%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT027-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 Jun 21 05:13:45 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 58
% Syntax : Number of formulae : 211 ( 161 unt; 0 typ; 0 def)
% Number of atoms : 275 ( 267 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 96 ( 39 ~; 35 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 216 ( 201 !; 0 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(a,b),join(a,join(b,c))),meet(c,join(a,join(b,c)))),join(a,join(b,c))) = join(a,join(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
join(join(meet(join(a,b),join(a,join(b,c))),meet(c,join(a,join(b,c)))),join(a,join(b,c))) = join(a,join(b,c)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',commutativity_of_meet) ).
tff(14,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,c),join(join(a,b),c)) = meet(join(join(a,b),c),join(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
meet(join(b,c),join(join(a,b),c)) = meet(join(join(a,b),c),join(b,c)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption) ).
tff(23,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(c,join(a,b))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
meet(a,join(c,join(a,b))) = a,
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(29,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)],[28]) ).
tff(30,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(31,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',commutativity_of_join) ).
tff(32,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,join(a,b)) = join(join(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
join(c,join(a,b)) = join(join(a,b),c),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
join(join(a,b),c) = join(c,join(a,b)),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
meet(a,join(join(a,b),c)) = meet(a,join(c,join(a,b))),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
meet(a,join(join(a,b),c)) = a,
inference(transitivity,[status(thm)],[38,27]) ).
tff(40,plain,
join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c))) = join(a,meet(join(join(a,b),c),join(b,c))),
inference(monotonicity,[status(thm)],[39,18]) ).
tff(41,plain,
join(a,meet(join(join(a,b),c),join(b,c))) = join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,meet(join(join(a,b),c),join(b,c))) = join(meet(join(join(a,b),c),join(b,c)),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
join(a,meet(join(join(a,b),c),join(b,c))) = join(meet(join(join(a,b),c),join(b,c)),a),
inference(unit_resolution,[status(thm)],[42,34]) ).
tff(44,plain,
join(meet(join(join(a,b),c),join(b,c)),a) = join(a,meet(join(join(a,b),c),join(b,c))),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
meet(a,join(c,join(a,b))) = meet(a,join(join(a,b),c)),
inference(symmetry,[status(thm)],[38]) ).
tff(46,plain,
a = meet(a,join(c,join(a,b))),
inference(symmetry,[status(thm)],[27]) ).
tff(47,plain,
a = meet(a,join(join(a,b),c)),
inference(transitivity,[status(thm)],[46,45]) ).
tff(48,plain,
meet(join(join(a,b),c),join(b,c)) = meet(join(b,c),join(join(a,b),c)),
inference(symmetry,[status(thm)],[18]) ).
tff(49,plain,
join(meet(join(join(a,b),c),join(b,c)),a) = join(meet(join(b,c),join(join(a,b),c)),meet(a,join(join(a,b),c))),
inference(monotonicity,[status(thm)],[48,47]) ).
tff(50,plain,
join(meet(join(b,c),join(join(a,b),c)),meet(a,join(join(a,b),c))) = join(meet(join(join(a,b),c),join(b,c)),a),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(b,c),join(join(meet(join(join(a,b),c),join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(b,c),join(join(a,b),c)))) = join(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
meet(join(b,c),join(join(meet(join(join(a,b),c),join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(b,c),join(join(a,b),c)))) = join(b,c),
inference(unit_resolution,[status(thm)],[51,25]) ).
tff(53,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(b,join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(a,b),c)) = join(join(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
join(join(meet(b,join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(a,b),c)) = join(join(a,b),c),
inference(unit_resolution,[status(thm)],[53,7]) ).
tff(55,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(56,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)],[55]) ).
tff(57,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(58,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(59,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(join(a,b),c),join(join(a,b),c)),c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
meet(meet(join(join(a,b),c),join(join(a,b),c)),c) = c,
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,meet(join(join(a,b),c),join(join(a,b),c))) = meet(meet(join(join(a,b),c),join(join(a,b),c)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
meet(c,meet(join(join(a,b),c),join(join(a,b),c))) = meet(meet(join(join(a,b),c),join(join(a,b),c)),c),
inference(unit_resolution,[status(thm)],[64,16]) ).
tff(66,plain,
^ [X: $i] :
refl(( ( meet(X,X) = X )
<=> ( meet(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
! [X: $i] : ( meet(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',idempotence_of_meet) ).
tff(70,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(join(join(a,b),c),join(join(a,b),c)) = join(join(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
meet(join(join(a,b),c),join(join(a,b),c)) = join(join(a,b),c),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
join(join(a,b),c) = meet(join(join(a,b),c),join(join(a,b),c)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
meet(c,join(join(a,b),c)) = meet(c,meet(join(join(a,b),c),join(join(a,b),c))),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
meet(c,join(join(a,b),c)) = c,
inference(transitivity,[status(thm)],[76,65,63]) ).
tff(78,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(b,join(c,join(b,a))) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
meet(b,join(c,join(b,a))) = b,
inference(unit_resolution,[status(thm)],[78,25]) ).
tff(80,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,a) = join(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
join(b,a) = join(a,b),
inference(unit_resolution,[status(thm)],[80,34]) ).
tff(82,plain,
join(c,join(b,a)) = join(c,join(a,b)),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
join(c,join(a,b)) = join(c,join(b,a)),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
join(join(a,b),c) = join(c,join(b,a)),
inference(transitivity,[status(thm)],[37,83]) ).
tff(85,plain,
meet(b,join(join(a,b),c)) = meet(b,join(c,join(b,a))),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
meet(b,join(join(a,b),c)) = b,
inference(transitivity,[status(thm)],[85,79]) ).
tff(87,plain,
join(meet(b,join(join(a,b),c)),meet(c,join(join(a,b),c))) = join(b,c),
inference(monotonicity,[status(thm)],[86,77]) ).
tff(88,plain,
join(b,c) = join(meet(b,join(join(a,b),c)),meet(c,join(join(a,b),c))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
join(join(b,c),join(join(a,b),c)) = join(join(meet(b,join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(a,b),c)),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
join(join(b,c),join(join(a,b),c)) = join(join(a,b),c),
inference(transitivity,[status(thm)],[89,54]) ).
tff(91,plain,
join(join(meet(join(join(a,b),c),join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(b,c),join(join(a,b),c))) = join(join(meet(join(join(a,b),c),join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(a,b),c)),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
join(join(meet(join(join(a,b),c),join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(a,b),c)) = join(join(meet(join(join(a,b),c),join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(b,c),join(join(a,b),c))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(join(a,b),c),join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(a,b),c)) = join(join(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
join(join(meet(join(join(a,b),c),join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(a,b),c)) = join(join(a,b),c),
inference(unit_resolution,[status(thm)],[93,7]) ).
tff(95,plain,
join(join(a,b),c) = join(join(meet(join(join(a,b),c),join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(a,b),c)),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
join(join(a,b),c) = join(join(meet(join(join(a,b),c),join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(b,c),join(join(a,b),c))),
inference(transitivity,[status(thm)],[95,92]) ).
tff(97,plain,
meet(join(b,c),join(join(a,b),c)) = meet(join(b,c),join(join(meet(join(join(a,b),c),join(join(a,b),c)),meet(c,join(join(a,b),c))),join(join(b,c),join(join(a,b),c)))),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
meet(join(b,c),join(join(a,b),c)) = join(b,c),
inference(transitivity,[status(thm)],[97,52]) ).
tff(99,plain,
join(meet(join(b,c),join(join(a,b),c)),meet(a,join(join(a,b),c))) = join(join(b,c),a),
inference(monotonicity,[status(thm)],[98,39]) ).
tff(100,plain,
join(join(b,c),a) = join(meet(join(b,c),join(join(a,b),c)),meet(a,join(join(a,b),c))),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(b,c),a) = join(a,join(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
join(join(b,c),a) = join(a,join(b,c)),
inference(unit_resolution,[status(thm)],[101,34]) ).
tff(103,plain,
join(a,join(b,c)) = join(join(b,c),a),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
join(a,join(b,c)) = join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c))),
inference(transitivity,[status(thm)],[103,100,50,44,41]) ).
tff(105,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(join(a,join(b,c)),join(a,b)),meet(join(a,join(b,c)),join(a,b))),join(a,b)) = join(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
join(join(meet(join(a,join(b,c)),join(a,b)),meet(join(a,join(b,c)),join(a,b))),join(a,b)) = join(a,b),
inference(unit_resolution,[status(thm)],[105,7]) ).
tff(107,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(join(a,b),join(a,b)) = join(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
meet(join(a,b),join(a,b)) = join(a,b),
inference(unit_resolution,[status(thm)],[107,72]) ).
tff(109,plain,
^ [X: $i] :
refl(( ( join(X,X) = X )
<=> ( join(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(110,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,axiom,
! [X: $i] : ( join(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT005-0.ax',idempotence_of_join) ).
tff(113,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [X: $i] : ( join(X,X) = X ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(join(a,join(b,c)),join(a,b)),meet(join(a,join(b,c)),join(a,b))) = meet(join(a,join(b,c)),join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
join(meet(join(a,join(b,c)),join(a,b)),meet(join(a,join(b,c)),join(a,b))) = meet(join(a,join(b,c)),join(a,b)),
inference(unit_resolution,[status(thm)],[116,115]) ).
tff(118,plain,
meet(join(a,join(b,c)),join(a,b)) = join(meet(join(a,join(b,c)),join(a,b)),meet(join(a,join(b,c)),join(a,b))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
join(meet(join(a,join(b,c)),join(a,b)),meet(join(a,b),join(a,b))) = join(join(meet(join(a,join(b,c)),join(a,b)),meet(join(a,join(b,c)),join(a,b))),join(a,b)),
inference(monotonicity,[status(thm)],[118,108]) ).
tff(120,plain,
join(a,b) = meet(join(a,b),join(a,b)),
inference(symmetry,[status(thm)],[108]) ).
tff(121,plain,
join(meet(join(a,join(b,c)),join(a,b)),join(a,b)) = join(meet(join(a,join(b,c)),join(a,b)),meet(join(a,b),join(a,b))),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,join(b,c)),join(a,b)),join(a,b)) = join(join(a,b),meet(join(a,join(b,c)),join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
join(meet(join(a,join(b,c)),join(a,b)),join(a,b)) = join(join(a,b),meet(join(a,join(b,c)),join(a,b))),
inference(unit_resolution,[status(thm)],[122,34]) ).
tff(124,plain,
join(join(a,b),meet(join(a,join(b,c)),join(a,b))) = join(meet(join(a,join(b,c)),join(a,b)),join(a,b)),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
join(meet(join(a,b),join(a,b)),meet(join(a,join(b,c)),join(a,b))) = join(join(a,b),meet(join(a,join(b,c)),join(a,b))),
inference(monotonicity,[status(thm)],[108]) ).
tff(126,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(a,b),join(join(a,join(b,c)),b)),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
meet(meet(join(a,b),join(join(a,join(b,c)),b)),b) = b,
inference(unit_resolution,[status(thm)],[126,61]) ).
tff(128,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(b,join(a,join(b,c))),meet(b,join(a,join(b,c)))),join(a,join(b,c))) = join(a,join(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
join(join(meet(b,join(a,join(b,c))),meet(b,join(a,join(b,c)))),join(a,join(b,c))) = join(a,join(b,c)),
inference(unit_resolution,[status(thm)],[128,7]) ).
tff(130,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(join(a,join(b,c)),join(a,join(b,c))) = join(a,join(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
meet(join(a,join(b,c)),join(a,join(b,c))) = join(a,join(b,c)),
inference(unit_resolution,[status(thm)],[130,72]) ).
tff(132,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(a,b),join(a,b)),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
meet(meet(join(a,b),join(a,b)),b) = b,
inference(unit_resolution,[status(thm)],[132,61]) ).
tff(134,plain,
b = meet(meet(join(a,b),join(a,b)),b),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(b,join(a,join(b,c))) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
meet(b,join(a,join(b,c))) = b,
inference(unit_resolution,[status(thm)],[135,25]) ).
tff(137,plain,
meet(b,join(a,join(b,c))) = meet(meet(join(a,b),join(a,b)),b),
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,plain,
join(meet(b,join(a,join(b,c))),meet(b,join(a,join(b,c)))) = join(meet(meet(join(a,b),join(a,b)),b),meet(meet(join(a,b),join(a,b)),b)),
inference(monotonicity,[status(thm)],[137,137]) ).
tff(139,plain,
join(meet(meet(join(a,b),join(a,b)),b),meet(meet(join(a,b),join(a,b)),b)) = join(meet(b,join(a,join(b,c))),meet(b,join(a,join(b,c)))),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
join(meet(meet(join(a,b),join(a,b)),b),meet(meet(join(a,b),join(a,b)),b)) = join(b,b),
inference(monotonicity,[status(thm)],[133,133]) ).
tff(141,plain,
join(b,b) = join(meet(meet(join(a,b),join(a,b)),b),meet(meet(join(a,b),join(a,b)),b)),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(b,b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
join(b,b) = b,
inference(unit_resolution,[status(thm)],[142,115]) ).
tff(144,plain,
b = join(b,b),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
meet(b,join(a,join(b,c))) = join(meet(b,join(a,join(b,c))),meet(b,join(a,join(b,c)))),
inference(transitivity,[status(thm)],[136,144,141,139]) ).
tff(146,plain,
join(meet(b,join(a,join(b,c))),meet(join(a,join(b,c)),join(a,join(b,c)))) = join(join(meet(b,join(a,join(b,c))),meet(b,join(a,join(b,c)))),join(a,join(b,c))),
inference(monotonicity,[status(thm)],[145,131]) ).
tff(147,plain,
join(a,join(b,c)) = meet(join(a,join(b,c)),join(a,join(b,c))),
inference(symmetry,[status(thm)],[131]) ).
tff(148,plain,
b = meet(b,join(a,join(b,c))),
inference(symmetry,[status(thm)],[136]) ).
tff(149,plain,
join(b,join(a,join(b,c))) = join(meet(b,join(a,join(b,c))),meet(join(a,join(b,c)),join(a,join(b,c)))),
inference(monotonicity,[status(thm)],[148,147]) ).
tff(150,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,join(a,join(b,c))) = join(join(a,join(b,c)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
join(b,join(a,join(b,c))) = join(join(a,join(b,c)),b),
inference(unit_resolution,[status(thm)],[150,34]) ).
tff(152,plain,
join(join(a,join(b,c)),b) = join(b,join(a,join(b,c))),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
join(join(a,join(b,c)),b) = join(join(b,c),a),
inference(transitivity,[status(thm)],[152,149,146,129,103]) ).
tff(154,plain,
join(a,b) = join(b,a),
inference(symmetry,[status(thm)],[81]) ).
tff(155,plain,
meet(join(a,b),join(join(a,join(b,c)),b)) = meet(join(b,a),join(join(b,c),a)),
inference(monotonicity,[status(thm)],[154,153]) ).
tff(156,plain,
meet(join(b,a),join(join(b,c),a)) = meet(join(a,b),join(join(a,join(b,c)),b)),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
meet(join(b,a),join(join(b,c),a)) = meet(join(a,b),join(a,join(b,c))),
inference(monotonicity,[status(thm)],[81,102]) ).
tff(158,plain,
meet(join(a,b),join(a,join(b,c))) = meet(join(b,a),join(join(b,c),a)),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),join(a,join(b,c))) = meet(join(a,join(b,c)),join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
meet(join(a,b),join(a,join(b,c))) = meet(join(a,join(b,c)),join(a,b)),
inference(unit_resolution,[status(thm)],[159,16]) ).
tff(161,plain,
meet(join(a,join(b,c)),join(a,b)) = meet(join(a,b),join(a,join(b,c))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
meet(join(a,join(b,c)),join(a,b)) = meet(join(a,b),join(join(a,join(b,c)),b)),
inference(transitivity,[status(thm)],[161,158,156]) ).
tff(163,plain,
meet(meet(join(a,join(b,c)),join(a,b)),b) = meet(meet(join(a,b),join(join(a,join(b,c)),b)),b),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,meet(join(a,join(b,c)),join(a,b))) = meet(meet(join(a,join(b,c)),join(a,b)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
meet(b,meet(join(a,join(b,c)),join(a,b))) = meet(meet(join(a,join(b,c)),join(a,b)),b),
inference(unit_resolution,[status(thm)],[164,16]) ).
tff(166,plain,
meet(b,meet(join(a,join(b,c)),join(a,b))) = b,
inference(transitivity,[status(thm)],[165,163,127]) ).
tff(167,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Z,Y)),Y) = Y )
| ( meet(meet(join(join(b,c),a),join(b,a)),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
meet(meet(join(join(b,c),a),join(b,a)),a) = a,
inference(unit_resolution,[status(thm)],[167,61]) ).
tff(169,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,meet(join(join(b,c),a),join(b,a))) = meet(meet(join(join(b,c),a),join(b,a)),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
meet(a,meet(join(join(b,c),a),join(b,a))) = meet(meet(join(join(b,c),a),join(b,a)),a),
inference(unit_resolution,[status(thm)],[169,16]) ).
tff(171,plain,
meet(join(join(b,c),a),join(b,a)) = meet(join(a,join(b,c)),join(a,b)),
inference(monotonicity,[status(thm)],[102,81]) ).
tff(172,plain,
meet(join(a,join(b,c)),join(a,b)) = meet(join(join(b,c),a),join(b,a)),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
meet(a,meet(join(a,join(b,c)),join(a,b))) = meet(a,meet(join(join(b,c),a),join(b,a))),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
meet(a,meet(join(a,join(b,c)),join(a,b))) = a,
inference(transitivity,[status(thm)],[173,170,168]) ).
tff(175,plain,
join(meet(a,meet(join(a,join(b,c)),join(a,b))),meet(b,meet(join(a,join(b,c)),join(a,b)))) = join(a,b),
inference(monotonicity,[status(thm)],[174,166]) ).
tff(176,plain,
join(meet(a,meet(join(a,join(b,c)),join(a,b))),meet(b,meet(join(a,join(b,c)),join(a,b)))) = meet(join(a,b),join(a,b)),
inference(transitivity,[status(thm)],[175,120]) ).
tff(177,plain,
join(join(meet(a,meet(join(a,join(b,c)),join(a,b))),meet(b,meet(join(a,join(b,c)),join(a,b)))),meet(join(a,join(b,c)),join(a,b))) = join(meet(join(a,b),join(a,b)),meet(join(a,join(b,c)),join(a,b))),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Z,Y)),Y) = Y )
| ( join(join(meet(a,meet(join(a,join(b,c)),join(a,b))),meet(b,meet(join(a,join(b,c)),join(a,b)))),meet(join(a,join(b,c)),join(a,b))) = meet(join(a,join(b,c)),join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
join(join(meet(a,meet(join(a,join(b,c)),join(a,b))),meet(b,meet(join(a,join(b,c)),join(a,b)))),meet(join(a,join(b,c)),join(a,b))) = meet(join(a,join(b,c)),join(a,b)),
inference(unit_resolution,[status(thm)],[178,7]) ).
tff(180,plain,
meet(join(a,join(b,c)),join(a,b)) = join(join(meet(a,meet(join(a,join(b,c)),join(a,b))),meet(b,meet(join(a,join(b,c)),join(a,b)))),meet(join(a,join(b,c)),join(a,b))),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
meet(join(a,b),join(a,join(b,c))) = join(a,b),
inference(transitivity,[status(thm)],[160,180,177,125,124,121,119,106]) ).
tff(182,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(c,join(a,join(c,b))) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(183,plain,
meet(c,join(a,join(c,b))) = c,
inference(unit_resolution,[status(thm)],[182,25]) ).
tff(184,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,b) = join(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(185,plain,
join(c,b) = join(b,c),
inference(unit_resolution,[status(thm)],[184,34]) ).
tff(186,plain,
join(a,join(c,b)) = join(a,join(b,c)),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
join(a,join(b,c)) = join(a,join(c,b)),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
meet(c,join(a,join(b,c))) = meet(c,join(a,join(c,b))),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
meet(c,join(a,join(b,c))) = c,
inference(transitivity,[status(thm)],[188,183]) ).
tff(190,plain,
join(meet(c,join(a,join(b,c))),meet(join(a,b),join(a,join(b,c)))) = join(c,join(a,b)),
inference(monotonicity,[status(thm)],[189,181]) ).
tff(191,plain,
meet(c,join(a,join(c,b))) = meet(c,join(a,join(b,c))),
inference(symmetry,[status(thm)],[188]) ).
tff(192,plain,
c = meet(c,join(a,join(c,b))),
inference(symmetry,[status(thm)],[183]) ).
tff(193,plain,
c = meet(c,join(a,join(b,c))),
inference(transitivity,[status(thm)],[192,191]) ).
tff(194,plain,
join(c,meet(join(a,join(b,c)),join(a,b))) = join(meet(c,join(a,join(b,c))),meet(join(a,b),join(a,join(b,c)))),
inference(monotonicity,[status(thm)],[193,161]) ).
tff(195,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,join(b,c)),join(a,b)),c) = join(c,meet(join(a,join(b,c)),join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(196,plain,
join(meet(join(a,join(b,c)),join(a,b)),c) = join(c,meet(join(a,join(b,c)),join(a,b))),
inference(unit_resolution,[status(thm)],[195,34]) ).
tff(197,plain,
join(meet(join(a,b),join(a,join(b,c))),meet(c,join(a,join(b,c)))) = join(meet(join(a,join(b,c)),join(a,b)),c),
inference(monotonicity,[status(thm)],[160,189]) ).
tff(198,plain,
join(meet(join(a,b),join(a,join(b,c))),meet(c,join(a,join(b,c)))) = join(join(a,b),c),
inference(transitivity,[status(thm)],[197,196,194,190,36]) ).
tff(199,plain,
join(join(meet(join(a,b),join(a,join(b,c))),meet(c,join(a,join(b,c)))),join(a,join(b,c))) = join(join(join(a,b),c),join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c)))),
inference(monotonicity,[status(thm)],[198,104]) ).
tff(200,plain,
join(join(join(a,b),c),join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c)))) = join(join(meet(join(a,b),join(a,join(b,c))),meet(c,join(a,join(b,c)))),join(a,join(b,c))),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(join(a,b),c),join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c)))) = join(join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c))),join(join(a,b),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
join(join(join(a,b),c),join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c)))) = join(join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c))),join(join(a,b),c)),
inference(unit_resolution,[status(thm)],[201,34]) ).
tff(203,plain,
join(join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c))),join(join(a,b),c)) = join(join(join(a,b),c),join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c)))),
inference(symmetry,[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(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c))),join(join(a,b),c)) = join(join(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(205,plain,
join(join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c))),join(join(a,b),c)) = join(join(a,b),c),
inference(unit_resolution,[status(thm)],[204,7]) ).
tff(206,plain,
join(join(a,b),c) = join(join(meet(a,join(join(a,b),c)),meet(join(b,c),join(join(a,b),c))),join(join(a,b),c)),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
join(join(a,b),c) = join(a,join(b,c)),
inference(transitivity,[status(thm)],[206,203,200,9]) ).
tff(208,plain,
( ( join(join(a,b),c) != join(a,join(b,c)) )
<=> ( join(join(a,b),c) != join(a,join(b,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(209,axiom,
join(join(a,b),c) != join(a,join(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_join) ).
tff(210,plain,
join(join(a,b),c) != join(a,join(b,c)),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
$false,
inference(unit_resolution,[status(thm)],[210,207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT027-1 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.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 Jun 19 19:27:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.52 % SZS status Unsatisfiable
% 0.19/0.52 % SZS output start Proof
% See solution above
% 0.19/0.54 % E exiting
%------------------------------------------------------------------------------