TSTP Solution File: LAT012-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT012-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:31:43 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 49
% Syntax : Number of formulae : 201 ( 157 unt; 4 typ; 0 def)
% Number of atoms : 245 ( 240 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 79 ( 35 ~; 31 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 201 ( 189 !; 0 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(X,join(Y,join(X,Z))) = X )
<=> ( meet(X,join(Y,join(X,Z))) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie2) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,b),join(meet(b,a),join(meet(a,b),meet(a,b)))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
meet(meet(a,b),join(meet(b,a),join(meet(a,b),meet(a,b)))) = meet(a,b),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
<=> ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie4) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(b,meet(a,b)),join(meet(a,b),a)),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
meet(meet(join(b,meet(a,b)),join(meet(a,b),a)),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
<=> ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie3) ).
tff(23,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(a,b),a),meet(a,meet(a,b))),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
join(join(meet(meet(a,b),a),meet(a,meet(a,b))),a) = a,
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,b),join(join(a,b),join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a)))))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
meet(meet(a,b),join(join(a,b),join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a)))))) = meet(a,b),
inference(unit_resolution,[status(thm)],[28,7]) ).
tff(30,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(X,meet(Y,meet(X,Z))) = X )
<=> ( join(X,meet(Y,meet(X,Z))) = X ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie1) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a)))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a)))) = meet(a,b),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
join(join(a,b),join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a))))) = join(join(a,b),meet(a,b)),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
join(join(a,b),meet(a,b)) = join(join(a,b),join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a))))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
meet(meet(a,b),join(join(a,b),meet(a,b))) = meet(meet(a,b),join(join(a,b),join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a)))))),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
meet(meet(a,b),join(join(a,b),meet(a,b))) = meet(a,b),
inference(transitivity,[status(thm)],[41,29]) ).
tff(43,plain,
meet(a,meet(meet(a,b),join(join(a,b),meet(a,b)))) = meet(a,meet(a,b)),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
meet(a,meet(a,b)) = meet(a,meet(meet(a,b),join(join(a,b),meet(a,b)))),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(a,b),join(a,join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a)))))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
meet(meet(a,b),join(a,join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a)))))) = meet(a,b),
inference(unit_resolution,[status(thm)],[45,7]) ).
tff(47,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(a,meet(a,meet(a,b))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
join(a,meet(a,meet(a,b))) = a,
inference(unit_resolution,[status(thm)],[47,36]) ).
tff(49,plain,
join(join(meet(a,a),meet(a,a)),join(a,meet(a,meet(a,b)))) = join(join(meet(a,a),meet(a,a)),a),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
join(join(meet(a,a),meet(a,a)),a) = join(join(meet(a,a),meet(a,a)),join(a,meet(a,meet(a,b)))),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(a,a),meet(a,a)),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
join(join(meet(a,a),meet(a,a)),a) = a,
inference(unit_resolution,[status(thm)],[51,25]) ).
tff(53,plain,
a = join(join(meet(a,a),meet(a,a)),a),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
a = join(join(meet(a,a),meet(a,a)),join(a,meet(a,meet(a,b)))),
inference(transitivity,[status(thm)],[53,50]) ).
tff(55,plain,
meet(a,a) = meet(a,join(join(meet(a,a),meet(a,a)),join(a,meet(a,meet(a,b))))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
meet(a,join(join(meet(a,a),meet(a,a)),join(a,meet(a,meet(a,b))))) = meet(a,a),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(join(meet(a,a),meet(a,a)),join(a,meet(a,meet(a,b))))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
meet(a,join(join(meet(a,a),meet(a,a)),join(a,meet(a,meet(a,b))))) = a,
inference(unit_resolution,[status(thm)],[57,7]) ).
tff(59,plain,
a = meet(a,join(join(meet(a,a),meet(a,a)),join(a,meet(a,meet(a,b))))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
a = meet(a,a),
inference(transitivity,[status(thm)],[59,56]) ).
tff(61,plain,
join(a,join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a))))) = join(meet(a,a),meet(a,b)),
inference(monotonicity,[status(thm)],[60,38]) ).
tff(62,plain,
join(meet(a,a),meet(a,b)) = join(a,join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a))))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(a,b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[63,16]) ).
tff(65,plain,
meet(a,b) = meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(a,b)),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
meet(a,a) = a,
inference(transitivity,[status(thm)],[55,58]) ).
tff(67,plain,
join(meet(a,a),meet(a,b)) = join(a,meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(a,b))),
inference(monotonicity,[status(thm)],[66,65]) ).
tff(68,plain,
join(a,meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(a,b))) = join(meet(a,a),meet(a,b)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(a,meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(a,b))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
join(a,meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(a,b))) = a,
inference(unit_resolution,[status(thm)],[69,36]) ).
tff(71,plain,
a = join(a,meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(a,b))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
a = join(a,join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a))))),
inference(transitivity,[status(thm)],[71,68,62]) ).
tff(73,plain,
meet(meet(a,b),a) = meet(meet(a,b),join(a,join(meet(a,b),meet(meet(b,a),meet(meet(a,b),meet(b,a)))))),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
meet(meet(a,b),a) = meet(a,b),
inference(transitivity,[status(thm)],[73,46]) ).
tff(75,plain,
join(meet(meet(a,b),a),meet(a,meet(a,b))) = join(meet(a,b),meet(a,meet(meet(a,b),join(join(a,b),meet(a,b))))),
inference(monotonicity,[status(thm)],[74,44]) ).
tff(76,plain,
join(meet(a,b),meet(a,meet(meet(a,b),join(join(a,b),meet(a,b))))) = join(meet(meet(a,b),a),meet(a,meet(a,b))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(a,b),meet(a,meet(meet(a,b),join(join(a,b),meet(a,b))))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
join(meet(a,b),meet(a,meet(meet(a,b),join(join(a,b),meet(a,b))))) = meet(a,b),
inference(unit_resolution,[status(thm)],[77,36]) ).
tff(79,plain,
meet(a,b) = join(meet(a,b),meet(a,meet(meet(a,b),join(join(a,b),meet(a,b))))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
meet(a,b) = join(meet(meet(a,b),a),meet(a,meet(a,b))),
inference(transitivity,[status(thm)],[79,76]) ).
tff(81,plain,
join(meet(a,b),a) = join(join(meet(meet(a,b),a),meet(a,meet(a,b))),a),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
join(meet(a,b),a) = a,
inference(transitivity,[status(thm)],[81,27]) ).
tff(83,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(a,meet(b,join(meet(a,b),b)))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
join(b,meet(a,meet(b,join(meet(a,b),b)))) = b,
inference(unit_resolution,[status(thm)],[83,36]) ).
tff(85,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(b,join(meet(a,b),join(b,meet(join(a,join(a,b)),meet(b,a))))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
meet(b,join(meet(a,b),join(b,meet(join(a,join(a,b)),meet(b,a))))) = b,
inference(unit_resolution,[status(thm)],[85,7]) ).
tff(87,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(join(a,join(a,b)),meet(b,a))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
join(b,meet(join(a,join(a,b)),meet(b,a))) = b,
inference(unit_resolution,[status(thm)],[87,36]) ).
tff(89,plain,
join(meet(a,b),join(b,meet(join(a,join(a,b)),meet(b,a)))) = join(meet(a,b),b),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
join(meet(a,b),b) = join(meet(a,b),join(b,meet(join(a,join(a,b)),meet(b,a)))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
meet(b,join(meet(a,b),b)) = meet(b,join(meet(a,b),join(b,meet(join(a,join(a,b)),meet(b,a))))),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
meet(b,join(meet(a,b),b)) = b,
inference(transitivity,[status(thm)],[91,86]) ).
tff(93,plain,
meet(a,meet(b,join(meet(a,b),b))) = meet(a,b),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
meet(a,b) = meet(a,meet(b,join(meet(a,b),b))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
join(b,meet(a,b)) = join(b,meet(a,meet(b,join(meet(a,b),b)))),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
join(b,meet(a,b)) = b,
inference(transitivity,[status(thm)],[95,84]) ).
tff(97,plain,
meet(join(b,meet(a,b)),join(meet(a,b),a)) = meet(b,a),
inference(monotonicity,[status(thm)],[96,82]) ).
tff(98,plain,
meet(b,a) = meet(join(b,meet(a,b)),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
meet(meet(b,a),meet(a,b)) = meet(meet(join(b,meet(a,b)),join(meet(a,b),a)),meet(a,b)),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
meet(meet(b,a),meet(a,b)) = meet(a,b),
inference(transitivity,[status(thm)],[99,18]) ).
tff(101,plain,
meet(meet(b,a),meet(meet(b,a),meet(a,b))) = meet(meet(join(b,meet(a,b)),join(meet(a,b),a)),meet(a,b)),
inference(monotonicity,[status(thm)],[98,100]) ).
tff(102,plain,
meet(meet(join(b,meet(a,b)),join(meet(a,b),a)),meet(a,b)) = meet(meet(b,a),meet(meet(b,a),meet(a,b))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
meet(a,b) = meet(meet(join(b,meet(a,b)),join(meet(a,b),a)),meet(a,b)),
inference(symmetry,[status(thm)],[18]) ).
tff(104,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(a,b),meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(meet(a,b),join(join(a,b),meet(a,b))))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
join(meet(a,b),meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(meet(a,b),join(join(a,b),meet(a,b))))) = meet(a,b),
inference(unit_resolution,[status(thm)],[104,36]) ).
tff(106,plain,
meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(meet(a,b),join(join(a,b),meet(a,b)))) = meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(a,b)),
inference(monotonicity,[status(thm)],[42]) ).
tff(107,plain,
meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(a,b)) = meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(meet(a,b),join(join(a,b),meet(a,b)))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
meet(a,b) = meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(meet(a,b),join(join(a,b),meet(a,b)))),
inference(transitivity,[status(thm)],[65,107]) ).
tff(109,plain,
join(meet(a,b),meet(a,b)) = join(meet(a,b),meet(meet(join(join(a,b),meet(a,b)),join(meet(a,b),b)),meet(meet(a,b),join(join(a,b),meet(a,b))))),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
join(meet(a,b),meet(a,b)) = meet(meet(b,a),meet(meet(b,a),meet(a,b))),
inference(transitivity,[status(thm)],[109,105,103,102]) ).
tff(111,plain,
join(meet(b,a),join(meet(a,b),meet(a,b))) = join(meet(b,a),meet(meet(b,a),meet(meet(b,a),meet(a,b)))),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
join(meet(b,a),meet(meet(b,a),meet(meet(b,a),meet(a,b)))) = join(meet(b,a),join(meet(a,b),meet(a,b))),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(b,a),meet(meet(b,a),meet(meet(b,a),meet(a,b)))) = meet(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
join(meet(b,a),meet(meet(b,a),meet(meet(b,a),meet(a,b)))) = meet(b,a),
inference(unit_resolution,[status(thm)],[113,36]) ).
tff(115,plain,
meet(b,a) = join(meet(b,a),meet(meet(b,a),meet(meet(b,a),meet(a,b)))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
meet(b,a) = join(meet(b,a),join(meet(a,b),meet(a,b))),
inference(transitivity,[status(thm)],[115,112]) ).
tff(117,plain,
meet(meet(a,b),meet(b,a)) = meet(meet(a,b),join(meet(b,a),join(meet(a,b),meet(a,b)))),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(meet(join(a,join(a,b)),meet(b,a)),b),meet(b,a)),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
join(join(meet(meet(join(a,join(a,b)),meet(b,a)),b),meet(b,a)),b) = b,
inference(unit_resolution,[status(thm)],[118,25]) ).
tff(120,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(join(a,join(a,b)),meet(b,a)),join(a,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)))) = meet(join(a,join(a,b)),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
meet(meet(join(a,join(a,b)),meet(b,a)),join(a,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)))) = meet(join(a,join(a,b)),meet(b,a)),
inference(unit_resolution,[status(thm)],[120,7]) ).
tff(122,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(a,join(a,b))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
meet(a,join(a,join(a,b))) = a,
inference(unit_resolution,[status(thm)],[122,7]) ).
tff(124,plain,
meet(b,meet(a,join(a,join(a,b)))) = meet(b,a),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
meet(b,a) = meet(b,meet(a,join(a,join(a,b)))),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)) = meet(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)) = meet(b,a),
inference(unit_resolution,[status(thm)],[126,25]) ).
tff(128,plain,
join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)) = meet(b,meet(a,join(a,join(a,b)))),
inference(transitivity,[status(thm)],[127,125]) ).
tff(129,plain,
join(a,join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a))) = join(a,meet(b,meet(a,join(a,join(a,b))))),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
join(a,meet(b,meet(a,join(a,join(a,b))))) = join(a,join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a))),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(a,meet(b,meet(a,join(a,join(a,b))))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
join(a,meet(b,meet(a,join(a,join(a,b))))) = a,
inference(unit_resolution,[status(thm)],[131,36]) ).
tff(133,plain,
a = join(a,meet(b,meet(a,join(a,join(a,b))))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(b,join(a,a))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
meet(a,join(b,join(a,a))) = a,
inference(unit_resolution,[status(thm)],[134,7]) ).
tff(136,plain,
meet(a,join(b,join(a,a))) = join(a,join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a))),
inference(transitivity,[status(thm)],[135,133,130]) ).
tff(137,plain,
meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(a,join(b,join(a,a)))) = meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(a,join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(a,join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)))) = meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(a,join(b,join(a,a)))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(a,join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)))) = join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(a,join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)))) = join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),
inference(unit_resolution,[status(thm)],[139,7]) ).
tff(141,plain,
join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)) = meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(a,join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)) = meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(a,join(b,join(a,a)))),
inference(transitivity,[status(thm)],[141,138]) ).
tff(143,plain,
join(a,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b))) = join(a,meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(a,join(b,join(a,a))))),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
join(a,meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(a,join(b,join(a,a))))) = join(a,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b))),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(a,meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(a,join(b,join(a,a))))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
join(a,meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(a,join(b,join(a,a))))) = a,
inference(unit_resolution,[status(thm)],[145,36]) ).
tff(147,plain,
a = join(a,meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(a,join(b,join(a,a))))),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
a = join(a,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b))),
inference(transitivity,[status(thm)],[147,144]) ).
tff(149,plain,
meet(meet(join(a,join(a,b)),meet(b,a)),a) = meet(meet(join(a,join(a,b)),meet(b,a)),join(a,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)))),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
meet(meet(join(a,join(a,b)),meet(b,a)),a) = meet(join(a,join(a,b)),meet(b,a)),
inference(transitivity,[status(thm)],[149,121]) ).
tff(151,plain,
meet(meet(b,a),meet(meet(join(a,join(a,b)),meet(b,a)),a)) = meet(meet(b,a),meet(join(a,join(a,b)),meet(b,a))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
meet(meet(b,a),meet(join(a,join(a,b)),meet(b,a))) = meet(meet(b,a),meet(meet(join(a,join(a,b)),meet(b,a)),a)),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(join(a,join(a,b)),meet(b,a)))) = join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(meet(join(a,join(a,b)),meet(b,a)),a))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(meet(join(a,join(a,b)),meet(b,a)),a))) = join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(join(a,join(a,b)),meet(b,a)))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(meet(join(a,join(a,b)),meet(b,a)),a))) = meet(join(a,join(a,b)),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(meet(join(a,join(a,b)),meet(b,a)),a))) = meet(join(a,join(a,b)),meet(b,a)),
inference(unit_resolution,[status(thm)],[155,36]) ).
tff(157,plain,
meet(join(a,join(a,b)),meet(b,a)) = join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(meet(join(a,join(a,b)),meet(b,a)),a))),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(meet(join(a,join(a,b)),meet(b,a)),join(b,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)))) = meet(join(a,join(a,b)),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
meet(meet(join(a,join(a,b)),meet(b,a)),join(b,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)))) = meet(join(a,join(a,b)),meet(b,a)),
inference(unit_resolution,[status(thm)],[158,7]) ).
tff(160,plain,
join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a))) = join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)),
inference(monotonicity,[status(thm)],[127]) ).
tff(161,plain,
join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)) = join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
meet(b,a) = join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)),
inference(symmetry,[status(thm)],[127]) ).
tff(163,plain,
meet(b,a) = join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a))),
inference(transitivity,[status(thm)],[162,161]) ).
tff(164,plain,
meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)) = meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)))),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)))) = meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)))) = join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)))) = join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),
inference(unit_resolution,[status(thm)],[166,7]) ).
tff(168,plain,
join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)) = meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)) = meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a)),
inference(transitivity,[status(thm)],[168,165]) ).
tff(170,plain,
join(b,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b))) = join(b,meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a))),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
join(b,meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a))) = join(b,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b))),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(b,meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(173,plain,
join(b,meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a))) = b,
inference(unit_resolution,[status(thm)],[172,36]) ).
tff(174,plain,
b = join(b,meet(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)),meet(b,a))),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
b = join(b,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b))),
inference(transitivity,[status(thm)],[174,171]) ).
tff(176,plain,
meet(meet(join(a,join(a,b)),meet(b,a)),b) = meet(meet(join(a,join(a,b)),meet(b,a)),join(b,join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),b)))),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
meet(meet(join(a,join(a,b)),meet(b,a)),b) = join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(join(a,join(a,b)),meet(b,a)))),
inference(transitivity,[status(thm)],[176,159,157,154]) ).
tff(178,plain,
join(meet(meet(join(a,join(a,b)),meet(b,a)),b),meet(b,a)) = join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(join(a,join(a,b)),meet(b,a)))),meet(b,a)),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(join(a,join(a,b)),meet(b,a)))),meet(b,a)) = join(meet(meet(join(a,join(a,b)),meet(b,a)),b),meet(b,a)),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(join(a,join(a,b)),meet(b,a)))),meet(b,a)) = meet(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(join(a,join(a,b)),meet(b,a)))),meet(b,a)) = meet(b,a),
inference(unit_resolution,[status(thm)],[180,25]) ).
tff(182,plain,
meet(b,a) = join(join(meet(join(a,join(a,b)),meet(b,a)),meet(meet(b,a),meet(join(a,join(a,b)),meet(b,a)))),meet(b,a)),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
meet(b,a) = join(meet(meet(join(a,join(a,b)),meet(b,a)),b),meet(b,a)),
inference(transitivity,[status(thm)],[182,179]) ).
tff(184,plain,
join(meet(b,a),b) = join(join(meet(meet(join(a,join(a,b)),meet(b,a)),b),meet(b,a)),b),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
join(meet(b,a),b) = b,
inference(transitivity,[status(thm)],[184,119]) ).
tff(186,plain,
join(a,meet(b,a)) = join(a,meet(b,meet(a,join(a,join(a,b))))),
inference(monotonicity,[status(thm)],[125]) ).
tff(187,plain,
join(a,meet(b,a)) = a,
inference(transitivity,[status(thm)],[186,132]) ).
tff(188,plain,
meet(join(a,meet(b,a)),join(meet(b,a),b)) = meet(a,b),
inference(monotonicity,[status(thm)],[187,185]) ).
tff(189,plain,
meet(meet(join(a,meet(b,a)),join(meet(b,a),b)),meet(b,a)) = meet(meet(a,b),meet(b,a)),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(a,meet(b,a)),join(meet(b,a),b)),meet(b,a)) = meet(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
meet(meet(join(a,meet(b,a)),join(meet(b,a),b)),meet(b,a)) = meet(b,a),
inference(unit_resolution,[status(thm)],[190,16]) ).
tff(192,plain,
meet(b,a) = meet(meet(join(a,meet(b,a)),join(meet(b,a),b)),meet(b,a)),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
meet(b,a) = meet(a,b),
inference(transitivity,[status(thm)],[192,189,117,9]) ).
tff(194,plain,
( ( meet(b,a) != meet(a,b) )
<=> ( meet(b,a) != meet(a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,axiom,
meet(b,a) != meet(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity_of_meet) ).
tff(196,plain,
meet(b,a) != meet(a,b),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
$false,
inference(unit_resolution,[status(thm)],[196,193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LAT012-1 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 10:51:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------