TSTP Solution File: LAT021-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT021-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 18:31:45 EDT 2022
% Result : Unsatisfiable 0.70s 0.73s
% Output : Proof 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 65
% Syntax : Number of formulae : 221 ( 165 unt; 5 typ; 0 def)
% Number of atoms : 283 ( 274 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 97 ( 38 ~; 34 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 8 ( 8 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 : 261 ( 241 !; 0 ?; 261 :)
% Comments :
%------------------------------------------------------------------------------
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( join(X,X) = X )
<=> ( join(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( join(X,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',idempotence_of_join) ).
tff(5,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( join(X,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(a,b),meet(a,b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
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(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
<=> ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',quasi_lattice2) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
| ( meet(join(meet(a,b),meet(a,b)),join(meet(a,b),a)) = join(meet(a,b),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
meet(join(meet(a,b),meet(a,b)),join(meet(a,b),a)) = join(meet(a,b),meet(a,b)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
meet(join(meet(a,b),meet(a,b)),join(meet(a,b),a)) = meet(meet(a,b),join(meet(a,b),a)),
inference(monotonicity,[status(thm)],[9]) ).
tff(20,plain,
meet(meet(a,b),join(meet(a,b),a)) = meet(join(meet(a,b),meet(a,b)),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
meet(meet(a,b),join(meet(a,b),a)) = meet(a,b),
inference(transitivity,[status(thm)],[20,18,9]) ).
tff(22,plain,
join(meet(meet(a,b),join(meet(a,b),a)),meet(a,c)) = join(meet(a,b),meet(a,c)),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(24,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)],[23]) ).
tff(25,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(26,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',commutativity_of_join) ).
tff(27,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(meet(a,b),join(meet(a,b),a)),meet(a,c)) = join(meet(a,c),meet(meet(a,b),join(meet(a,b),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
join(meet(meet(a,b),join(meet(a,b),a)),meet(a,c)) = join(meet(a,c),meet(meet(a,b),join(meet(a,b),a))),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
join(meet(a,c),meet(meet(a,b),join(meet(a,b),a))) = join(meet(meet(a,b),join(meet(a,b),a)),meet(a,c)),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(a,c),meet(a,c)) = meet(a,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
join(meet(a,c),meet(a,c)) = meet(a,c),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
| ( meet(join(meet(a,c),meet(a,c)),join(meet(a,c),a)) = join(meet(a,c),meet(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
meet(join(meet(a,c),meet(a,c)),join(meet(a,c),a)) = join(meet(a,c),meet(a,c)),
inference(unit_resolution,[status(thm)],[35,16]) ).
tff(37,plain,
meet(join(meet(a,c),meet(a,c)),join(meet(a,c),a)) = meet(meet(a,c),join(meet(a,c),a)),
inference(monotonicity,[status(thm)],[34]) ).
tff(38,plain,
meet(meet(a,c),join(meet(a,c),a)) = meet(join(meet(a,c),meet(a,c)),join(meet(a,c),a)),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
meet(meet(a,c),join(meet(a,c),a)) = meet(a,c),
inference(transitivity,[status(thm)],[38,36,34]) ).
tff(40,plain,
join(meet(meet(a,c),join(meet(a,c),a)),meet(meet(a,b),join(meet(a,b),a))) = join(meet(a,c),meet(meet(a,b),join(meet(a,b),a))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',associativity_of_meet) ).
tff(45,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,b),join(meet(a,b),a)) = meet(a,meet(b,join(meet(a,b),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
meet(meet(a,b),join(meet(a,b),a)) = meet(a,meet(b,join(meet(a,b),a))),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
meet(a,meet(b,join(meet(a,b),a))) = meet(meet(a,b),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(52,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)],[51]) ).
tff(53,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(54,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',commutativity_of_meet) ).
tff(55,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(b,join(meet(a,b),a)),a) = meet(a,meet(b,join(meet(a,b),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
meet(meet(b,join(meet(a,b),a)),a) = meet(a,meet(b,join(meet(a,b),a))),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(a,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
join(a,a) = a,
inference(unit_resolution,[status(thm)],[60,7]) ).
tff(62,plain,
meet(meet(b,join(meet(a,b),a)),join(a,a)) = meet(meet(b,join(meet(a,b),a)),a),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(b,join(meet(a,b),a)),join(a,a)) = meet(b,meet(join(meet(a,b),a),join(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
meet(meet(b,join(meet(a,b),a)),join(a,a)) = meet(b,meet(join(meet(a,b),a),join(a,a))),
inference(unit_resolution,[status(thm)],[63,47]) ).
tff(65,plain,
meet(b,meet(join(meet(a,b),a),join(a,a))) = meet(meet(b,join(meet(a,b),a)),join(a,a)),
inference(symmetry,[status(thm)],[64]) ).
tff(66,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(67,plain,
join(a,meet(a,b)) = join(meet(a,b),a),
inference(unit_resolution,[status(thm)],[66,29]) ).
tff(68,plain,
join(meet(a,b),a) = join(a,meet(a,b)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
meet(join(meet(a,b),a),join(a,a)) = meet(join(a,meet(a,b)),join(a,a)),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
meet(join(a,meet(a,b)),join(a,a)) = meet(join(meet(a,b),a),join(a,a)),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
| ( meet(join(a,meet(a,b)),join(a,a)) = join(a,meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
meet(join(a,meet(a,b)),join(a,a)) = join(a,meet(a,b)),
inference(unit_resolution,[status(thm)],[71,16]) ).
tff(73,plain,
join(a,meet(a,b)) = meet(join(a,meet(a,b)),join(a,a)),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
join(meet(a,b),a) = meet(join(meet(a,b),a),join(a,a)),
inference(transitivity,[status(thm)],[68,73,70]) ).
tff(75,plain,
meet(b,join(meet(a,b),a)) = meet(b,meet(join(meet(a,b),a),join(a,a))),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
meet(b,join(meet(a,b),a)) = meet(meet(a,b),join(meet(a,b),a)),
inference(transitivity,[status(thm)],[75,65,62,59,50]) ).
tff(77,plain,
join(meet(a,c),meet(a,c)) = meet(join(meet(a,c),meet(a,c)),join(meet(a,c),a)),
inference(symmetry,[status(thm)],[36]) ).
tff(78,plain,
meet(a,c) = join(meet(a,c),meet(a,c)),
inference(symmetry,[status(thm)],[34]) ).
tff(79,plain,
meet(a,c) = meet(meet(a,c),join(meet(a,c),a)),
inference(transitivity,[status(thm)],[78,77,37]) ).
tff(80,plain,
join(meet(a,c),meet(b,join(meet(a,b),a))) = join(meet(meet(a,c),join(meet(a,c),a)),meet(meet(a,b),join(meet(a,b),a))),
inference(monotonicity,[status(thm)],[79,76]) ).
tff(81,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) )
<=> ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bowden) ).
tff(85,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) )
| ( join(join(meet(a,c),meet(b,join(meet(a,b),a))),meet(join(meet(a,c),b),join(meet(a,b),a))) = join(meet(a,c),meet(b,join(meet(a,b),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
join(join(meet(a,c),meet(b,join(meet(a,b),a))),meet(join(meet(a,c),b),join(meet(a,b),a))) = join(meet(a,c),meet(b,join(meet(a,b),a))),
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,a) = meet(a,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
meet(c,a) = meet(a,c),
inference(unit_resolution,[status(thm)],[90,57]) ).
tff(92,plain,
meet(a,c) = meet(c,a),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
join(b,meet(a,c)) = join(b,meet(c,a)),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,meet(a,c)) = join(meet(a,c),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
join(b,meet(a,c)) = join(meet(a,c),b),
inference(unit_resolution,[status(thm)],[94,29]) ).
tff(96,plain,
join(meet(a,c),b) = join(b,meet(a,c)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
join(meet(a,c),b) = join(b,meet(c,a)),
inference(transitivity,[status(thm)],[96,93]) ).
tff(98,plain,
meet(join(meet(a,c),b),join(meet(a,b),a)) = meet(join(b,meet(c,a)),join(meet(a,b),a)),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
meet(join(b,meet(c,a)),join(meet(a,b),a)) = meet(join(meet(a,c),b),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,meet(c,a)),join(meet(a,b),a)) = meet(join(meet(a,b),a),join(b,meet(c,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
meet(join(b,meet(c,a)),join(meet(a,b),a)) = meet(join(meet(a,b),a),join(b,meet(c,a))),
inference(unit_resolution,[status(thm)],[100,57]) ).
tff(102,plain,
meet(join(meet(a,b),a),join(b,meet(c,a))) = meet(join(b,meet(c,a)),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
join(b,meet(c,a)) = join(b,meet(a,c)),
inference(symmetry,[status(thm)],[93]) ).
tff(104,plain,
join(b,meet(c,a)) = join(meet(a,c),b),
inference(transitivity,[status(thm)],[103,95]) ).
tff(105,plain,
meet(join(meet(a,b),a),join(b,meet(c,a))) = meet(join(meet(a,b),a),join(meet(a,c),b)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
meet(join(meet(a,b),a),join(meet(a,c),b)) = meet(join(meet(a,b),a),join(b,meet(c,a))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
meet(join(meet(a,b),a),join(meet(a,c),b)) = meet(meet(join(meet(a,b),a),join(a,a)),join(b,meet(c,a))),
inference(monotonicity,[status(thm)],[74,97]) ).
tff(108,plain,
meet(meet(join(meet(a,b),a),join(a,a)),join(b,meet(c,a))) = meet(join(meet(a,b),a),join(meet(a,c),b)),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(meet(a,b),a),join(a,a)),join(b,meet(c,a))) = meet(join(meet(a,b),a),meet(join(a,a),join(b,meet(c,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
meet(meet(join(meet(a,b),a),join(a,a)),join(b,meet(c,a))) = meet(join(meet(a,b),a),meet(join(a,a),join(b,meet(c,a)))),
inference(unit_resolution,[status(thm)],[109,47]) ).
tff(111,plain,
meet(join(meet(a,b),a),meet(join(a,a),join(b,meet(c,a)))) = meet(meet(join(meet(a,b),a),join(a,a)),join(b,meet(c,a))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
<=> ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(113,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',quasi_lattice1) ).
tff(116,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[116]) ).
tff(118,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(a,join(b,c)),meet(a,b)) = meet(a,join(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
join(meet(a,join(b,c)),meet(a,b)) = meet(a,join(b,c)),
inference(unit_resolution,[status(thm)],[119,118]) ).
tff(121,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,a) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
meet(b,a) = meet(a,b),
inference(unit_resolution,[status(thm)],[121,57]) ).
tff(123,plain,
join(meet(a,join(b,c)),meet(b,a)) = join(meet(a,join(b,c)),meet(a,b)),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
| ( meet(join(meet(a,join(b,c)),meet(b,a)),join(meet(a,join(b,c)),b)) = join(meet(a,join(b,c)),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
meet(join(meet(a,join(b,c)),meet(b,a)),join(meet(a,join(b,c)),b)) = join(meet(a,join(b,c)),meet(b,a)),
inference(unit_resolution,[status(thm)],[124,16]) ).
tff(126,plain,
join(meet(a,join(b,c)),meet(a,b)) = join(meet(a,join(b,c)),meet(b,a)),
inference(symmetry,[status(thm)],[123]) ).
tff(127,plain,
meet(a,join(b,c)) = join(meet(a,join(b,c)),meet(a,b)),
inference(symmetry,[status(thm)],[120]) ).
tff(128,plain,
meet(a,join(b,c)) = join(meet(a,join(b,c)),meet(b,a)),
inference(transitivity,[status(thm)],[127,126]) ).
tff(129,plain,
meet(meet(a,join(b,c)),join(meet(a,join(b,c)),b)) = meet(join(meet(a,join(b,c)),meet(b,a)),join(meet(a,join(b,c)),b)),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,join(b,c)),b),meet(a,join(b,c))) = meet(meet(a,join(b,c)),join(meet(a,join(b,c)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
meet(join(meet(a,join(b,c)),b),meet(a,join(b,c))) = meet(meet(a,join(b,c)),join(meet(a,join(b,c)),b)),
inference(unit_resolution,[status(thm)],[130,57]) ).
tff(132,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,c),a) = meet(a,join(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
meet(join(b,c),a) = meet(a,join(b,c)),
inference(unit_resolution,[status(thm)],[132,57]) ).
tff(134,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,b) = join(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
join(c,b) = join(b,c),
inference(unit_resolution,[status(thm)],[134,29]) ).
tff(136,plain,
join(b,c) = join(c,b),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
meet(a,join(b,c)) = meet(a,join(c,b)),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
join(meet(a,join(b,c)),meet(a,c)) = join(meet(a,join(c,b)),meet(a,c)),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
join(meet(a,join(c,b)),meet(a,c)) = join(meet(a,join(b,c)),meet(a,c)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(a,join(c,b)),meet(a,c)) = meet(a,join(c,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
join(meet(a,join(c,b)),meet(a,c)) = meet(a,join(c,b)),
inference(unit_resolution,[status(thm)],[140,118]) ).
tff(142,plain,
meet(a,join(c,b)) = join(meet(a,join(c,b)),meet(a,c)),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
meet(a,join(b,c)) = join(meet(a,join(b,c)),meet(a,c)),
inference(transitivity,[status(thm)],[137,142,139]) ).
tff(144,plain,
join(meet(a,join(b,c)),b) = join(join(meet(a,join(b,c)),meet(a,c)),b),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
join(join(meet(a,join(b,c)),meet(a,c)),b) = join(meet(a,join(b,c)),b),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(147,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',associativity_of_join) ).
tff(150,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[150]) ).
tff(152,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(a,join(b,c)),meet(a,c)),b) = join(meet(a,join(b,c)),join(meet(a,c),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
join(join(meet(a,join(b,c)),meet(a,c)),b) = join(meet(a,join(b,c)),join(meet(a,c),b)),
inference(unit_resolution,[status(thm)],[153,152]) ).
tff(155,plain,
join(meet(a,join(b,c)),join(meet(a,c),b)) = join(join(meet(a,join(b,c)),meet(a,c)),b),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
join(meet(a,join(b,c)),join(meet(a,c),b)) = join(meet(a,join(b,c)),join(b,meet(c,a))),
inference(monotonicity,[status(thm)],[97]) ).
tff(157,plain,
join(meet(a,join(b,c)),join(b,meet(c,a))) = join(meet(a,join(b,c)),join(meet(a,c),b)),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,join(b,c)),join(b,meet(c,a))) = join(join(b,meet(c,a)),meet(a,join(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
join(meet(a,join(b,c)),join(b,meet(c,a))) = join(join(b,meet(c,a)),meet(a,join(b,c))),
inference(unit_resolution,[status(thm)],[158,29]) ).
tff(160,plain,
join(join(b,meet(c,a)),meet(a,join(b,c))) = join(meet(a,join(b,c)),join(b,meet(c,a))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
meet(a,join(b,c)) = meet(join(b,c),a),
inference(symmetry,[status(thm)],[133]) ).
tff(162,plain,
join(join(b,meet(c,a)),meet(a,join(b,c))) = join(join(b,meet(c,a)),meet(join(b,c),a)),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
join(join(b,meet(c,a)),meet(join(b,c),a)) = join(join(b,meet(c,a)),meet(a,join(b,c))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)) )
| ( join(join(b,meet(c,a)),meet(join(b,c),a)) = join(b,meet(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
join(join(b,meet(c,a)),meet(join(b,c),a)) = join(b,meet(c,a)),
inference(unit_resolution,[status(thm)],[164,87]) ).
tff(166,plain,
join(b,meet(c,a)) = join(join(b,meet(c,a)),meet(join(b,c),a)),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
join(b,meet(c,a)) = join(meet(a,join(b,c)),b),
inference(transitivity,[status(thm)],[166,163,160,157,155,145]) ).
tff(168,plain,
meet(join(b,meet(c,a)),meet(join(b,c),a)) = meet(join(meet(a,join(b,c)),b),meet(a,join(b,c))),
inference(monotonicity,[status(thm)],[167,133]) ).
tff(169,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(b,meet(c,a)),join(b,c)),a) = meet(join(b,meet(c,a)),meet(join(b,c),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
meet(meet(join(b,meet(c,a)),join(b,c)),a) = meet(join(b,meet(c,a)),meet(join(b,c),a)),
inference(unit_resolution,[status(thm)],[169,47]) ).
tff(171,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
| ( meet(join(b,meet(c,a)),join(b,c)) = join(b,meet(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(172,plain,
meet(join(b,meet(c,a)),join(b,c)) = join(b,meet(c,a)),
inference(unit_resolution,[status(thm)],[171,16]) ).
tff(173,plain,
join(b,meet(c,a)) = meet(join(b,meet(c,a)),join(b,c)),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
meet(join(b,meet(c,a)),a) = meet(meet(join(b,meet(c,a)),join(b,c)),a),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,meet(c,a)),a) = meet(a,join(b,meet(c,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,plain,
meet(join(b,meet(c,a)),a) = meet(a,join(b,meet(c,a))),
inference(unit_resolution,[status(thm)],[175,57]) ).
tff(177,plain,
meet(a,join(b,meet(c,a))) = meet(join(b,meet(c,a)),a),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
join(meet(a,join(b,c)),b) = join(b,meet(c,a)),
inference(transitivity,[status(thm)],[144,154,156,159,162,165]) ).
tff(179,plain,
meet(a,join(meet(a,join(b,c)),b)) = meet(a,join(b,meet(c,a))),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
meet(join(a,a),join(b,meet(c,a))) = meet(a,join(meet(a,join(b,c)),b)),
inference(monotonicity,[status(thm)],[61,167]) ).
tff(181,plain,
meet(join(a,a),join(b,meet(c,a))) = meet(a,join(b,c)),
inference(transitivity,[status(thm)],[180,179,177,174,170,168,131,129,125,123,120]) ).
tff(182,plain,
meet(join(meet(a,b),a),meet(join(a,a),join(b,meet(c,a)))) = meet(join(meet(a,b),a),meet(a,join(b,c))),
inference(monotonicity,[status(thm)],[181]) ).
tff(183,plain,
meet(join(meet(a,b),a),meet(a,join(b,c))) = meet(join(meet(a,b),a),meet(join(a,a),join(b,meet(c,a)))),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,b),a),meet(a,join(b,c))) = meet(meet(a,join(b,c)),join(meet(a,b),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
meet(join(meet(a,b),a),meet(a,join(b,c))) = meet(meet(a,join(b,c)),join(meet(a,b),a)),
inference(unit_resolution,[status(thm)],[184,57]) ).
tff(186,plain,
meet(meet(a,join(b,c)),join(meet(a,b),a)) = meet(join(meet(a,b),a),meet(a,join(b,c))),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),meet(a,join(b,c))) = join(meet(a,join(b,c)),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
join(meet(a,b),meet(a,join(b,c))) = join(meet(a,join(b,c)),meet(a,b)),
inference(unit_resolution,[status(thm)],[187,29]) ).
tff(189,plain,
join(meet(a,join(b,c)),meet(a,b)) = join(meet(a,b),meet(a,join(b,c))),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
meet(a,join(b,c)) = join(meet(a,b),meet(a,join(b,c))),
inference(transitivity,[status(thm)],[127,189]) ).
tff(191,plain,
meet(meet(a,join(b,c)),join(meet(a,b),a)) = meet(join(meet(a,b),meet(a,join(b,c))),join(meet(a,b),a)),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
meet(join(meet(a,b),meet(a,join(b,c))),join(meet(a,b),a)) = meet(meet(a,join(b,c)),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
| ( meet(join(meet(a,b),meet(a,join(b,c))),join(meet(a,b),a)) = join(meet(a,b),meet(a,join(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(194,plain,
meet(join(meet(a,b),meet(a,join(b,c))),join(meet(a,b),a)) = join(meet(a,b),meet(a,join(b,c))),
inference(unit_resolution,[status(thm)],[193,16]) ).
tff(195,plain,
join(meet(a,b),meet(a,join(b,c))) = meet(join(meet(a,b),meet(a,join(b,c))),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
meet(a,join(b,c)) = meet(join(meet(a,c),b),join(meet(a,b),a)),
inference(transitivity,[status(thm)],[127,189,195,192,186,183,111,108,106,102,99]) ).
tff(197,plain,
join(meet(meet(a,c),join(meet(a,c),a)),meet(meet(a,b),join(meet(a,b),a))) = join(meet(a,c),meet(b,join(meet(a,b),a))),
inference(symmetry,[status(thm)],[80]) ).
tff(198,plain,
join(meet(a,c),meet(meet(a,b),join(meet(a,b),a))) = join(meet(meet(a,c),join(meet(a,c),a)),meet(meet(a,b),join(meet(a,b),a))),
inference(symmetry,[status(thm)],[40]) ).
tff(199,plain,
join(meet(a,c),meet(meet(a,b),join(meet(a,b),a))) = join(meet(a,c),meet(b,join(meet(a,b),a))),
inference(transitivity,[status(thm)],[198,197]) ).
tff(200,plain,
join(join(meet(a,c),meet(meet(a,b),join(meet(a,b),a))),meet(a,join(b,c))) = join(join(meet(a,c),meet(b,join(meet(a,b),a))),meet(join(meet(a,c),b),join(meet(a,b),a))),
inference(monotonicity,[status(thm)],[199,196]) ).
tff(201,plain,
join(meet(a,b),meet(a,c)) = join(meet(meet(a,b),join(meet(a,b),a)),meet(a,c)),
inference(symmetry,[status(thm)],[22]) ).
tff(202,plain,
join(meet(a,b),meet(a,c)) = join(meet(a,c),meet(meet(a,b),join(meet(a,b),a))),
inference(transitivity,[status(thm)],[201,31]) ).
tff(203,plain,
join(join(meet(a,b),meet(a,c)),meet(a,join(b,c))) = join(join(meet(a,c),meet(meet(a,b),join(meet(a,b),a))),meet(a,join(b,c))),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(meet(a,b),meet(a,c)),meet(a,join(b,c))) = join(meet(a,join(b,c)),join(meet(a,b),meet(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
join(join(meet(a,b),meet(a,c)),meet(a,join(b,c))) = join(meet(a,join(b,c)),join(meet(a,b),meet(a,c))),
inference(unit_resolution,[status(thm)],[204,29]) ).
tff(206,plain,
join(meet(a,join(b,c)),join(meet(a,b),meet(a,c))) = join(join(meet(a,b),meet(a,c)),meet(a,join(b,c))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(a,join(b,c)),meet(a,b)),meet(a,c)) = join(meet(a,join(b,c)),join(meet(a,b),meet(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(208,plain,
join(join(meet(a,join(b,c)),meet(a,b)),meet(a,c)) = join(meet(a,join(b,c)),join(meet(a,b),meet(a,c))),
inference(unit_resolution,[status(thm)],[207,152]) ).
tff(209,plain,
meet(a,join(c,b)) = meet(a,join(b,c)),
inference(symmetry,[status(thm)],[137]) ).
tff(210,plain,
meet(a,join(c,b)) = join(meet(a,join(b,c)),meet(a,b)),
inference(transitivity,[status(thm)],[209,127]) ).
tff(211,plain,
join(meet(a,join(c,b)),meet(a,c)) = join(join(meet(a,join(b,c)),meet(a,b)),meet(a,c)),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
meet(a,join(b,c)) = join(meet(a,b),meet(a,c)),
inference(transitivity,[status(thm)],[137,142,211,208,206,203,200,89,80,40,32,22]) ).
tff(213,plain,
( ( meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) )
<=> ( meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(214,axiom,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
tff(215,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(modus_ponens,[status(thm)],[214,213]) ).
tff(216,plain,
$false,
inference(unit_resolution,[status(thm)],[215,212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT021-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 10:47:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.70/0.73 % SZS status Unsatisfiable
% 0.70/0.73 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------