,c),
inference(unit_resolution,[status(thm)],[609,33]) ).
tff(611,plain,
join(meet(b,c),c) = c,
inference(transitivity,[status(thm)],[174,206,203,179,177,165]) ).
tff(612,plain,
join(join(meet(a,b),join(c,a)),join(meet(b,c),c)) = join(join(meet(a,b),join(c,a)),c),
inference(monotonicity,[status(thm)],[611]) ).
tff(613,plain,
join(join(meet(a,b),join(c,a)),c) = join(join(meet(a,b),join(c,a)),join(meet(b,c),c)),
inference(symmetry,[status(thm)],[612]) ).
tff(614,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(meet(a,b),join(c,a)),c) = join(c,join(meet(a,b),join(c,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(615,plain,
join(join(meet(a,b),join(c,a)),c) = join(c,join(meet(a,b),join(c,a))),
inference(unit_resolution,[status(thm)],[614,60]) ).
tff(616,plain,
join(c,join(meet(a,b),join(c,a))) = join(join(meet(a,b),join(c,a)),c),
inference(symmetry,[status(thm)],[615]) ).
tff(617,plain,
join(meet(a,b),join(c,a)) = join(join(meet(a,b),join(c,a)),join(meet(b,c),c)),
inference(transitivity,[status(thm)],[263,260,616,613]) ).
tff(618,plain,
meet(meet(b,c),join(meet(a,b),join(c,a))) = meet(meet(b,c),join(join(meet(a,b),join(c,a)),join(meet(b,c),c))),
inference(monotonicity,[status(thm)],[617]) ).
tff(619,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,b),join(c,a)),meet(b,c)) = meet(meet(b,c),join(meet(a,b),join(c,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(620,plain,
meet(join(meet(a,b),join(c,a)),meet(b,c)) = meet(meet(b,c),join(meet(a,b),join(c,a))),
inference(unit_resolution,[status(thm)],[619,44]) ).
tff(621,plain,
meet(join(meet(a,b),join(c,a)),meet(b,c)) = meet(b,c),
inference(transitivity,[status(thm)],[620,618,610]) ).
tff(622,plain,
join(meet(join(meet(a,b),join(c,a)),meet(b,c)),meet(b,meet(b,c))) = join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))),
inference(monotonicity,[status(thm)],[621,348]) ).
tff(623,plain,
join(meet(b,c),join(meet(b,meet(b,c)),meet(b,meet(b,c)))) = join(meet(join(meet(a,b),join(c,a)),meet(b,c)),meet(b,meet(b,c))),
inference(symmetry,[status(thm)],[622]) ).
tff(624,plain,
meet(b,c) = join(meet(join(meet(a,b),join(c,a)),meet(b,c)),meet(b,meet(b,c))),
inference(transitivity,[status(thm)],[362,361,623]) ).
tff(625,plain,
join(meet(b,c),meet(b,c)) = join(join(meet(join(meet(a,b),join(c,a)),meet(b,c)),meet(b,meet(b,c))),meet(b,c)),
inference(monotonicity,[status(thm)],[624]) ).
tff(626,plain,
join(meet(b,c),meet(b,c)) = meet(b,c),
inference(transitivity,[status(thm)],[625,608]) ).
tff(627,plain,
join(meet(meet(a,b),c),join(meet(b,c),meet(b,c))) = join(meet(meet(a,b),c),meet(b,c)),
inference(monotonicity,[status(thm)],[626]) ).
tff(628,plain,
join(meet(meet(a,b),c),meet(b,c)) = join(meet(meet(a,b),c),join(meet(b,c),meet(b,c))),
inference(symmetry,[status(thm)],[627]) ).
tff(629,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(meet(a,b),c),b),meet(meet(b,c),b)),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(630,plain,
join(join(meet(meet(meet(a,b),c),b),meet(meet(b,c),b)),b) = b,
inference(unit_resolution,[status(thm)],[629,18]) ).
tff(631,plain,
meet(meet(b,c),b) = meet(b,c),
inference(transitivity,[status(thm)],[370,373]) ).
tff(632,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(meet(a,b),c),join(b,join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(633,plain,
meet(meet(meet(a,b),c),join(b,join(meet(meet(a,b),c),meet(a,b)))) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[632,33]) ).
tff(634,plain,
join(b,join(meet(meet(a,b),c),meet(a,b))) = join(b,meet(a,b)),
inference(monotonicity,[status(thm)],[412]) ).
tff(635,plain,
join(b,meet(a,b)) = join(b,join(meet(meet(a,b),c),meet(a,b))),
inference(symmetry,[status(thm)],[634]) ).
tff(636,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,meet(a,b)) = join(meet(a,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(637,plain,
join(b,meet(a,b)) = join(meet(a,b),b),
inference(unit_resolution,[status(thm)],[636,60]) ).
tff(638,plain,
join(meet(a,b),b) = join(b,meet(a,b)),
inference(symmetry,[status(thm)],[637]) ).
tff(639,plain,
join(meet(a,b),b) = join(join(meet(a,b),meet(a,b)),b),
inference(monotonicity,[status(thm)],[424]) ).
tff(640,plain,
join(join(meet(a,b),meet(a,b)),b) = join(meet(a,b),b),
inference(symmetry,[status(thm)],[639]) ).
tff(641,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(a,b),meet(a,b)),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(642,plain,
join(join(meet(a,b),meet(a,b)),b) = b,
inference(unit_resolution,[status(thm)],[641,18]) ).
tff(643,plain,
b = join(join(meet(a,b),meet(a,b)),b),
inference(symmetry,[status(thm)],[642]) ).
tff(644,plain,
b = join(b,join(meet(meet(a,b),c),meet(a,b))),
inference(transitivity,[status(thm)],[643,640,638,635]) ).
tff(645,plain,
meet(meet(meet(a,b),c),b) = meet(meet(meet(a,b),c),join(b,join(meet(meet(a,b),c),meet(a,b)))),
inference(monotonicity,[status(thm)],[644]) ).
tff(646,plain,
meet(meet(meet(a,b),c),b) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[645,633]) ).
tff(647,plain,
join(meet(meet(meet(a,b),c),b),meet(meet(b,c),b)) = join(meet(meet(a,b),c),meet(b,c)),
inference(monotonicity,[status(thm)],[646,631]) ).
tff(648,plain,
join(meet(meet(a,b),c),meet(b,c)) = join(meet(meet(meet(a,b),c),b),meet(meet(b,c),b)),
inference(symmetry,[status(thm)],[647]) ).
tff(649,plain,
join(join(meet(meet(a,b),c),meet(b,c)),b) = join(join(meet(meet(meet(a,b),c),b),meet(meet(b,c),b)),b),
inference(monotonicity,[status(thm)],[648]) ).
tff(650,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,join(meet(meet(a,b),c),meet(b,c))) = join(join(meet(meet(a,b),c),meet(b,c)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(651,plain,
join(b,join(meet(meet(a,b),c),meet(b,c))) = join(join(meet(meet(a,b),c),meet(b,c)),b),
inference(unit_resolution,[status(thm)],[650,60]) ).
tff(652,plain,
join(b,join(meet(meet(a,b),c),meet(b,c))) = b,
inference(transitivity,[status(thm)],[651,649,630]) ).
tff(653,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,b),c),meet(b,c)),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(654,plain,
join(join(meet(meet(a,b),c),meet(b,c)),c) = c,
inference(unit_resolution,[status(thm)],[653,18]) ).
tff(655,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,join(meet(meet(a,b),c),meet(b,c))) = join(join(meet(meet(a,b),c),meet(b,c)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(656,plain,
join(c,join(meet(meet(a,b),c),meet(b,c))) = join(join(meet(meet(a,b),c),meet(b,c)),c),
inference(unit_resolution,[status(thm)],[655,60]) ).
tff(657,plain,
join(c,join(meet(meet(a,b),c),meet(b,c))) = c,
inference(transitivity,[status(thm)],[656,654]) ).
tff(658,plain,
meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))) = meet(c,b),
inference(monotonicity,[status(thm)],[657,652]) ).
tff(659,plain,
meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))) = meet(b,c),
inference(transitivity,[status(thm)],[658,323]) ).
tff(660,plain,
meet(meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))) = meet(meet(b,c),join(meet(meet(a,b),c),join(meet(b,c),meet(b,c)))),
inference(monotonicity,[status(thm)],[659,628]) ).
tff(661,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))) = join(meet(meet(a,b),c),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(662,plain,
meet(meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))) = join(meet(meet(a,b),c),meet(b,c)),
inference(unit_resolution,[status(thm)],[661,7]) ).
tff(663,plain,
join(meet(meet(a,b),c),meet(b,c)) = meet(meet(join(c,join(meet(meet(a,b),c),meet(b,c))),join(b,join(meet(meet(a,b),c),meet(b,c)))),join(meet(meet(a,b),c),meet(b,c))),
inference(symmetry,[status(thm)],[662]) ).
tff(664,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,c),meet(meet(a,b),c)) = join(meet(meet(a,b),c),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(665,plain,
join(meet(b,c),meet(meet(a,b),c)) = join(meet(meet(a,b),c),meet(b,c)),
inference(unit_resolution,[status(thm)],[664,60]) ).
tff(666,plain,
join(meet(b,c),meet(meet(a,b),c)) = meet(b,c),
inference(transitivity,[status(thm)],[665,663,660,606]) ).
tff(667,plain,
meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))) = meet(a,meet(b,c)),
inference(monotonicity,[status(thm)],[500,666]) ).
tff(668,plain,
meet(a,meet(b,c)) = meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[667]) ).
tff(669,plain,
meet(meet(a,meet(b,c)),meet(meet(a,b),c)) = meet(meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[668]) ).
tff(670,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(meet(a,b),c),meet(a,meet(b,c))) = meet(meet(a,meet(b,c)),meet(meet(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(671,plain,
meet(meet(meet(a,b),c),meet(a,meet(b,c))) = meet(meet(a,meet(b,c)),meet(meet(a,b),c)),
inference(unit_resolution,[status(thm)],[670,44]) ).
tff(672,plain,
meet(meet(meet(a,b),c),meet(a,meet(b,c))) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[671,669,604]) ).
tff(673,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))) = meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(674,plain,
meet(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))) = meet(meet(a,meet(b,c)),join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(unit_resolution,[status(thm)],[673,44]) ).
tff(675,plain,
meet(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[674,596]) ).
tff(676,plain,
join(meet(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))),meet(meet(meet(a,b),c),meet(a,meet(b,c)))) = join(meet(a,meet(b,c)),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[675,672]) ).
tff(677,plain,
join(meet(a,meet(b,c)),meet(meet(a,b),c)) = join(meet(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))),meet(meet(meet(a,b),c),meet(a,meet(b,c)))),
inference(symmetry,[status(thm)],[676]) ).
tff(678,plain,
join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(meet(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))),meet(meet(meet(a,b),c),meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[592,590,677]) ).
tff(679,plain,
join(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))) = join(join(meet(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))),meet(meet(meet(a,b),c),meet(a,meet(b,c)))),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[678]) ).
tff(680,plain,
join(join(meet(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))),meet(meet(meet(a,b),c),meet(a,meet(b,c)))),meet(a,meet(b,c))) = join(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))),
inference(symmetry,[status(thm)],[679]) ).
tff(681,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))),meet(meet(meet(a,b),c),meet(a,meet(b,c)))),meet(a,meet(b,c))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(682,plain,
join(join(meet(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))),meet(meet(meet(a,b),c),meet(a,meet(b,c)))),meet(a,meet(b,c))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[681,18]) ).
tff(683,plain,
meet(a,meet(b,c)) = join(join(meet(join(meet(meet(a,b),c),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),meet(a,meet(b,c))),meet(meet(meet(a,b),c),meet(a,meet(b,c)))),meet(a,meet(b,c))),
inference(symmetry,[status(thm)],[682]) ).
tff(684,plain,
meet(a,meet(b,c)) = join(meet(meet(a,meet(b,c)),c),meet(meet(a,b),c)),
inference(transitivity,[status(thm)],[683,680,602,600,594,592,590,587]) ).
tff(685,plain,
join(meet(a,meet(b,c)),c) = join(join(meet(meet(a,meet(b,c)),c),meet(meet(a,b),c)),c),
inference(monotonicity,[status(thm)],[684]) ).
tff(686,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,meet(a,meet(b,c))) = join(meet(a,meet(b,c)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(687,plain,
join(c,meet(a,meet(b,c))) = join(meet(a,meet(b,c)),c),
inference(unit_resolution,[status(thm)],[686,60]) ).
tff(688,plain,
join(c,meet(a,meet(b,c))) = c,
inference(transitivity,[status(thm)],[687,685,563]) ).
tff(689,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,meet(b,c)),meet(a,b)),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(a,b))),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(690,plain,
join(join(meet(meet(a,meet(b,c)),meet(a,b)),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(a,b))),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[689,18]) ).
tff(691,plain,
meet(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)) = meet(meet(join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)),join(meet(a,b),meet(meet(a,b),c))),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[558]) ).
tff(692,plain,
meet(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))) = meet(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[548]) ).
tff(693,plain,
meet(meet(join(meet(a,b),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),join(c,join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))))),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))) = meet(meet(meet(a,b),c),meet(meet(c,a),meet(a,b))),
inference(symmetry,[status(thm)],[546]) ).
tff(694,plain,
join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))) = meet(meet(join(meet(a,b),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),join(c,join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))))),join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b))))),
inference(symmetry,[status(thm)],[102]) ).
tff(695,plain,
meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(a,b)) = meet(meet(meet(c,a),meet(a,b)),join(meet(a,b),join(meet(meet(c,a),meet(a,b)),meet(meet(a,b),c)))),
inference(monotonicity,[status(thm)],[531,67]) ).
tff(696,plain,
meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(a,b)) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[695,71,105,77,80,104,89,103,96,99,694,693,692,691,560]) ).
tff(697,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(join(meet(meet(a,b),c),a),meet(a,meet(b,c))),join(b,meet(a,meet(b,c)))),meet(a,meet(b,c))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(698,plain,
meet(meet(join(join(meet(meet(a,b),c),a),meet(a,meet(b,c))),join(b,meet(a,meet(b,c)))),meet(a,meet(b,c))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[697,7]) ).
tff(699,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,meet(b,c)),b),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),b)),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(700,plain,
join(join(meet(meet(a,meet(b,c)),b),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),b)),b) = b,
inference(unit_resolution,[status(thm)],[699,18]) ).
tff(701,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),join(b,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c)))) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(702,plain,
meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),join(b,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c)))) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),
inference(unit_resolution,[status(thm)],[701,33]) ).
tff(703,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(meet(a,b),c),a),meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c)) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(704,plain,
join(join(meet(join(meet(meet(a,b),c),a),meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c)) = meet(b,c),
inference(unit_resolution,[status(thm)],[703,18]) ).
tff(705,plain,
join(meet(join(meet(meet(a,b),c),a),meet(b,c)),meet(meet(a,b),meet(b,c))) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),
inference(monotonicity,[status(thm)],[568]) ).
tff(706,plain,
join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))) = join(meet(join(meet(meet(a,b),c),a),meet(b,c)),meet(meet(a,b),meet(b,c))),
inference(symmetry,[status(thm)],[705]) ).
tff(707,plain,
join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c)) = join(join(meet(join(meet(meet(a,b),c),a),meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c)),
inference(monotonicity,[status(thm)],[706]) ).
tff(708,plain,
join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c)) = meet(b,c),
inference(transitivity,[status(thm)],[707,704]) ).
tff(709,plain,
join(b,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c))) = join(b,meet(b,c)),
inference(monotonicity,[status(thm)],[708]) ).
tff(710,plain,
join(b,meet(b,c)) = join(b,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[709]) ).
tff(711,plain,
b = join(b,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c))),
inference(transitivity,[status(thm)],[368,365,357,710]) ).
tff(712,plain,
meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),b) = meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),join(b,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c)))),
inference(monotonicity,[status(thm)],[711]) ).
tff(713,plain,
meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),b) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),
inference(transitivity,[status(thm)],[712,702]) ).
tff(714,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,meet(b,c)),join(meet(meet(a,b),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(715,plain,
meet(meet(a,meet(b,c)),join(meet(meet(a,b),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c))))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[714,33]) ).
tff(716,plain,
join(meet(meet(a,b),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))) = join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[572]) ).
tff(717,plain,
join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c))) = join(meet(meet(a,b),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(symmetry,[status(thm)],[716]) ).
tff(718,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c))) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(719,plain,
join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c))) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),
inference(unit_resolution,[status(thm)],[718,60]) ).
tff(720,plain,
join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))) = join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c))),
inference(symmetry,[status(thm)],[719]) ).
tff(721,plain,
join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))) = join(meet(meet(a,b),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[720,717]) ).
tff(722,plain,
meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))) = meet(meet(a,meet(b,c)),join(meet(meet(a,b),meet(b,c)),join(meet(a,meet(b,c)),meet(a,meet(b,c))))),
inference(monotonicity,[status(thm)],[721]) ).
tff(723,plain,
meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[722,715]) ).
tff(724,plain,
join(meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[723,723]) ).
tff(725,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = join(meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))))),
inference(symmetry,[status(thm)],[724]) ).
tff(726,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,meet(b,c)),join(b,join(meet(a,meet(b,c)),meet(b,c)))) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(727,plain,
meet(meet(a,meet(b,c)),join(b,join(meet(a,meet(b,c)),meet(b,c)))) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[726,33]) ).
tff(728,plain,
join(b,join(meet(a,meet(b,c)),meet(b,c))) = join(b,meet(b,c)),
inference(monotonicity,[status(thm)],[576]) ).
tff(729,plain,
join(b,meet(b,c)) = join(b,join(meet(a,meet(b,c)),meet(b,c))),
inference(symmetry,[status(thm)],[728]) ).
tff(730,plain,
b = join(b,join(meet(a,meet(b,c)),meet(b,c))),
inference(transitivity,[status(thm)],[368,365,357,729]) ).
tff(731,plain,
meet(meet(a,meet(b,c)),b) = meet(meet(a,meet(b,c)),join(b,join(meet(a,meet(b,c)),meet(b,c)))),
inference(monotonicity,[status(thm)],[730]) ).
tff(732,plain,
meet(meet(a,meet(b,c)),b) = join(meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))))),
inference(transitivity,[status(thm)],[731,727,573,725]) ).
tff(733,plain,
join(meet(meet(a,meet(b,c)),b),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),b)) = join(join(meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))))),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),
inference(monotonicity,[status(thm)],[732,713]) ).
tff(734,plain,
join(join(meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))))),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))) = join(meet(meet(a,meet(b,c)),b),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),b)),
inference(symmetry,[status(thm)],[733]) ).
tff(735,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))))),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(736,plain,
join(join(meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))))),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),
inference(unit_resolution,[status(thm)],[735,18]) ).
tff(737,plain,
join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))) = join(join(meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))))),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),
inference(symmetry,[status(thm)],[736]) ).
tff(738,plain,
join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))) = join(meet(meet(a,meet(b,c)),b),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),b)),
inference(transitivity,[status(thm)],[737,734]) ).
tff(739,plain,
join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),b) = join(join(meet(meet(a,meet(b,c)),b),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),b)),b),
inference(monotonicity,[status(thm)],[738]) ).
tff(740,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))) = join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(741,plain,
join(b,join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))) = join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),b),
inference(unit_resolution,[status(thm)],[740,60]) ).
tff(742,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(meet(a,b),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(743,plain,
meet(meet(join(meet(a,b),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(a,b),c),
inference(unit_resolution,[status(thm)],[742,7]) ).
tff(744,plain,
meet(meet(c,a),meet(a,b)) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[105,77,80,104,89,103,96,99,694,693,692,691,560]) ).
tff(745,plain,
join(meet(a,b),meet(meet(a,b),c)) = meet(a,b),
inference(transitivity,[status(thm)],[554,401,411,408,305]) ).
tff(746,plain,
meet(join(meet(a,b),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))) = meet(meet(a,b),meet(b,c)),
inference(monotonicity,[status(thm)],[745,666]) ).
tff(747,plain,
meet(meet(a,b),meet(b,c)) = meet(join(meet(a,b),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))),
inference(symmetry,[status(thm)],[746]) ).
tff(748,plain,
meet(meet(meet(a,b),meet(b,c)),meet(meet(c,a),meet(a,b))) = meet(meet(join(meet(a,b),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[747,744]) ).
tff(749,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(meet(c,a),meet(a,b)),meet(meet(a,b),meet(b,c))) = meet(meet(meet(a,b),meet(b,c)),meet(meet(c,a),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(750,plain,
meet(meet(meet(c,a),meet(a,b)),meet(meet(a,b),meet(b,c))) = meet(meet(meet(a,b),meet(b,c)),meet(meet(c,a),meet(a,b))),
inference(unit_resolution,[status(thm)],[749,44]) ).
tff(751,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,b),c),meet(meet(meet(a,b),meet(b,c)),c)),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(752,plain,
join(join(meet(meet(a,b),c),meet(meet(meet(a,b),meet(b,c)),c)),c) = c,
inference(unit_resolution,[status(thm)],[751,18]) ).
tff(753,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(meet(a,b),meet(b,c)),join(c,join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c))))) = meet(meet(a,b),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(754,plain,
meet(meet(meet(a,b),meet(b,c)),join(c,join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c))))) = meet(meet(a,b),meet(b,c)),
inference(unit_resolution,[status(thm)],[753,33]) ).
tff(755,plain,
join(c,join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c)))) = join(c,join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),
inference(monotonicity,[status(thm)],[719]) ).
tff(756,plain,
join(c,join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))) = join(c,join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c)))),
inference(symmetry,[status(thm)],[755]) ).
tff(757,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))) = join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(758,plain,
join(c,join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))) = join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c),
inference(unit_resolution,[status(thm)],[757,60]) ).
tff(759,plain,
join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c) = join(c,join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),
inference(symmetry,[status(thm)],[758]) ).
tff(760,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),join(c,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c)))) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(761,plain,
meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),join(c,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c)))) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),
inference(unit_resolution,[status(thm)],[760,33]) ).
tff(762,plain,
join(c,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c))) = join(c,meet(b,c)),
inference(monotonicity,[status(thm)],[708]) ).
tff(763,plain,
join(c,meet(b,c)) = join(c,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c))),
inference(symmetry,[status(thm)],[762]) ).
tff(764,plain,
c = join(c,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c))),
inference(transitivity,[status(thm)],[582,581,580,579,205,763]) ).
tff(765,plain,
meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c) = meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),join(c,join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),meet(b,c)))),
inference(monotonicity,[status(thm)],[764]) ).
tff(766,plain,
meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),
inference(transitivity,[status(thm)],[765,761]) ).
tff(767,plain,
meet(meet(a,meet(b,c)),c) = join(meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))))),
inference(transitivity,[status(thm)],[584,565,573,725]) ).
tff(768,plain,
join(meet(meet(a,meet(b,c)),c),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c)) = join(join(meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))))),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),
inference(monotonicity,[status(thm)],[767,766]) ).
tff(769,plain,
join(join(meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),meet(meet(a,meet(b,c)),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))))),join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))) = join(meet(meet(a,meet(b,c)),c),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c)),
inference(symmetry,[status(thm)],[768]) ).
tff(770,plain,
join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))) = join(meet(meet(a,meet(b,c)),c),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c)),
inference(transitivity,[status(thm)],[737,769]) ).
tff(771,plain,
join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c) = join(join(meet(meet(a,meet(b,c)),c),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c)),c),
inference(monotonicity,[status(thm)],[770]) ).
tff(772,plain,
join(join(meet(meet(a,meet(b,c)),c),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c)),c) = join(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c),
inference(symmetry,[status(thm)],[771]) ).
tff(773,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(a,meet(b,c)),c),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c)),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(774,plain,
join(join(meet(meet(a,meet(b,c)),c),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c)),c) = c,
inference(unit_resolution,[status(thm)],[773,18]) ).
tff(775,plain,
c = join(join(meet(meet(a,meet(b,c)),c),meet(join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),c)),c),
inference(symmetry,[status(thm)],[774]) ).
tff(776,plain,
c = join(c,join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c)))),
inference(transitivity,[status(thm)],[775,772,759,756]) ).
tff(777,plain,
meet(meet(meet(a,b),meet(b,c)),c) = meet(meet(meet(a,b),meet(b,c)),join(c,join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c))))),
inference(monotonicity,[status(thm)],[776]) ).
tff(778,plain,
meet(meet(meet(a,b),meet(b,c)),c) = meet(meet(a,b),meet(b,c)),
inference(transitivity,[status(thm)],[777,754]) ).
tff(779,plain,
meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))) = meet(meet(meet(c,a),meet(a,b)),meet(meet(a,b),meet(b,c))),
inference(monotonicity,[status(thm)],[531]) ).
tff(780,plain,
meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))) = meet(meet(c,a),meet(a,b)),
inference(transitivity,[status(thm)],[779,750,748,743,561,558,548,546,102,100,97,92,90,83,81,78,11]) ).
tff(781,plain,
meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))) = join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),
inference(transitivity,[status(thm)],[779,750,748,743,561,558,548,546,102]) ).
tff(782,plain,
join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c)))) = join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))),
inference(monotonicity,[status(thm)],[781,780]) ).
tff(783,plain,
join(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(c,a),meet(a,b))) = join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c)))),
inference(symmetry,[status(thm)],[782]) ).
tff(784,plain,
meet(meet(a,b),c) = join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c)))),
inference(transitivity,[status(thm)],[561,558,548,546,102,100,97,92,90,83,81,78,11,25,783]) ).
tff(785,plain,
join(meet(meet(a,b),c),meet(meet(meet(a,b),meet(b,c)),c)) = join(join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c)))),meet(meet(a,b),meet(b,c))),
inference(monotonicity,[status(thm)],[784,778]) ).
tff(786,plain,
join(join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c)))),meet(meet(a,b),meet(b,c))) = join(meet(meet(a,b),c),meet(meet(meet(a,b),meet(b,c)),c)),
inference(symmetry,[status(thm)],[785]) ).
tff(787,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c)))),meet(meet(a,b),meet(b,c))) = meet(meet(a,b),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(788,plain,
join(join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c)))),meet(meet(a,b),meet(b,c))) = meet(meet(a,b),meet(b,c)),
inference(unit_resolution,[status(thm)],[787,18]) ).
tff(789,plain,
meet(meet(a,b),meet(b,c)) = join(join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c)))),meet(meet(a,b),meet(b,c))),
inference(symmetry,[status(thm)],[788]) ).
tff(790,plain,
meet(meet(a,b),meet(b,c)) = join(meet(meet(a,b),c),meet(meet(meet(a,b),meet(b,c)),c)),
inference(transitivity,[status(thm)],[789,786]) ).
tff(791,plain,
join(meet(meet(a,b),meet(b,c)),c) = join(join(meet(meet(a,b),c),meet(meet(meet(a,b),meet(b,c)),c)),c),
inference(monotonicity,[status(thm)],[790]) ).
tff(792,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,meet(meet(a,b),meet(b,c))) = join(meet(meet(a,b),meet(b,c)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(793,plain,
join(c,meet(meet(a,b),meet(b,c))) = join(meet(meet(a,b),meet(b,c)),c),
inference(unit_resolution,[status(thm)],[792,60]) ).
tff(794,plain,
join(c,meet(meet(a,b),meet(b,c))) = c,
inference(transitivity,[status(thm)],[793,791,752]) ).
tff(795,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(c,meet(a,b)),meet(meet(b,c),meet(a,b))),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(796,plain,
join(join(meet(c,meet(a,b)),meet(meet(b,c),meet(a,b))),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[795,18]) ).
tff(797,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(b,c),meet(a,b)) = meet(meet(a,b),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(798,plain,
meet(meet(b,c),meet(a,b)) = meet(meet(a,b),meet(b,c)),
inference(unit_resolution,[status(thm)],[797,44]) ).
tff(799,plain,
meet(c,meet(a,b)) = join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c)))),
inference(transitivity,[status(thm)],[49,561,558,548,546,102,100,97,92,90,83,81,78,11,25,783]) ).
tff(800,plain,
join(meet(c,meet(a,b)),meet(meet(b,c),meet(a,b))) = join(join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c)))),meet(meet(a,b),meet(b,c))),
inference(monotonicity,[status(thm)],[799,798]) ).
tff(801,plain,
join(join(meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c))),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(meet(a,b),meet(b,c)))),meet(meet(a,b),meet(b,c))) = join(meet(c,meet(a,b)),meet(meet(b,c),meet(a,b))),
inference(symmetry,[status(thm)],[800]) ).
tff(802,plain,
meet(meet(a,b),meet(b,c)) = join(meet(c,meet(a,b)),meet(meet(b,c),meet(a,b))),
inference(transitivity,[status(thm)],[789,801]) ).
tff(803,plain,
join(meet(meet(a,b),meet(b,c)),meet(a,b)) = join(join(meet(c,meet(a,b)),meet(meet(b,c),meet(a,b))),meet(a,b)),
inference(monotonicity,[status(thm)],[802]) ).
tff(804,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),meet(meet(a,b),meet(b,c))) = join(meet(meet(a,b),meet(b,c)),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(805,plain,
join(meet(a,b),meet(meet(a,b),meet(b,c))) = join(meet(meet(a,b),meet(b,c)),meet(a,b)),
inference(unit_resolution,[status(thm)],[804,60]) ).
tff(806,plain,
join(meet(a,b),meet(meet(a,b),meet(b,c))) = meet(a,b),
inference(transitivity,[status(thm)],[805,803,796]) ).
tff(807,plain,
meet(join(meet(a,b),meet(meet(a,b),meet(b,c))),join(c,meet(meet(a,b),meet(b,c)))) = meet(meet(a,b),c),
inference(monotonicity,[status(thm)],[806,794]) ).
tff(808,plain,
meet(join(meet(a,b),meet(meet(a,b),meet(b,c))),join(c,meet(meet(a,b),meet(b,c)))) = meet(meet(c,a),meet(a,b)),
inference(transitivity,[status(thm)],[807,561,558,548,546,102,100,97,92,90,83,81,78,11]) ).
tff(809,plain,
meet(meet(join(meet(a,b),meet(meet(a,b),meet(b,c))),join(c,meet(meet(a,b),meet(b,c)))),meet(meet(a,b),meet(b,c))) = meet(meet(meet(c,a),meet(a,b)),meet(meet(a,b),meet(b,c))),
inference(monotonicity,[status(thm)],[808]) ).
tff(810,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(meet(a,b),meet(meet(a,b),meet(b,c))),join(c,meet(meet(a,b),meet(b,c)))),meet(meet(a,b),meet(b,c))) = meet(meet(a,b),meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(811,plain,
meet(meet(join(meet(a,b),meet(meet(a,b),meet(b,c))),join(c,meet(meet(a,b),meet(b,c)))),meet(meet(a,b),meet(b,c))) = meet(meet(a,b),meet(b,c)),
inference(unit_resolution,[status(thm)],[810,7]) ).
tff(812,plain,
meet(meet(a,b),meet(b,c)) = meet(meet(join(meet(a,b),meet(meet(a,b),meet(b,c))),join(c,meet(meet(a,b),meet(b,c)))),meet(meet(a,b),meet(b,c))),
inference(symmetry,[status(thm)],[811]) ).
tff(813,plain,
meet(meet(a,b),meet(b,c)) = meet(meet(a,b),c),
inference(transitivity,[status(thm)],[812,809,750,748,743]) ).
tff(814,plain,
join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c))) = join(meet(meet(a,b),c),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[813]) ).
tff(815,plain,
join(meet(meet(a,b),c),meet(a,meet(b,c))) = join(meet(meet(a,b),meet(b,c)),meet(a,meet(b,c))),
inference(symmetry,[status(thm)],[814]) ).
tff(816,plain,
meet(a,meet(b,c)) = join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c))),
inference(transitivity,[status(thm)],[683,680,602,600,594,592,815,719]) ).
tff(817,plain,
join(b,meet(a,meet(b,c))) = join(b,join(meet(a,meet(b,c)),meet(meet(a,b),meet(b,c)))),
inference(monotonicity,[status(thm)],[816]) ).
tff(818,plain,
join(b,meet(a,meet(b,c))) = b,
inference(transitivity,[status(thm)],[817,741,739,700]) ).
tff(819,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(meet(b,c),join(meet(meet(a,b),c),a)),meet(meet(b,c),join(meet(meet(a,b),c),a))),join(meet(meet(a,b),c),a)) = join(meet(meet(a,b),c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(820,plain,
join(join(meet(meet(b,c),join(meet(meet(a,b),c),a)),meet(meet(b,c),join(meet(meet(a,b),c),a))),join(meet(meet(a,b),c),a)) = join(meet(meet(a,b),c),a),
inference(unit_resolution,[status(thm)],[819,18]) ).
tff(821,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(b,c),a) = meet(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(822,plain,
meet(meet(b,c),a) = meet(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[821,44]) ).
tff(823,plain,
meet(meet(b,c),join(meet(meet(a,b),c),a)) = meet(meet(b,c),a),
inference(monotonicity,[status(thm)],[498]) ).
tff(824,plain,
meet(meet(b,c),join(meet(meet(a,b),c),a)) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[823,822]) ).
tff(825,plain,
join(meet(meet(b,c),join(meet(meet(a,b),c),a)),meet(meet(b,c),join(meet(meet(a,b),c),a))) = join(meet(a,meet(b,c)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[824,824]) ).
tff(826,plain,
join(meet(a,meet(b,c)),meet(a,meet(b,c))) = join(meet(meet(b,c),join(meet(meet(a,b),c),a)),meet(meet(b,c),join(meet(meet(a,b),c),a))),
inference(symmetry,[status(thm)],[825]) ).
tff(827,plain,
meet(a,meet(b,c)) = join(meet(meet(b,c),join(meet(meet(a,b),c),a)),meet(meet(b,c),join(meet(meet(a,b),c),a))),
inference(transitivity,[status(thm)],[573,826]) ).
tff(828,plain,
join(meet(a,meet(b,c)),join(meet(meet(a,b),c),a)) = join(join(meet(meet(b,c),join(meet(meet(a,b),c),a)),meet(meet(b,c),join(meet(meet(a,b),c),a))),join(meet(meet(a,b),c),a)),
inference(monotonicity,[status(thm)],[827]) ).
tff(829,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(meet(meet(a,b),c),a),meet(a,meet(b,c))) = join(meet(a,meet(b,c)),join(meet(meet(a,b),c),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(830,plain,
join(join(meet(meet(a,b),c),a),meet(a,meet(b,c))) = join(meet(a,meet(b,c)),join(meet(meet(a,b),c),a)),
inference(unit_resolution,[status(thm)],[829,60]) ).
tff(831,plain,
join(join(meet(meet(a,b),c),a),meet(a,meet(b,c))) = a,
inference(transitivity,[status(thm)],[830,828,820,495,492,438,436,245]) ).
tff(832,plain,
meet(join(join(meet(meet(a,b),c),a),meet(a,meet(b,c))),join(b,meet(a,meet(b,c)))) = meet(a,b),
inference(monotonicity,[status(thm)],[831,818]) ).
tff(833,plain,
meet(a,b) = meet(join(join(meet(meet(a,b),c),a),meet(a,meet(b,c))),join(b,meet(a,meet(b,c)))),
inference(symmetry,[status(thm)],[832]) ).
tff(834,plain,
meet(meet(a,b),meet(a,meet(b,c))) = meet(meet(join(join(meet(meet(a,b),c),a),meet(a,meet(b,c))),join(b,meet(a,meet(b,c)))),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[833]) ).
tff(835,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(a,meet(b,c)),meet(a,b)) = meet(meet(a,b),meet(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(836,plain,
meet(meet(a,meet(b,c)),meet(a,b)) = meet(meet(a,b),meet(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[835,44]) ).
tff(837,plain,
meet(meet(a,meet(b,c)),meet(a,b)) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[836,834,698]) ).
tff(838,plain,
join(meet(meet(a,meet(b,c)),meet(a,b)),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(a,b))) = join(meet(a,meet(b,c)),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[837,696]) ).
tff(839,plain,
join(meet(a,meet(b,c)),meet(meet(a,b),c)) = join(meet(meet(a,meet(b,c)),meet(a,b)),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(a,b))),
inference(symmetry,[status(thm)],[838]) ).
tff(840,plain,
meet(a,meet(b,c)) = join(meet(meet(a,meet(b,c)),meet(a,b)),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(a,b))),
inference(transitivity,[status(thm)],[683,680,602,600,594,592,590,839]) ).
tff(841,plain,
join(meet(a,meet(b,c)),meet(a,b)) = join(join(meet(meet(a,meet(b,c)),meet(a,b)),meet(join(meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),meet(meet(a,b),meet(meet(c,a),meet(a,b)))),meet(a,b))),meet(a,b)),
inference(monotonicity,[status(thm)],[840]) ).
tff(842,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),meet(a,meet(b,c))) = join(meet(a,meet(b,c)),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(843,plain,
join(meet(a,b),meet(a,meet(b,c))) = join(meet(a,meet(b,c)),meet(a,b)),
inference(unit_resolution,[status(thm)],[842,60]) ).
tff(844,plain,
join(meet(a,b),meet(a,meet(b,c))) = meet(a,b),
inference(transitivity,[status(thm)],[843,841,690]) ).
tff(845,plain,
meet(join(meet(a,b),meet(a,meet(b,c))),join(c,meet(a,meet(b,c)))) = meet(meet(a,b),c),
inference(monotonicity,[status(thm)],[844,688]) ).
tff(846,plain,
meet(join(meet(a,b),meet(a,meet(b,c))),join(c,meet(a,meet(b,c)))) = meet(meet(c,a),meet(a,b)),
inference(transitivity,[status(thm)],[845,561,558,548,546,102,100,97,92,90,83,81,78,11]) ).
tff(847,plain,
meet(meet(join(meet(a,b),meet(a,meet(b,c))),join(c,meet(a,meet(b,c)))),meet(a,meet(b,c))) = meet(meet(meet(c,a),meet(a,b)),meet(a,meet(b,c))),
inference(monotonicity,[status(thm)],[846]) ).
tff(848,plain,
meet(meet(meet(c,a),meet(a,b)),meet(a,meet(b,c))) = meet(meet(join(meet(a,b),meet(a,meet(b,c))),join(c,meet(a,meet(b,c)))),meet(a,meet(b,c))),
inference(symmetry,[status(thm)],[847]) ).
tff(849,plain,
meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))) = meet(meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))),meet(meet(a,b),c)),
inference(monotonicity,[status(thm)],[668,744]) ).
tff(850,plain,
meet(meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))),meet(meet(a,b),c)) = meet(meet(a,meet(b,c)),meet(meet(c,a),meet(a,b))),
inference(symmetry,[status(thm)],[849]) ).
tff(851,plain,
meet(meet(a,b),c) = meet(meet(join(join(meet(meet(a,b),c),a),meet(meet(a,b),c)),join(meet(b,c),meet(meet(a,b),c))),meet(meet(a,b),c)),
inference(symmetry,[status(thm)],[604]) ).
tff(852,plain,
meet(meet(a,b),c) = meet(a,meet(b,c)),
inference(transitivity,[status(thm)],[851,850,86,848,9]) ).
tff(853,plain,
( ( meet(meet(a,b),c) != meet(a,meet(b,c)) )
<=> ( meet(meet(a,b),c) != meet(a,meet(b,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(854,axiom,
meet(meet(a,b),c) != meet(a,meet(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_meet) ).
tff(855,plain,
meet(meet(a,b),c) != meet(a,meet(b,c)),
inference(modus_ponens,[status(thm)],[854,853]) ).
tff(856,plain,
$false,
inference(unit_resolution,[status(thm)],[855,852]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT026-1 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n019.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 10:51:20 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 8.50/5.72 % SZS status Unsatisfiable
% 8.50/5.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------