%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT002-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:13:42 AM UTC 2025
% Result : Unsatisfiable 29.54s 29.69s
% Output : Proof 29.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 85
% Syntax : Number of formulae : 248 ( 151 unt; 0 typ; 0 def)
% Number of atoms : 519 ( 403 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 472 ( 219 ~; 205 |; 0 &)
% ( 48 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 369 ( 343 !; 0 ?; 369 :)
% Comments :
%------------------------------------------------------------------------------
tff(complement_type,type,
complement: ( $i * $i ) > $o ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(r1_type,type,
r1: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(r2_type,type,
r2: $i ).
tff(a_type,type,
a: $i ).
tff(n0_type,type,
n0: $i ).
tff(n1_type,type,
n1: $i ).
tff(1,plain,
( complement(r2,meet(a,b))
<=> complement(r2,meet(a,b)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
complement(r2,meet(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_meet_b) ).
tff(3,plain,
complement(r2,meet(a,b)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
<=> ( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
<=> ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
<=> ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-2.ax',complement_meet) ).
tff(8,plain,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r2,meet(a,b))
| ( meet(r2,meet(a,b)) = n0 ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r2,meet(a,b))
| ( meet(r2,meet(a,b)) = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r2,meet(a,b))
| ( meet(r2,meet(a,b)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r2,meet(a,b))
| ( meet(r2,meet(a,b)) = n0 ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
meet(r2,meet(a,b)) = n0,
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(16,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)],[15]) ).
tff(17,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(18,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(19,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,a) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
meet(b,a) = meet(a,b),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
meet(r2,meet(b,a)) = meet(r2,meet(a,b)),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,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(26,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)],[25]) ).
tff(27,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(28,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
tff(29,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,b),a) = meet(r2,meet(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
meet(meet(r2,b),a) = meet(r2,meet(b,a)),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,meet(r2,b)) = meet(meet(r2,b),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
meet(a,meet(r2,b)) = meet(meet(r2,b),a),
inference(unit_resolution,[status(thm)],[34,21]) ).
tff(36,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(40,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(r2,b),meet(meet(r2,b),a)) = meet(r2,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
join(meet(r2,b),meet(meet(r2,b),a)) = meet(r2,b),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
meet(r2,meet(b,a)) = meet(meet(r2,b),a),
inference(symmetry,[status(thm)],[33]) ).
tff(46,plain,
meet(r2,meet(a,b)) = meet(r2,meet(b,a)),
inference(symmetry,[status(thm)],[24]) ).
tff(47,plain,
n0 = meet(r2,meet(a,b)),
inference(symmetry,[status(thm)],[14]) ).
tff(48,plain,
( complement(r1,join(a,b))
<=> complement(r1,join(a,b)) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
complement(r1,join(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_join_b) ).
tff(50,plain,
complement(r1,join(a,b)),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r1,join(a,b))
| ( meet(r1,join(a,b)) = n0 ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r1,join(a,b))
| ( meet(r1,join(a,b)) = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r1,join(a,b))
| ( meet(r1,join(a,b)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r1,join(a,b))
| ( meet(r1,join(a,b)) = n0 ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
meet(r1,join(a,b)) = n0,
inference(unit_resolution,[status(thm)],[53,10,50]) ).
tff(55,plain,
meet(r1,join(a,b)) = meet(meet(r2,b),a),
inference(transitivity,[status(thm)],[54,47,46,45]) ).
tff(56,plain,
join(meet(r2,b),meet(r1,join(a,b))) = join(meet(r2,b),meet(meet(r2,b),a)),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(61,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(b,join(b,a)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
meet(b,join(b,a)) = b,
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(67,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)],[66]) ).
tff(68,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(69,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(70,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,a) = join(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
join(b,a) = join(a,b),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
join(a,b) = join(b,a),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
meet(b,join(a,b)) = meet(b,join(b,a)),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
meet(b,join(a,b)) = b,
inference(transitivity,[status(thm)],[76,65]) ).
tff(78,plain,
meet(r2,meet(b,join(a,b))) = meet(r2,b),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,b),join(a,b)) = meet(r2,meet(b,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
meet(meet(r2,b),join(a,b)) = meet(r2,meet(b,join(a,b))),
inference(unit_resolution,[status(thm)],[79,31]) ).
tff(81,plain,
meet(meet(r2,b),join(a,b)) = meet(r2,b),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
<=> ( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-1.ax',modular) ).
tff(86,plain,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,b),join(a,b)) != meet(r2,b) )
| ( meet(join(a,b),join(meet(r2,b),r1)) = join(meet(r2,b),meet(r1,join(a,b))) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,b),join(a,b)) != meet(r2,b) )
| ( meet(join(a,b),join(meet(r2,b),r1)) = join(meet(r2,b),meet(r1,join(a,b))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,b),join(a,b)) != meet(r2,b) )
| ( meet(join(a,b),join(meet(r2,b),r1)) = join(meet(r2,b),meet(r1,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,b),join(a,b)) != meet(r2,b) )
| ( meet(join(a,b),join(meet(r2,b),r1)) = join(meet(r2,b),meet(r1,join(a,b))) ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
meet(join(a,b),join(meet(r2,b),r1)) = join(meet(r2,b),meet(r1,join(a,b))),
inference(unit_resolution,[status(thm)],[91,88,81]) ).
tff(93,plain,
meet(join(a,b),join(meet(r2,b),r1)) = meet(r2,b),
inference(transitivity,[status(thm)],[92,56,44]) ).
tff(94,plain,
meet(a,meet(join(a,b),join(meet(r2,b),r1))) = meet(a,meet(r2,b)),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,join(a,b)),join(meet(r2,b),r1)) = meet(a,meet(join(a,b),join(meet(r2,b),r1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
meet(meet(a,join(a,b)),join(meet(r2,b),r1)) = meet(a,meet(join(a,b),join(meet(r2,b),r1))),
inference(unit_resolution,[status(thm)],[95,31]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,b)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
meet(a,join(a,b)) = a,
inference(unit_resolution,[status(thm)],[97,63]) ).
tff(99,plain,
a = meet(a,join(a,b)),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
meet(a,join(meet(r2,b),r1)) = meet(meet(a,join(a,b)),join(meet(r2,b),r1)),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
meet(a,join(meet(r2,b),r1)) = n0,
inference(transitivity,[status(thm)],[100,96,94,35,33,24,14]) ).
tff(102,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ complement(X,Y)
| ( join(X,Y) = n1 ) )
<=> ( ~ complement(X,Y)
| ( join(X,Y) = n1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) )
<=> ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) )
<=> ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,axiom,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-2.ax',complement_join) ).
tff(106,plain,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) )
| ~ complement(r1,join(a,b))
| ( join(r1,join(a,b)) = n1 ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) )
| ~ complement(r1,join(a,b))
| ( join(r1,join(a,b)) = n1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) )
| ~ complement(r1,join(a,b))
| ( join(r1,join(a,b)) = n1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) )
| ~ complement(r1,join(a,b))
| ( join(r1,join(a,b)) = n1 ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
join(r1,join(a,b)) = n1,
inference(unit_resolution,[status(thm)],[111,108,50]) ).
tff(113,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(114,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)],[113]) ).
tff(115,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(116,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
tff(117,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(r1,a),b) = join(r1,join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
join(join(r1,a),b) = join(r1,join(a,b)),
inference(unit_resolution,[status(thm)],[120,119]) ).
tff(122,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,join(r1,a)) = join(join(r1,a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
join(b,join(r1,a)) = join(join(r1,a),b),
inference(unit_resolution,[status(thm)],[122,72]) ).
tff(124,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(b,join(b,join(r1,a))) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
meet(b,join(b,join(r1,a))) = b,
inference(unit_resolution,[status(thm)],[124,63]) ).
tff(126,plain,
join(join(r1,a),b) = join(b,join(r1,a)),
inference(symmetry,[status(thm)],[123]) ).
tff(127,plain,
join(r1,join(a,b)) = join(join(r1,a),b),
inference(symmetry,[status(thm)],[121]) ).
tff(128,plain,
n1 = join(r1,join(a,b)),
inference(symmetry,[status(thm)],[112]) ).
tff(129,plain,
n1 = join(b,join(r1,a)),
inference(transitivity,[status(thm)],[128,127,126]) ).
tff(130,plain,
meet(b,n1) = meet(b,join(b,join(r1,a))),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) )
| ~ complement(r2,meet(a,b))
| ( join(r2,meet(a,b)) = n1 ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) )
| ~ complement(r2,meet(a,b))
| ( join(r2,meet(a,b)) = n1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) )
| ~ complement(r2,meet(a,b))
| ( join(r2,meet(a,b)) = n1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( join(X,Y) = n1 ) )
| ~ complement(r2,meet(a,b))
| ( join(r2,meet(a,b)) = n1 ) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
join(r2,meet(a,b)) = n1,
inference(unit_resolution,[status(thm)],[133,108,3]) ).
tff(135,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),r2) = join(r2,meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
join(meet(a,b),r2) = join(r2,meet(a,b)),
inference(unit_resolution,[status(thm)],[135,72]) ).
tff(137,plain,
join(meet(a,b),r2) = n1,
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,plain,
meet(b,join(meet(a,b),r2)) = meet(b,n1),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(a,b),join(meet(a,b),b)) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
meet(meet(a,b),join(meet(a,b),b)) = meet(a,b),
inference(unit_resolution,[status(thm)],[139,63]) ).
tff(141,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),b) = join(b,meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
join(meet(a,b),b) = join(b,meet(a,b)),
inference(unit_resolution,[status(thm)],[141,72]) ).
tff(143,plain,
join(b,meet(a,b)) = join(meet(a,b),b),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
meet(a,b) = meet(b,a),
inference(symmetry,[status(thm)],[23]) ).
tff(145,plain,
join(b,meet(a,b)) = join(b,meet(b,a)),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
join(b,meet(b,a)) = join(b,meet(a,b)),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(b,meet(b,a)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
join(b,meet(b,a)) = b,
inference(unit_resolution,[status(thm)],[147,42]) ).
tff(149,plain,
b = join(b,meet(b,a)),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
b = join(meet(a,b),b),
inference(transitivity,[status(thm)],[149,146,143]) ).
tff(151,plain,
meet(meet(a,b),b) = meet(meet(a,b),join(meet(a,b),b)),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
meet(meet(a,b),b) = meet(a,b),
inference(transitivity,[status(thm)],[151,140]) ).
tff(153,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,b),b) != meet(a,b) )
| ( meet(b,join(meet(a,b),r2)) = join(meet(a,b),meet(r2,b)) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,b),b) != meet(a,b) )
| ( meet(b,join(meet(a,b),r2)) = join(meet(a,b),meet(r2,b)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,b),b) != meet(a,b) )
| ( meet(b,join(meet(a,b),r2)) = join(meet(a,b),meet(r2,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,b),b) != meet(a,b) )
| ( meet(b,join(meet(a,b),r2)) = join(meet(a,b),meet(r2,b)) ) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
meet(b,join(meet(a,b),r2)) = join(meet(a,b),meet(r2,b)),
inference(unit_resolution,[status(thm)],[155,88,152]) ).
tff(157,plain,
join(meet(a,b),meet(r2,b)) = meet(b,join(meet(a,b),r2)),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(r2,b),meet(a,b)) = join(meet(a,b),meet(r2,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
join(meet(r2,b),meet(a,b)) = join(meet(a,b),meet(r2,b)),
inference(unit_resolution,[status(thm)],[158,72]) ).
tff(160,plain,
join(meet(r2,b),meet(a,b)) = b,
inference(transitivity,[status(thm)],[159,157,138,130,125]) ).
tff(161,plain,
join(join(meet(r2,b),meet(a,b)),join(r1,a)) = join(b,join(r1,a)),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(r2,b),meet(a,b)),join(r1,a)) = join(meet(r2,b),join(meet(a,b),join(r1,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
join(join(meet(r2,b),meet(a,b)),join(r1,a)) = join(meet(r2,b),join(meet(a,b),join(r1,a))),
inference(unit_resolution,[status(thm)],[162,119]) ).
tff(164,plain,
join(meet(r2,b),join(meet(a,b),join(r1,a))) = join(join(meet(r2,b),meet(a,b)),join(r1,a)),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),join(r1,a)) = join(join(r1,a),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
join(meet(a,b),join(r1,a)) = join(join(r1,a),meet(a,b)),
inference(unit_resolution,[status(thm)],[165,72]) ).
tff(167,plain,
join(join(r1,a),meet(a,b)) = join(meet(a,b),join(r1,a)),
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(r1,a),meet(a,b)) = join(r1,join(a,meet(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
join(join(r1,a),meet(a,b)) = join(r1,join(a,meet(a,b))),
inference(unit_resolution,[status(thm)],[168,119]) ).
tff(170,plain,
join(r1,join(a,meet(a,b))) = join(join(r1,a),meet(a,b)),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(a,meet(a,b)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
join(a,meet(a,b)) = a,
inference(unit_resolution,[status(thm)],[171,42]) ).
tff(173,plain,
join(r1,join(a,meet(a,b))) = join(r1,a),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
join(r1,a) = join(r1,join(a,meet(a,b))),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
join(r1,a) = join(meet(a,b),join(r1,a)),
inference(transitivity,[status(thm)],[174,170,167]) ).
tff(176,plain,
join(meet(r2,b),join(r1,a)) = join(meet(r2,b),join(meet(a,b),join(r1,a))),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(r1,a),meet(r2,b)) = join(meet(r2,b),join(r1,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(178,plain,
join(join(r1,a),meet(r2,b)) = join(meet(r2,b),join(r1,a)),
inference(unit_resolution,[status(thm)],[177,72]) ).
tff(179,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,r2) = meet(r2,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
meet(b,r2) = meet(r2,b),
inference(unit_resolution,[status(thm)],[179,21]) ).
tff(181,plain,
join(join(r1,a),meet(b,r2)) = join(join(r1,a),meet(r2,b)),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
meet(r2,b) = meet(b,r2),
inference(symmetry,[status(thm)],[180]) ).
tff(183,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,r1) = join(r1,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
join(a,r1) = join(r1,a),
inference(unit_resolution,[status(thm)],[183,72]) ).
tff(185,plain,
join(join(a,r1),meet(r2,b)) = join(join(r1,a),meet(b,r2)),
inference(monotonicity,[status(thm)],[184,182]) ).
tff(186,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(a,r1),meet(r2,b)) = join(a,join(r1,meet(r2,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
join(join(a,r1),meet(r2,b)) = join(a,join(r1,meet(r2,b))),
inference(unit_resolution,[status(thm)],[186,119]) ).
tff(188,plain,
join(a,join(r1,meet(r2,b))) = join(join(a,r1),meet(r2,b)),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(r1,meet(r2,b)) = join(meet(r2,b),r1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
join(r1,meet(r2,b)) = join(meet(r2,b),r1),
inference(unit_resolution,[status(thm)],[189,72]) ).
tff(191,plain,
join(meet(r2,b),r1) = join(r1,meet(r2,b)),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(r1,join(r1,join(a,b))) = r1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
meet(r1,join(r1,join(a,b))) = r1,
inference(unit_resolution,[status(thm)],[192,63]) ).
tff(194,plain,
meet(r1,n1) = meet(r1,join(r1,join(a,b))),
inference(monotonicity,[status(thm)],[128]) ).
tff(195,plain,
meet(r1,n1) = r1,
inference(transitivity,[status(thm)],[194,193]) ).
tff(196,plain,
join(meet(r2,b),meet(r1,n1)) = join(meet(r2,b),r1),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(join(a,b),join(join(a,b),r1)) = join(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(198,plain,
meet(join(a,b),join(join(a,b),r1)) = join(a,b),
inference(unit_resolution,[status(thm)],[197,63]) ).
tff(199,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(a,b),r1) = join(r1,join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(200,plain,
join(join(a,b),r1) = join(r1,join(a,b)),
inference(unit_resolution,[status(thm)],[199,72]) ).
tff(201,plain,
join(r1,join(a,b)) = join(join(a,b),r1),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
join(join(r1,a),b) = join(join(a,b),r1),
inference(transitivity,[status(thm)],[121,201]) ).
tff(203,plain,
meet(join(a,b),join(join(r1,a),b)) = meet(join(a,b),join(join(a,b),r1)),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
n1 = join(join(r1,a),b),
inference(transitivity,[status(thm)],[128,127]) ).
tff(205,plain,
meet(join(a,b),n1) = meet(join(a,b),join(join(r1,a),b)),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
meet(join(a,b),n1) = join(a,b),
inference(transitivity,[status(thm)],[205,203,198]) ).
tff(207,plain,
meet(meet(r2,b),meet(join(a,b),n1)) = meet(meet(r2,b),join(a,b)),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(r2,b),join(a,b)),n1) = meet(meet(r2,b),meet(join(a,b),n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
meet(meet(meet(r2,b),join(a,b)),n1) = meet(meet(r2,b),meet(join(a,b),n1)),
inference(unit_resolution,[status(thm)],[208,31]) ).
tff(210,plain,
meet(r2,meet(b,join(a,b))) = meet(meet(r2,b),join(a,b)),
inference(symmetry,[status(thm)],[80]) ).
tff(211,plain,
meet(r2,b) = meet(r2,meet(b,join(a,b))),
inference(symmetry,[status(thm)],[78]) ).
tff(212,plain,
meet(r2,b) = meet(meet(r2,b),join(a,b)),
inference(transitivity,[status(thm)],[211,210]) ).
tff(213,plain,
meet(meet(r2,b),n1) = meet(meet(meet(r2,b),join(a,b)),n1),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
meet(meet(r2,b),n1) = meet(r2,b),
inference(transitivity,[status(thm)],[213,209,207,80,78]) ).
tff(215,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,b),n1) != meet(r2,b) )
| ( meet(n1,join(meet(r2,b),r1)) = join(meet(r2,b),meet(r1,n1)) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,b),n1) != meet(r2,b) )
| ( meet(n1,join(meet(r2,b),r1)) = join(meet(r2,b),meet(r1,n1)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(216,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,b),n1) != meet(r2,b) )
| ( meet(n1,join(meet(r2,b),r1)) = join(meet(r2,b),meet(r1,n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,b),n1) != meet(r2,b) )
| ( meet(n1,join(meet(r2,b),r1)) = join(meet(r2,b),meet(r1,n1)) ) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
meet(n1,join(meet(r2,b),r1)) = join(meet(r2,b),meet(r1,n1)),
inference(unit_resolution,[status(thm)],[217,88,214]) ).
tff(219,plain,
meet(n1,join(meet(r2,b),r1)) = join(r1,meet(r2,b)),
inference(transitivity,[status(thm)],[218,196,191]) ).
tff(220,plain,
join(a,meet(n1,join(meet(r2,b),r1))) = join(a,join(r1,meet(r2,b))),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
join(meet(r2,b),meet(r1,n1)) = meet(n1,join(meet(r2,b),r1)),
inference(symmetry,[status(thm)],[218]) ).
tff(222,plain,
join(meet(r2,b),r1) = join(meet(r2,b),meet(r1,n1)),
inference(symmetry,[status(thm)],[196]) ).
tff(223,plain,
join(meet(r2,b),r1) = meet(n1,join(meet(r2,b),r1)),
inference(transitivity,[status(thm)],[222,221]) ).
tff(224,plain,
join(a,join(meet(r2,b),r1)) = join(a,meet(n1,join(meet(r2,b),r1))),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
join(a,join(meet(r2,b),r1)) = n1,
inference(transitivity,[status(thm)],[224,220,188,185,181,178,176,164,161,123,121,112]) ).
tff(226,plain,
^ [Y: $i,X: $i] :
refl(( ( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) )
<=> ( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(227,plain,
( ! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) )
<=> ! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) ) ),
inference(quant_intro,[status(thm)],[226]) ).
tff(228,plain,
( ! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) )
<=> ! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(229,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ( meet(X,Y) != n0 )
| ( join(X,Y) != n1 ) )
<=> ( ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) ) )),
( ( ( meet(X,Y) != n0 )
| ( join(X,Y) != n1 )
| complement(X,Y) )
<=> ( ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 )
| complement(X,Y) ) )),
rewrite(( ( ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 )
| complement(X,Y) )
<=> ( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) ) )),
( ( ( meet(X,Y) != n0 )
| ( join(X,Y) != n1 )
| complement(X,Y) )
<=> ( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(230,plain,
( ! [Y: $i,X: $i] :
( ( meet(X,Y) != n0 )
| ( join(X,Y) != n1 )
| complement(X,Y) )
<=> ! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) ) ),
inference(quant_intro,[status(thm)],[229]) ).
tff(231,axiom,
! [Y: $i,X: $i] :
( ( meet(X,Y) != n0 )
| ( join(X,Y) != n1 )
| complement(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-2.ax',meet_join_complement) ).
tff(232,plain,
! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) ),
inference(modus_ponens,[status(thm)],[232,228]) ).
tff(234,plain,
! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) ),
inference(skolemize,[status(sab)],[233]) ).
tff(235,plain,
! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) ),
inference(modus_ponens,[status(thm)],[234,227]) ).
tff(236,plain,
( ( ~ ! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) )
| complement(a,join(meet(r2,b),r1))
| ( join(a,join(meet(r2,b),r1)) != n1 )
| ( meet(a,join(meet(r2,b),r1)) != n0 ) )
<=> ( ~ ! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) )
| complement(a,join(meet(r2,b),r1))
| ( join(a,join(meet(r2,b),r1)) != n1 )
| ( meet(a,join(meet(r2,b),r1)) != n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(237,plain,
( ~ ! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) )
| complement(a,join(meet(r2,b),r1))
| ( join(a,join(meet(r2,b),r1)) != n1 )
| ( meet(a,join(meet(r2,b),r1)) != n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(238,plain,
( ~ ! [Y: $i,X: $i] :
( complement(X,Y)
| ( join(X,Y) != n1 )
| ( meet(X,Y) != n0 ) )
| complement(a,join(meet(r2,b),r1))
| ( join(a,join(meet(r2,b),r1)) != n1 )
| ( meet(a,join(meet(r2,b),r1)) != n0 ) ),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
complement(a,join(meet(r2,b),r1)),
inference(unit_resolution,[status(thm)],[238,235,225,101]) ).
tff(240,plain,
^ [W: $i] :
refl(( ~ complement(a,W)
<=> ~ complement(a,W) )),
inference(bind,[status(th)],[]) ).
tff(241,plain,
( ! [W: $i] : ~ complement(a,W)
<=> ! [W: $i] : ~ complement(a,W) ),
inference(quant_intro,[status(thm)],[240]) ).
tff(242,plain,
( ! [W: $i] : ~ complement(a,W)
<=> ! [W: $i] : ~ complement(a,W) ),
inference(rewrite,[status(thm)],[]) ).
tff(243,axiom,
! [W: $i] : ~ complement(a,W),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_complememt_exists) ).
tff(244,plain,
! [W: $i] : ~ complement(a,W),
inference(modus_ponens,[status(thm)],[243,242]) ).
tff(245,plain,
! [W: $i] : ~ complement(a,W),
inference(skolemize,[status(sab)],[244]) ).
tff(246,plain,
! [W: $i] : ~ complement(a,W),
inference(modus_ponens,[status(thm)],[245,241]) ).
tff(247,plain,
( ~ ! [W: $i] : ~ complement(a,W)
| ~ complement(a,join(meet(r2,b),r1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
$false,
inference(unit_resolution,[status(thm)],[247,246,239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT002-1 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:23:47 EDT 2025
% 0.11/0.33 % CPUTime :
% 29.54/29.69 % SZS status Unsatisfiable
% 29.54/29.69 % SZS output start Proof
% See solution above
% 29.54/29.73 % E exiting
%------------------------------------------------------------------------------