%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT022-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:13:44 AM UTC 2025
% Result : Unsatisfiable 78.82s 79.01s
% Output : Proof 78.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 71
% Syntax : Number of formulae : 265 ( 204 unt; 0 typ; 0 def)
% Number of atoms : 344 ( 334 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 116 ( 46 ~; 42 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 9 ( 9 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 : 296 ( 275 !; 0 ?; 296 :)
% 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,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',commutativity_of_join) ).
tff(5,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,c),meet(a,b)) = join(meet(a,b),meet(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
join(meet(a,c),meet(a,b)) = join(meet(a,b),meet(a,c)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.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(b,a) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
meet(b,a) = meet(a,b),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
join(meet(a,c),meet(b,a)) = join(meet(a,c),meet(a,b)),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,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(21,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)],[20]) ).
tff(22,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(23,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',quasi_lattice2) ).
tff(24,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)],[23,22]) ).
tff(25,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)],[24]) ).
tff(26,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)],[25,21]) ).
tff(27,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(b,a)),join(meet(a,c),b)) = join(meet(a,c),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
meet(join(meet(a,c),meet(b,a)),join(meet(a,c),b)) = join(meet(a,c),meet(b,a)),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,c),b) = join(b,meet(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
join(meet(a,c),b) = join(b,meet(a,c)),
inference(unit_resolution,[status(thm)],[29,7]) ).
tff(31,plain,
join(b,meet(a,c)) = join(meet(a,c),b),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
join(meet(a,c),meet(a,b)) = join(meet(a,c),meet(b,a)),
inference(symmetry,[status(thm)],[19]) ).
tff(33,plain,
join(meet(a,b),meet(a,c)) = join(meet(a,c),meet(a,b)),
inference(symmetry,[status(thm)],[9]) ).
tff(34,plain,
join(meet(a,b),meet(a,c)) = join(meet(a,c),meet(b,a)),
inference(transitivity,[status(thm)],[33,32]) ).
tff(35,plain,
meet(join(meet(a,b),meet(a,c)),join(b,meet(a,c))) = meet(join(meet(a,c),meet(b,a)),join(meet(a,c),b)),
inference(monotonicity,[status(thm)],[34,31]) ).
tff(36,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,meet(a,c)),join(meet(a,b),meet(a,c))) = meet(join(meet(a,b),meet(a,c)),join(b,meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
meet(join(b,meet(a,c)),join(meet(a,b),meet(a,c))) = meet(join(meet(a,b),meet(a,c)),join(b,meet(a,c))),
inference(unit_resolution,[status(thm)],[36,16]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',quasi_lattice1) ).
tff(42,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)],[41,40]) ).
tff(43,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)],[42]) ).
tff(44,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)],[43,39]) ).
tff(45,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(join(b,meet(a,c)),join(meet(a,b),meet(a,c))),meet(join(b,meet(a,c)),meet(a,b))) = meet(join(b,meet(a,c)),join(meet(a,b),meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
join(meet(join(b,meet(a,c)),join(meet(a,b),meet(a,c))),meet(join(b,meet(a,c)),meet(a,b))) = meet(join(b,meet(a,c)),join(meet(a,b),meet(a,c))),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,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(48,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)],[47]) ).
tff(49,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(50,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',associativity_of_meet) ).
tff(51,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(b,meet(a,c)),a),b) = meet(join(b,meet(a,c)),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
meet(meet(join(b,meet(a,c)),a),b) = meet(join(b,meet(a,c)),meet(a,b)),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,meet(a,c)),a) = meet(a,join(b,meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
meet(join(b,meet(a,c)),a) = meet(a,join(b,meet(a,c))),
inference(unit_resolution,[status(thm)],[56,16]) ).
tff(58,plain,
meet(meet(join(b,meet(a,c)),a),b) = meet(meet(a,join(b,meet(a,c))),b),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
meet(meet(a,join(b,meet(a,c))),b) = meet(meet(join(b,meet(a,c)),a),b),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,meet(a,join(b,meet(a,c)))) = meet(meet(a,join(b,meet(a,c))),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
meet(b,meet(a,join(b,meet(a,c)))) = meet(meet(a,join(b,meet(a,c))),b),
inference(unit_resolution,[status(thm)],[60,16]) ).
tff(62,plain,
meet(a,join(meet(a,c),b)) = meet(a,join(b,meet(a,c))),
inference(monotonicity,[status(thm)],[30]) ).
tff(63,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(meet(a,c),b)),meet(a,meet(a,c))) = meet(a,join(meet(a,c),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
join(meet(a,join(meet(a,c),b)),meet(a,meet(a,c))) = meet(a,join(meet(a,c),b)),
inference(unit_resolution,[status(thm)],[63,44]) ).
tff(65,plain,
meet(a,join(b,meet(a,c))) = meet(a,join(meet(a,c),b)),
inference(symmetry,[status(thm)],[62]) ).
tff(66,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,meet(a,c))),meet(a,b)) = meet(a,join(b,meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
join(meet(a,join(b,meet(a,c))),meet(a,b)) = meet(a,join(b,meet(a,c))),
inference(unit_resolution,[status(thm)],[66,44]) ).
tff(68,plain,
join(meet(a,join(b,meet(a,c))),meet(a,b)) = meet(a,join(meet(a,c),b)),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,plain,
join(join(meet(a,join(b,meet(a,c))),meet(a,b)),meet(a,meet(a,c))) = join(meet(a,join(meet(a,c),b)),meet(a,meet(a,c))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,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(71,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)],[70]) ).
tff(72,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(73,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',associativity_of_join) ).
tff(74,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(a,join(b,meet(a,c))),meet(a,b)),meet(a,meet(a,c))) = join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,meet(a,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
join(join(meet(a,join(b,meet(a,c))),meet(a,b)),meet(a,meet(a,c))) = join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,meet(a,c)))),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,meet(a,c)))) = join(join(meet(a,join(b,meet(a,c))),meet(a,b)),meet(a,meet(a,c))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
^ [X: $i] :
refl(( ( meet(X,X) = X )
<=> ( meet(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
! [X: $i] : ( meet(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_of_meet) ).
tff(84,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(a,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
meet(a,a) = a,
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
a = meet(a,a),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
meet(a,c) = meet(meet(a,a),c),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
meet(meet(a,a),c) = meet(a,c),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,a),c) = meet(a,meet(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
meet(meet(a,a),c) = meet(a,meet(a,c)),
inference(unit_resolution,[status(thm)],[92,53]) ).
tff(94,plain,
meet(a,meet(a,c)) = meet(meet(a,a),c),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
meet(a,meet(a,c)) = meet(a,c),
inference(transitivity,[status(thm)],[94,91]) ).
tff(96,plain,
join(meet(a,b),meet(a,meet(a,c))) = join(meet(a,b),meet(a,c)),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
join(meet(a,b),meet(a,c)) = join(meet(a,b),meet(a,meet(a,c))),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))) = join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,meet(a,c)))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))) = meet(a,join(b,meet(a,c))),
inference(transitivity,[status(thm)],[98,79,69,64,62]) ).
tff(100,plain,
meet(b,join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c)))) = meet(b,meet(a,join(b,meet(a,c)))),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
meet(b,join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c)))) = meet(join(b,meet(a,c)),meet(a,b)),
inference(transitivity,[status(thm)],[100,61,59,55]) ).
tff(102,plain,
meet(join(meet(a,b),meet(a,c)),join(b,meet(a,c))) = meet(join(b,meet(a,c)),join(meet(a,b),meet(a,c))),
inference(symmetry,[status(thm)],[37]) ).
tff(103,plain,
meet(join(meet(a,c),meet(b,a)),join(meet(a,c),b)) = meet(join(meet(a,b),meet(a,c)),join(b,meet(a,c))),
inference(symmetry,[status(thm)],[35]) ).
tff(104,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,c)),join(meet(a,b),a)) = join(meet(a,b),meet(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
meet(join(meet(a,b),meet(a,c)),join(meet(a,b),a)) = join(meet(a,b),meet(a,c)),
inference(unit_resolution,[status(thm)],[104,26]) ).
tff(106,plain,
meet(join(meet(a,b),meet(a,c)),join(meet(a,b),a)) = join(meet(a,c),meet(b,a)),
inference(transitivity,[status(thm)],[105,33,32]) ).
tff(107,plain,
meet(meet(join(meet(a,b),meet(a,c)),join(meet(a,b),a)),join(b,meet(a,c))) = meet(join(meet(a,c),meet(b,a)),join(meet(a,c),b)),
inference(monotonicity,[status(thm)],[106,31]) ).
tff(108,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(meet(a,b),meet(a,c)),join(meet(a,b),a)),join(b,meet(a,c))) = meet(join(meet(a,b),meet(a,c)),meet(join(meet(a,b),a),join(b,meet(a,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
meet(meet(join(meet(a,b),meet(a,c)),join(meet(a,b),a)),join(b,meet(a,c))) = meet(join(meet(a,b),meet(a,c)),meet(join(meet(a,b),a),join(b,meet(a,c)))),
inference(unit_resolution,[status(thm)],[108,53]) ).
tff(110,plain,
meet(join(meet(a,b),meet(a,c)),meet(join(meet(a,b),a),join(b,meet(a,c)))) = meet(meet(join(meet(a,b),meet(a,c)),join(meet(a,b),a)),join(b,meet(a,c))),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(join(meet(a,b),a),join(b,meet(a,c))),join(meet(a,b),meet(a,c))) = meet(join(meet(a,b),meet(a,c)),meet(join(meet(a,b),a),join(b,meet(a,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
meet(meet(join(meet(a,b),a),join(b,meet(a,c))),join(meet(a,b),meet(a,c))) = meet(join(meet(a,b),meet(a,c)),meet(join(meet(a,b),a),join(b,meet(a,c)))),
inference(unit_resolution,[status(thm)],[111,16]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,meet(a,c)),join(meet(a,b),a)) = meet(join(meet(a,b),a),join(b,meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
meet(join(b,meet(a,c)),join(meet(a,b),a)) = meet(join(meet(a,b),a),join(b,meet(a,c))),
inference(unit_resolution,[status(thm)],[113,16]) ).
tff(115,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,join(meet(a,b),a)) = meet(join(meet(a,b),a),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
meet(a,join(meet(a,b),a)) = meet(join(meet(a,b),a),a),
inference(unit_resolution,[status(thm)],[115,16]) ).
tff(117,plain,
meet(join(meet(a,b),a),a) = meet(a,join(meet(a,b),a)),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
^ [X: $i] :
refl(( ( join(X,X) = X )
<=> ( join(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,axiom,
! [X: $i] : ( join(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_of_join) ).
tff(122,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [X: $i] : ( join(X,X) = X ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(a,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
join(a,a) = a,
inference(unit_resolution,[status(thm)],[125,124]) ).
tff(127,plain,
a = join(a,a),
inference(symmetry,[status(thm)],[126]) ).
tff(128,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(129,plain,
join(a,meet(a,b)) = join(meet(a,b),a),
inference(unit_resolution,[status(thm)],[128,7]) ).
tff(130,plain,
join(meet(a,b),a) = join(a,meet(a,b)),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
meet(join(meet(a,b),a),a) = meet(join(a,meet(a,b)),join(a,a)),
inference(monotonicity,[status(thm)],[130,127]) ).
tff(132,plain,
meet(join(a,meet(a,b)),join(a,a)) = meet(join(meet(a,b),a),a),
inference(symmetry,[status(thm)],[131]) ).
tff(133,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(134,plain,
meet(join(a,meet(a,b)),join(a,a)) = join(a,meet(a,b)),
inference(unit_resolution,[status(thm)],[133,26]) ).
tff(135,plain,
join(a,meet(a,b)) = meet(join(a,meet(a,b)),join(a,a)),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
join(meet(a,b),a) = meet(a,join(meet(a,b),a)),
inference(transitivity,[status(thm)],[130,135,132,117]) ).
tff(137,plain,
meet(join(b,meet(a,c)),join(meet(a,b),a)) = meet(join(b,meet(a,c)),meet(a,join(meet(a,b),a))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
meet(join(b,meet(a,c)),meet(a,join(meet(a,b),a))) = meet(join(b,meet(a,c)),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(b,meet(a,c)),a),join(meet(a,b),a)) = meet(join(b,meet(a,c)),meet(a,join(meet(a,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
meet(meet(join(b,meet(a,c)),a),join(meet(a,b),a)) = meet(join(b,meet(a,c)),meet(a,join(meet(a,b),a))),
inference(unit_resolution,[status(thm)],[139,53]) ).
tff(141,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),meet(a,join(b,meet(a,c)))) = join(meet(a,join(b,meet(a,c))),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
join(meet(a,b),meet(a,join(b,meet(a,c)))) = join(meet(a,join(b,meet(a,c))),meet(a,b)),
inference(unit_resolution,[status(thm)],[141,7]) ).
tff(143,plain,
join(meet(a,join(b,meet(a,c))),meet(a,b)) = join(meet(a,b),meet(a,join(b,meet(a,c)))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
meet(a,join(b,meet(a,c))) = join(meet(a,join(b,meet(a,c))),meet(a,b)),
inference(symmetry,[status(thm)],[67]) ).
tff(145,plain,
meet(join(b,meet(a,c)),a) = join(meet(a,b),meet(a,join(b,meet(a,c)))),
inference(transitivity,[status(thm)],[57,144,143]) ).
tff(146,plain,
meet(meet(join(b,meet(a,c)),a),join(meet(a,b),a)) = meet(join(meet(a,b),meet(a,join(b,meet(a,c)))),join(meet(a,b),a)),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
meet(join(meet(a,b),meet(a,join(b,meet(a,c)))),join(meet(a,b),a)) = meet(meet(join(b,meet(a,c)),a),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[146]) ).
tff(148,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,meet(a,c)))),join(meet(a,b),a)) = join(meet(a,b),meet(a,join(b,meet(a,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
meet(join(meet(a,b),meet(a,join(b,meet(a,c)))),join(meet(a,b),a)) = join(meet(a,b),meet(a,join(b,meet(a,c)))),
inference(unit_resolution,[status(thm)],[148,26]) ).
tff(150,plain,
join(meet(a,b),meet(a,join(b,meet(a,c)))) = meet(join(meet(a,b),meet(a,join(b,meet(a,c)))),join(meet(a,b),a)),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
meet(a,join(b,meet(a,c))) = meet(join(meet(a,b),a),join(b,meet(a,c))),
inference(transitivity,[status(thm)],[144,143,150,147,140,138,114]) ).
tff(152,plain,
meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))) = meet(meet(join(meet(a,b),a),join(b,meet(a,c))),join(meet(a,b),meet(a,c))),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))) = meet(join(b,meet(a,c)),join(meet(a,b),meet(a,c))),
inference(transitivity,[status(thm)],[152,112,110,107,103,102]) ).
tff(154,plain,
join(meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))),meet(b,join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))))) = join(meet(join(b,meet(a,c)),join(meet(a,b),meet(a,c))),meet(join(b,meet(a,c)),meet(a,b))),
inference(monotonicity,[status(thm)],[153,101]) ).
tff(155,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) )
<=> ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) ) )),
inference(bind,[status(th)],[]) ).
tff(156,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_dual_modularity) ).
tff(159,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) ),
inference(skolemize,[status(sab)],[159]) ).
tff(161,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) )
| ( join(meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))),meet(b,join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))))) = meet(join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))),join(b,meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
join(meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))),meet(b,join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))))) = meet(join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))),join(b,meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))))),
inference(unit_resolution,[status(thm)],[162,161]) ).
tff(164,plain,
meet(join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))),join(b,meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))))) = join(meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))),meet(b,join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))))),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))) = join(meet(a,c),meet(a,b)),
inference(transitivity,[status(thm)],[152,112,110,107,28,19]) ).
tff(166,plain,
join(b,meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c)))) = join(b,join(meet(a,c),meet(a,b))),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
join(b,join(meet(a,c),meet(a,b))) = join(b,meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c)))),
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(b,meet(a,c)),meet(a,b)) = join(b,join(meet(a,c),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
join(join(b,meet(a,c)),meet(a,b)) = join(b,join(meet(a,c),meet(a,b))),
inference(unit_resolution,[status(thm)],[168,76]) ).
tff(170,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(b,meet(a,c)),meet(a,b)) = join(meet(a,b),join(b,meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(171,plain,
join(join(b,meet(a,c)),meet(a,b)) = join(meet(a,b),join(b,meet(a,c))),
inference(unit_resolution,[status(thm)],[170,7]) ).
tff(172,plain,
join(meet(a,b),join(b,meet(a,c))) = join(join(b,meet(a,c)),meet(a,b)),
inference(symmetry,[status(thm)],[171]) ).
tff(173,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(a,c)),join(b,a)) = join(b,meet(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
meet(join(b,meet(a,c)),join(b,a)) = join(b,meet(a,c)),
inference(unit_resolution,[status(thm)],[173,26]) ).
tff(175,plain,
join(b,meet(a,c)) = meet(join(b,meet(a,c)),join(b,a)),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
meet(a,b) = meet(b,a),
inference(symmetry,[status(thm)],[18]) ).
tff(177,plain,
join(meet(a,b),join(b,meet(a,c))) = join(meet(b,a),meet(join(b,meet(a,c)),join(b,a))),
inference(monotonicity,[status(thm)],[176,175]) ).
tff(178,plain,
join(meet(b,a),meet(join(b,meet(a,c)),join(b,a))) = join(meet(a,b),join(b,meet(a,c))),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Z,join(X,Y))) = meet(join(X,Y),join(Z,meet(X,Y))) )
| ( join(meet(b,a),meet(join(b,meet(a,c)),join(b,a))) = meet(join(b,a),join(join(b,meet(a,c)),meet(b,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
join(meet(b,a),meet(join(b,meet(a,c)),join(b,a))) = meet(join(b,a),join(join(b,meet(a,c)),meet(b,a))),
inference(unit_resolution,[status(thm)],[179,161]) ).
tff(181,plain,
meet(join(b,a),join(join(b,meet(a,c)),meet(b,a))) = join(meet(b,a),meet(join(b,meet(a,c)),join(b,a))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
join(join(b,meet(a,c)),meet(b,a)) = join(join(b,meet(a,c)),meet(a,b)),
inference(monotonicity,[status(thm)],[18]) ).
tff(183,plain,
meet(join(b,a),join(join(b,meet(a,c)),meet(b,a))) = meet(join(b,a),join(join(b,meet(a,c)),meet(a,b))),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
meet(join(b,a),join(join(b,meet(a,c)),meet(a,b))) = meet(join(b,a),join(join(b,meet(a,c)),meet(b,a))),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(join(b,a),join(join(b,meet(a,c)),meet(a,b))),meet(join(b,a),join(b,meet(a,c)))) = meet(join(b,a),join(join(b,meet(a,c)),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
join(meet(join(b,a),join(join(b,meet(a,c)),meet(a,b))),meet(join(b,a),join(b,meet(a,c)))) = meet(join(b,a),join(join(b,meet(a,c)),meet(a,b))),
inference(unit_resolution,[status(thm)],[185,44]) ).
tff(187,plain,
meet(a,join(b,meet(a,c))) = meet(join(b,meet(a,c)),a),
inference(symmetry,[status(thm)],[57]) ).
tff(188,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,b) = join(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
join(a,b) = join(b,a),
inference(unit_resolution,[status(thm)],[188,7]) ).
tff(190,plain,
meet(join(b,meet(a,c)),join(a,b)) = meet(join(b,meet(a,c)),join(b,a)),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
meet(join(b,meet(a,c)),join(b,a)) = meet(join(b,meet(a,c)),join(a,b)),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
join(b,meet(a,c)) = meet(join(b,meet(a,c)),join(a,b)),
inference(transitivity,[status(thm)],[175,191]) ).
tff(193,plain,
join(join(b,meet(a,c)),meet(a,join(b,meet(a,c)))) = join(meet(join(b,meet(a,c)),join(a,b)),meet(join(b,meet(a,c)),a)),
inference(monotonicity,[status(thm)],[192,187]) ).
tff(194,plain,
join(meet(join(b,meet(a,c)),join(a,b)),meet(join(b,meet(a,c)),a)) = join(join(b,meet(a,c)),meet(a,join(b,meet(a,c)))),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(join(b,meet(a,c)),join(a,b)),meet(join(b,meet(a,c)),a)) = meet(join(b,meet(a,c)),join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(196,plain,
join(meet(join(b,meet(a,c)),join(a,b)),meet(join(b,meet(a,c)),a)) = meet(join(b,meet(a,c)),join(a,b)),
inference(unit_resolution,[status(thm)],[195,44]) ).
tff(197,plain,
meet(join(b,meet(a,c)),join(a,b)) = join(meet(join(b,meet(a,c)),join(a,b)),meet(join(b,meet(a,c)),a)),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,a),join(b,meet(a,c))) = meet(join(b,meet(a,c)),join(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
meet(join(b,a),join(b,meet(a,c))) = meet(join(b,meet(a,c)),join(b,a)),
inference(unit_resolution,[status(thm)],[198,16]) ).
tff(200,plain,
meet(join(b,a),join(b,meet(a,c))) = join(join(b,meet(a,c)),meet(a,join(b,meet(a,c)))),
inference(transitivity,[status(thm)],[199,191,197,194]) ).
tff(201,plain,
meet(join(b,a),join(join(b,meet(a,c)),meet(a,b))) = join(meet(a,b),join(b,meet(a,c))),
inference(transitivity,[status(thm)],[184,181,178]) ).
tff(202,plain,
join(meet(join(b,a),join(join(b,meet(a,c)),meet(a,b))),meet(join(b,a),join(b,meet(a,c)))) = join(join(meet(a,b),join(b,meet(a,c))),join(join(b,meet(a,c)),meet(a,join(b,meet(a,c))))),
inference(monotonicity,[status(thm)],[201,200]) ).
tff(203,plain,
join(join(meet(a,b),join(b,meet(a,c))),join(join(b,meet(a,c)),meet(a,join(b,meet(a,c))))) = join(meet(join(b,a),join(join(b,meet(a,c)),meet(a,b))),meet(join(b,a),join(b,meet(a,c)))),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(meet(a,b),join(b,meet(a,c))),join(b,meet(a,c))),meet(a,join(b,meet(a,c)))) = join(join(meet(a,b),join(b,meet(a,c))),join(join(b,meet(a,c)),meet(a,join(b,meet(a,c))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(205,plain,
join(join(join(meet(a,b),join(b,meet(a,c))),join(b,meet(a,c))),meet(a,join(b,meet(a,c)))) = join(join(meet(a,b),join(b,meet(a,c))),join(join(b,meet(a,c)),meet(a,join(b,meet(a,c))))),
inference(unit_resolution,[status(thm)],[204,76]) ).
tff(206,plain,
meet(join(b,meet(a,c)),join(b,a)) = meet(join(b,a),join(b,meet(a,c))),
inference(symmetry,[status(thm)],[199]) ).
tff(207,plain,
join(b,meet(a,c)) = meet(join(b,a),join(b,meet(a,c))),
inference(transitivity,[status(thm)],[175,206]) ).
tff(208,plain,
join(meet(a,b),join(b,meet(a,c))) = meet(join(b,a),join(join(b,meet(a,c)),meet(a,b))),
inference(transitivity,[status(thm)],[177,180,183]) ).
tff(209,plain,
join(join(meet(a,b),join(b,meet(a,c))),join(b,meet(a,c))) = join(meet(join(b,a),join(join(b,meet(a,c)),meet(a,b))),meet(join(b,a),join(b,meet(a,c)))),
inference(monotonicity,[status(thm)],[208,207]) ).
tff(210,plain,
join(join(meet(a,b),join(b,meet(a,c))),join(b,meet(a,c))) = join(meet(a,b),join(b,meet(a,c))),
inference(transitivity,[status(thm)],[209,186,184,181,178]) ).
tff(211,plain,
join(join(join(meet(a,b),join(b,meet(a,c))),join(b,meet(a,c))),meet(a,join(b,meet(a,c)))) = join(join(meet(a,b),join(b,meet(a,c))),meet(join(b,meet(a,c)),a)),
inference(monotonicity,[status(thm)],[210,187]) ).
tff(212,plain,
join(join(meet(a,b),join(b,meet(a,c))),meet(join(b,meet(a,c)),a)) = join(join(join(meet(a,b),join(b,meet(a,c))),join(b,meet(a,c))),meet(a,join(b,meet(a,c)))),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
join(join(meet(a,b),join(b,meet(a,c))),meet(join(b,meet(a,c)),a)) = join(join(join(b,meet(a,c)),meet(a,b)),meet(a,join(b,meet(a,c)))),
inference(monotonicity,[status(thm)],[172,57]) ).
tff(214,plain,
join(join(join(b,meet(a,c)),meet(a,b)),meet(a,join(b,meet(a,c)))) = join(join(meet(a,b),join(b,meet(a,c))),meet(join(b,meet(a,c)),a)),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(b,meet(a,c)),meet(a,b)),meet(a,join(b,meet(a,c)))) = join(join(b,meet(a,c)),join(meet(a,b),meet(a,join(b,meet(a,c))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
join(join(join(b,meet(a,c)),meet(a,b)),meet(a,join(b,meet(a,c)))) = join(join(b,meet(a,c)),join(meet(a,b),meet(a,join(b,meet(a,c))))),
inference(unit_resolution,[status(thm)],[215,76]) ).
tff(217,plain,
join(join(b,meet(a,c)),join(meet(a,b),meet(a,join(b,meet(a,c))))) = join(join(join(b,meet(a,c)),meet(a,b)),meet(a,join(b,meet(a,c)))),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
join(meet(a,b),meet(a,join(b,meet(a,c)))) = meet(join(b,meet(a,c)),a),
inference(transitivity,[status(thm)],[142,67,187]) ).
tff(219,plain,
join(join(b,meet(a,c)),join(meet(a,b),meet(a,join(b,meet(a,c))))) = join(meet(join(b,meet(a,c)),join(a,b)),meet(join(b,meet(a,c)),a)),
inference(monotonicity,[status(thm)],[192,218]) ).
tff(220,plain,
join(meet(join(b,meet(a,c)),join(a,b)),meet(join(b,meet(a,c)),a)) = join(join(b,meet(a,c)),join(meet(a,b),meet(a,join(b,meet(a,c))))),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
join(b,meet(a,c)) = join(b,meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c)))),
inference(transitivity,[status(thm)],[175,191,197,220,217,214,212,205,203,186,184,181,178,172,169,167]) ).
tff(222,plain,
join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,meet(a,c)))) = join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))),
inference(symmetry,[status(thm)],[98]) ).
tff(223,plain,
join(meet(a,join(meet(a,c),b)),meet(a,meet(a,c))) = join(join(meet(a,join(b,meet(a,c))),meet(a,b)),meet(a,meet(a,c))),
inference(symmetry,[status(thm)],[69]) ).
tff(224,plain,
meet(a,join(meet(a,c),b)) = join(meet(a,join(meet(a,c),b)),meet(a,meet(a,c))),
inference(symmetry,[status(thm)],[64]) ).
tff(225,plain,
meet(join(b,meet(a,c)),a) = meet(meet(join(b,meet(a,c)),join(b,a)),a),
inference(monotonicity,[status(thm)],[175]) ).
tff(226,plain,
meet(meet(join(b,meet(a,c)),join(b,a)),a) = meet(join(b,meet(a,c)),a),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(b,meet(a,c)),join(b,a)),a) = meet(join(b,meet(a,c)),meet(join(b,a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(228,plain,
meet(meet(join(b,meet(a,c)),join(b,a)),a) = meet(join(b,meet(a,c)),meet(join(b,a),a)),
inference(unit_resolution,[status(thm)],[227,53]) ).
tff(229,plain,
meet(join(b,meet(a,c)),meet(join(b,a),a)) = meet(meet(join(b,meet(a,c)),join(b,a)),a),
inference(symmetry,[status(thm)],[228]) ).
tff(230,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(join(b,a),a),join(b,meet(a,c))) = meet(join(b,meet(a,c)),meet(join(b,a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(231,plain,
meet(meet(join(b,a),a),join(b,meet(a,c))) = meet(join(b,meet(a,c)),meet(join(b,a),a)),
inference(unit_resolution,[status(thm)],[230,16]) ).
tff(232,plain,
meet(meet(join(b,a),a),join(b,meet(a,c))) = join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))),
inference(transitivity,[status(thm)],[231,229,226,57,65,224,223,78,222]) ).
tff(233,plain,
meet(meet(meet(join(b,a),a),join(b,meet(a,c))),join(b,meet(a,c))) = meet(join(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))),join(b,meet(meet(a,join(b,meet(a,c))),join(meet(a,b),meet(a,c))))),
inference(monotonicity,[status(thm)],[232,221]) ).
tff(234,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(join(b,a),a),join(b,meet(a,c))),join(b,meet(a,c))) = meet(meet(join(b,a),a),meet(join(b,meet(a,c)),join(b,meet(a,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(235,plain,
meet(meet(meet(join(b,a),a),join(b,meet(a,c))),join(b,meet(a,c))) = meet(meet(join(b,a),a),meet(join(b,meet(a,c)),join(b,meet(a,c)))),
inference(unit_resolution,[status(thm)],[234,53]) ).
tff(236,plain,
meet(meet(join(b,a),a),meet(join(b,meet(a,c)),join(b,meet(a,c)))) = meet(meet(meet(join(b,a),a),join(b,meet(a,c))),join(b,meet(a,c))),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(join(b,meet(a,c)),join(b,a)),meet(join(b,meet(a,c)),b)) = meet(join(b,meet(a,c)),join(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(238,plain,
join(meet(join(b,meet(a,c)),join(b,a)),meet(join(b,meet(a,c)),b)) = meet(join(b,meet(a,c)),join(b,a)),
inference(unit_resolution,[status(thm)],[237,44]) ).
tff(239,plain,
join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)) = join(meet(join(b,meet(a,c)),join(b,a)),meet(join(b,meet(a,c)),b)),
inference(monotonicity,[status(thm)],[175]) ).
tff(240,plain,
join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)) = join(b,meet(a,c)),
inference(transitivity,[status(thm)],[239,238,174]) ).
tff(241,plain,
meet(join(b,a),join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b))) = meet(join(b,a),join(b,meet(a,c))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
meet(join(b,a),join(b,meet(a,c))) = meet(join(b,a),join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
join(b,meet(a,c)) = meet(join(b,a),join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b))),
inference(transitivity,[status(thm)],[175,206,242]) ).
tff(244,plain,
join(join(b,meet(a,c)),join(b,meet(a,c))) = join(meet(join(b,a),join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b))),meet(join(b,a),join(b,meet(a,c)))),
inference(monotonicity,[status(thm)],[243,207]) ).
tff(245,plain,
join(meet(join(b,a),join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b))),meet(join(b,a),join(b,meet(a,c)))) = join(join(b,meet(a,c)),join(b,meet(a,c))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(join(b,a),join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b))),meet(join(b,a),join(b,meet(a,c)))) = meet(join(b,a),join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(247,plain,
join(meet(join(b,a),join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b))),meet(join(b,a),join(b,meet(a,c)))) = meet(join(b,a),join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b))),
inference(unit_resolution,[status(thm)],[246,44]) ).
tff(248,plain,
meet(join(b,a),join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b))) = join(meet(join(b,a),join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b))),meet(join(b,a),join(b,meet(a,c)))),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
join(b,meet(a,c)) = join(join(b,meet(a,c)),join(b,meet(a,c))),
inference(transitivity,[status(thm)],[175,206,242,248,245]) ).
tff(250,plain,
join(meet(join(b,meet(a,c)),join(b,a)),meet(join(b,meet(a,c)),b)) = join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)),
inference(symmetry,[status(thm)],[239]) ).
tff(251,plain,
meet(join(b,meet(a,c)),join(b,a)) = join(meet(join(b,meet(a,c)),join(b,a)),meet(join(b,meet(a,c)),b)),
inference(symmetry,[status(thm)],[238]) ).
tff(252,plain,
join(b,meet(a,c)) = join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)),
inference(transitivity,[status(thm)],[175,251,250]) ).
tff(253,plain,
meet(join(b,meet(a,c)),join(b,meet(a,c))) = meet(join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)),join(join(b,meet(a,c)),join(b,meet(a,c)))),
inference(monotonicity,[status(thm)],[252,249]) ).
tff(254,plain,
meet(join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)),join(join(b,meet(a,c)),join(b,meet(a,c)))) = meet(join(b,meet(a,c)),join(b,meet(a,c))),
inference(symmetry,[status(thm)],[253]) ).
tff(255,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
| ( meet(join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)),join(join(b,meet(a,c)),join(b,meet(a,c)))) = join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(256,plain,
meet(join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)),join(join(b,meet(a,c)),join(b,meet(a,c)))) = join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)),
inference(unit_resolution,[status(thm)],[255,26]) ).
tff(257,plain,
join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)) = meet(join(join(b,meet(a,c)),meet(join(b,meet(a,c)),b)),join(join(b,meet(a,c)),join(b,meet(a,c)))),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
join(b,meet(a,c)) = meet(join(b,meet(a,c)),join(b,meet(a,c))),
inference(transitivity,[status(thm)],[175,251,250,257,254]) ).
tff(259,plain,
meet(meet(join(b,a),a),join(b,meet(a,c))) = meet(meet(join(b,a),a),meet(join(b,meet(a,c)),join(b,meet(a,c)))),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
meet(join(b,meet(a,c)),meet(join(b,a),a)) = meet(meet(join(b,a),a),join(b,meet(a,c))),
inference(symmetry,[status(thm)],[231]) ).
tff(261,plain,
meet(a,join(b,meet(a,c))) = join(meet(a,b),meet(a,c)),
inference(transitivity,[status(thm)],[187,225,228,260,259,236,233,164,154,46,37,35,28,19,9]) ).
tff(262,plain,
( ( meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)) )
<=> ( meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(263,axiom,
meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_modularity) ).
tff(264,plain,
meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)),
inference(modus_ponens,[status(thm)],[263,262]) ).
tff(265,plain,
$false,
inference(unit_resolution,[status(thm)],[264,261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT022-1 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 19:28:05 EDT 2025
% 0.17/0.32 % CPUTime :
% 78.82/79.01 % SZS status Unsatisfiable
% 78.82/79.01 % SZS output start Proof
% See solution above
% 78.82/79.04 % E exiting
%------------------------------------------------------------------------------