TSTP Solution File: LAT005-4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT005-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:31:41 EDT 2022
% Result : Unsatisfiable 3.60s 2.58s
% Output : Proof 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 93
% Syntax : Number of formulae : 309 ( 208 unt; 9 typ; 0 def)
% Number of atoms : 454 ( 445 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 265 ( 119 ~; 108 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 296 ( 280 !; 0 ?; 296 :)
% Comments :
%------------------------------------------------------------------------------
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(r2_type,type,
r2: $i ).
tff(b_type,type,
b: $i ).
tff(r1_type,type,
r1: $i ).
tff(a_type,type,
a: $i ).
tff(n0_type,type,
n0: $i ).
tff(b2_type,type,
b2: $i ).
tff(a2_type,type,
a2: $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/sandbox2/benchmark/Axioms/LAT001-0.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,meet(r2,join(r1,meet(b,r2)))),meet(r2,meet(a,b))) = join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r2,meet(a,b))) = join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( ( join(X,meet(r2,meet(a,b))) = X )
<=> ( join(X,meet(r2,meet(a,b))) = X ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : ( join(X,meet(r2,meet(a,b))) = X )
<=> ! [X: $i] : ( join(X,meet(r2,meet(a,b))) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X: $i] :
rewrite(
( ( join(X,n0) = X )
<=> ( join(X,meet(r2,meet(a,b))) = X ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [X: $i] : ( join(X,n0) = X )
<=> ! [X: $i] : ( join(X,meet(r2,meet(a,b))) = X ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [X: $i] : ( join(X,n0) = X )
<=> ! [X: $i] : ( join(X,n0) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
! [X: $i] : ( join(X,n0) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-1.ax',x_join_0) ).
tff(16,plain,
! [X: $i] : ( join(X,n0) = X ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] : ( join(X,meet(r2,meet(a,b))) = X ),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
! [X: $i] : ( join(X,meet(r2,meet(a,b))) = X ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] : ( join(X,meet(r2,meet(a,b))) = X ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ~ ! [X: $i] : ( join(X,meet(r2,meet(a,b))) = X )
| ( join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r2,meet(a,b))) = meet(a,meet(r2,join(r1,meet(b,r2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r2,meet(a,b))) = meet(a,meet(r2,join(r1,meet(b,r2)))),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
meet(a,meet(r2,join(r1,meet(b,r2)))) = join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r2,meet(a,b))),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
meet(a,meet(r2,join(r1,meet(b,r2)))) = join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))),
inference(transitivity,[status(thm)],[22,9]) ).
tff(24,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(25,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)],[24]) ).
tff(26,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(27,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(28,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))),meet(r2,meet(a,b))) = meet(meet(r2,meet(a,b)),join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
meet(join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))),meet(r2,meet(a,b))) = meet(meet(r2,meet(a,b)),join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2)))))),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
meet(meet(r2,meet(a,b)),join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2)))))) = meet(join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))),meet(r2,meet(a,b))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(35,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)],[34]) ).
tff(36,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(37,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(38,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(r2,meet(a,b)),join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2)))))) = meet(r2,meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
meet(meet(r2,meet(a,b)),join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2)))))) = meet(r2,meet(a,b)),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
meet(r2,meet(a,b)) = meet(meet(r2,meet(a,b)),join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2)))))),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(r2,meet(a,b)),join(meet(r2,meet(a,b)),meet(a,r2))) = meet(r2,meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
meet(meet(r2,meet(a,b)),join(meet(r2,meet(a,b)),meet(a,r2))) = meet(r2,meet(a,b)),
inference(unit_resolution,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(r2,meet(a,b)),meet(a,r2)) = join(meet(a,r2),meet(r2,meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
join(meet(r2,meet(a,b)),meet(a,r2)) = join(meet(a,r2),meet(r2,meet(a,b))),
inference(unit_resolution,[status(thm)],[46,7]) ).
tff(48,plain,
join(meet(a,r2),meet(r2,meet(a,b))) = join(meet(r2,meet(a,b)),meet(a,r2)),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(r2,a) = meet(a,r2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
meet(r2,a) = meet(a,r2),
inference(unit_resolution,[status(thm)],[49,30]) ).
tff(51,plain,
meet(a,r2) = meet(r2,a),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
meet(meet(a,r2),b) = meet(meet(r2,a),b),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
meet(meet(r2,a),b) = meet(meet(a,r2),b),
inference(symmetry,[status(thm)],[52]) ).
tff(54,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(55,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)],[54]) ).
tff(56,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(57,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
tff(58,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,a),b) = meet(r2,meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
meet(meet(r2,a),b) = meet(r2,meet(a,b)),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
meet(r2,meet(a,b)) = meet(meet(r2,a),b),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
meet(r2,meet(a,b)) = meet(meet(a,r2),b),
inference(transitivity,[status(thm)],[63,53]) ).
tff(65,plain,
join(meet(a,r2),meet(r2,meet(a,b))) = join(meet(a,r2),meet(meet(a,r2),b)),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
join(meet(a,r2),meet(meet(a,r2),b)) = join(meet(a,r2),meet(r2,meet(a,b))),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(68,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)],[67]) ).
tff(69,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(70,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(71,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(a,r2),meet(meet(a,r2),b)) = meet(a,r2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
join(meet(a,r2),meet(meet(a,r2),b)) = meet(a,r2),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
meet(a,r2) = join(meet(a,r2),meet(meet(a,r2),b)),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
meet(a,r2) = join(meet(r2,meet(a,b)),meet(a,r2)),
inference(transitivity,[status(thm)],[76,66,48]) ).
tff(78,plain,
meet(meet(r2,meet(a,b)),meet(a,r2)) = meet(meet(r2,meet(a,b)),join(meet(r2,meet(a,b)),meet(a,r2))),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(a,r2),meet(r2,meet(a,b))) = meet(meet(r2,meet(a,b)),meet(a,r2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
meet(meet(a,r2),meet(r2,meet(a,b))) = meet(meet(r2,meet(a,b)),meet(a,r2)),
inference(unit_resolution,[status(thm)],[79,30]) ).
tff(81,plain,
( ( meet(r1,join(a,b)) = n0 )
<=> ( meet(r1,join(a,b)) = meet(r2,meet(a,b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( meet(r1,join(a,b)) = n0 )
<=> ( meet(r1,join(a,b)) = n0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
meet(r1,join(a,b)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1_complement_join_a_b_2) ).
tff(84,plain,
meet(r1,join(a,b)) = n0,
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
meet(r1,join(a,b)) = meet(r2,meet(a,b)),
inference(modus_ponens,[status(thm)],[84,81]) ).
tff(86,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(r1,join(r1,meet(b,r2))) = r1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
meet(r1,join(r1,meet(b,r2))) = r1,
inference(unit_resolution,[status(thm)],[86,40]) ).
tff(88,plain,
meet(meet(r1,join(r1,meet(b,r2))),join(a,b)) = meet(r1,join(a,b)),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r1,join(r1,meet(b,r2))),join(a,b)) = meet(r1,meet(join(r1,meet(b,r2)),join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
meet(meet(r1,join(r1,meet(b,r2))),join(a,b)) = meet(r1,meet(join(r1,meet(b,r2)),join(a,b))),
inference(unit_resolution,[status(thm)],[89,60]) ).
tff(91,plain,
meet(r1,meet(join(r1,meet(b,r2)),join(a,b))) = meet(meet(r1,join(r1,meet(b,r2))),join(a,b)),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(join(r1,meet(b,r2)),join(a,b)),r1) = meet(r1,meet(join(r1,meet(b,r2)),join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
meet(meet(join(r1,meet(b,r2)),join(a,b)),r1) = meet(r1,meet(join(r1,meet(b,r2)),join(a,b))),
inference(unit_resolution,[status(thm)],[92,30]) ).
tff(94,plain,
meet(meet(join(r1,meet(b,r2)),join(a,b)),r1) = meet(r2,meet(a,b)),
inference(transitivity,[status(thm)],[93,91,88,85]) ).
tff(95,plain,
meet(meet(a,r2),meet(meet(join(r1,meet(b,r2)),join(a,b)),r1)) = meet(meet(a,r2),meet(r2,meet(a,b))),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(a,r2),meet(join(r1,meet(b,r2)),join(a,b))),r1) = meet(meet(a,r2),meet(meet(join(r1,meet(b,r2)),join(a,b)),r1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
meet(meet(meet(a,r2),meet(join(r1,meet(b,r2)),join(a,b))),r1) = meet(meet(a,r2),meet(meet(join(r1,meet(b,r2)),join(a,b)),r1)),
inference(unit_resolution,[status(thm)],[96,60]) ).
tff(98,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),join(r1,meet(b,r2))) = meet(join(r1,meet(b,r2)),join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
meet(join(a,b),join(r1,meet(b,r2))) = meet(join(r1,meet(b,r2)),join(a,b)),
inference(unit_resolution,[status(thm)],[98,30]) ).
tff(100,plain,
meet(join(r1,meet(b,r2)),join(a,b)) = meet(join(a,b),join(r1,meet(b,r2))),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
meet(meet(a,r2),meet(join(r1,meet(b,r2)),join(a,b))) = meet(meet(a,r2),meet(join(a,b),join(r1,meet(b,r2)))),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
meet(meet(a,r2),meet(join(a,b),join(r1,meet(b,r2)))) = meet(meet(a,r2),meet(join(r1,meet(b,r2)),join(a,b))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(a,r2),join(a,b)),join(r1,meet(b,r2))) = meet(meet(a,r2),meet(join(a,b),join(r1,meet(b,r2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
meet(meet(meet(a,r2),join(a,b)),join(r1,meet(b,r2))) = meet(meet(a,r2),meet(join(a,b),join(r1,meet(b,r2)))),
inference(unit_resolution,[status(thm)],[103,60]) ).
tff(105,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,b)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
meet(a,join(a,b)) = a,
inference(unit_resolution,[status(thm)],[105,40]) ).
tff(107,plain,
meet(r2,meet(a,join(a,b))) = meet(r2,a),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,a),join(a,b)) = meet(r2,meet(a,join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
meet(meet(r2,a),join(a,b)) = meet(r2,meet(a,join(a,b))),
inference(unit_resolution,[status(thm)],[108,60]) ).
tff(110,plain,
meet(meet(a,r2),join(a,b)) = meet(meet(r2,a),join(a,b)),
inference(monotonicity,[status(thm)],[51]) ).
tff(111,plain,
meet(meet(a,r2),join(a,b)) = meet(a,r2),
inference(transitivity,[status(thm)],[110,109,107,50]) ).
tff(112,plain,
meet(meet(meet(a,r2),join(a,b)),join(r1,meet(b,r2))) = meet(meet(a,r2),join(r1,meet(b,r2))),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
meet(meet(a,r2),join(r1,meet(b,r2))) = meet(meet(meet(a,r2),join(a,b)),join(r1,meet(b,r2))),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,r2),join(r1,meet(b,r2))) = meet(a,meet(r2,join(r1,meet(b,r2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
meet(meet(a,r2),join(r1,meet(b,r2))) = meet(a,meet(r2,join(r1,meet(b,r2)))),
inference(unit_resolution,[status(thm)],[114,60]) ).
tff(116,plain,
meet(a,meet(r2,join(r1,meet(b,r2)))) = meet(meet(a,r2),join(r1,meet(b,r2))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
meet(a,meet(r2,join(r1,meet(b,r2)))) = meet(meet(a,r2),meet(join(r1,meet(b,r2)),join(a,b))),
inference(transitivity,[status(thm)],[116,113,104,102]) ).
tff(118,plain,
meet(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) = meet(meet(meet(a,r2),meet(join(r1,meet(b,r2)),join(a,b))),r1),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
meet(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) = meet(join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))),meet(r2,meet(a,b))),
inference(transitivity,[status(thm)],[118,97,95,80,78,45,43,33]) ).
tff(120,plain,
( ( meet(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) = meet(a,meet(r2,join(r1,meet(b,r2)))) )
<=> ( meet(join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))),meet(r2,meet(a,b))) = join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))) ) ),
inference(monotonicity,[status(thm)],[119,23]) ).
tff(121,plain,
( ( meet(join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))),meet(r2,meet(a,b))) = join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))) )
<=> ( meet(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) = meet(a,meet(r2,join(r1,meet(b,r2)))) ) ),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),join(r1,meet(a,r2))) = meet(join(r1,meet(a,r2)),join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
meet(join(a,b),join(r1,meet(a,r2))) = meet(join(r1,meet(a,r2)),join(a,b)),
inference(unit_resolution,[status(thm)],[122,30]) ).
tff(124,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,r2),r1) = join(r1,meet(a,r2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
join(meet(a,r2),r1) = join(r1,meet(a,r2)),
inference(unit_resolution,[status(thm)],[124,7]) ).
tff(126,plain,
join(r1,meet(a,r2)) = join(meet(a,r2),r1),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
meet(join(a,b),join(r1,meet(a,r2))) = meet(join(a,b),join(meet(a,r2),r1)),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
meet(join(a,b),join(meet(a,r2),r1)) = meet(join(a,b),join(r1,meet(a,r2))),
inference(symmetry,[status(thm)],[127]) ).
tff(129,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(130,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)],[129]) ).
tff(131,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(132,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-1.ax',modular) ).
tff(133,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)],[132,131]) ).
tff(134,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)],[133]) ).
tff(135,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)],[134,130]) ).
tff(136,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,r2),join(a,b)) != meet(a,r2) )
| ( meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),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(a,r2),join(a,b)) != meet(a,r2) )
| ( meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),meet(r1,join(a,b))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,r2),join(a,b)) != meet(a,r2) )
| ( meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),meet(r1,join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,r2),join(a,b)) != meet(a,r2) )
| ( meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),meet(r1,join(a,b))) ) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
( ( meet(meet(a,r2),join(a,b)) != meet(a,r2) )
| ( meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),meet(r1,join(a,b))) ) ),
inference(unit_resolution,[status(thm)],[138,135]) ).
tff(140,plain,
meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),meet(r1,join(a,b))),
inference(unit_resolution,[status(thm)],[139,111]) ).
tff(141,plain,
join(meet(a,r2),meet(r1,join(a,b))) = meet(join(a,b),join(meet(a,r2),r1)),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
meet(r1,join(a,b)) = meet(meet(a,r2),b),
inference(transitivity,[status(thm)],[85,63,53]) ).
tff(143,plain,
join(meet(a,r2),meet(r1,join(a,b))) = join(meet(a,r2),meet(meet(a,r2),b)),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
join(meet(a,r2),meet(meet(a,r2),b)) = join(meet(a,r2),meet(r1,join(a,b))),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
meet(a,r2) = meet(join(r1,meet(a,r2)),join(a,b)),
inference(transitivity,[status(thm)],[76,144,141,128,123]) ).
tff(146,plain,
meet(meet(a,r2),join(r1,meet(b,r2))) = meet(meet(join(r1,meet(a,r2)),join(a,b)),join(r1,meet(b,r2))),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
meet(meet(join(r1,meet(a,r2)),join(a,b)),join(r1,meet(b,r2))) = meet(meet(a,r2),join(r1,meet(b,r2))),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(r1,meet(b,r2)),meet(join(r1,meet(a,r2)),join(a,b))) = meet(meet(join(r1,meet(a,r2)),join(a,b)),join(r1,meet(b,r2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
meet(join(r1,meet(b,r2)),meet(join(r1,meet(a,r2)),join(a,b))) = meet(meet(join(r1,meet(a,r2)),join(a,b)),join(r1,meet(b,r2))),
inference(unit_resolution,[status(thm)],[148,30]) ).
tff(150,plain,
meet(join(r1,meet(a,r2)),join(a,b)) = meet(join(a,b),join(r1,meet(a,r2))),
inference(symmetry,[status(thm)],[123]) ).
tff(151,plain,
meet(join(r1,meet(b,r2)),meet(join(r1,meet(a,r2)),join(a,b))) = meet(join(r1,meet(b,r2)),meet(join(a,b),join(r1,meet(a,r2)))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
meet(join(r1,meet(b,r2)),meet(join(a,b),join(r1,meet(a,r2)))) = meet(join(r1,meet(b,r2)),meet(join(r1,meet(a,r2)),join(a,b))),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(r1,meet(b,r2)),join(a,b)),join(r1,meet(a,r2))) = meet(join(r1,meet(b,r2)),meet(join(a,b),join(r1,meet(a,r2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
meet(meet(join(r1,meet(b,r2)),join(a,b)),join(r1,meet(a,r2))) = meet(join(r1,meet(b,r2)),meet(join(a,b),join(r1,meet(a,r2)))),
inference(unit_resolution,[status(thm)],[153,60]) ).
tff(155,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(b,r2),meet(meet(b,r2),a)) = meet(b,r2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
join(meet(b,r2),meet(meet(b,r2),a)) = meet(b,r2),
inference(unit_resolution,[status(thm)],[155,73]) ).
tff(157,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(r2,b) = meet(b,r2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
meet(r2,b) = meet(b,r2),
inference(unit_resolution,[status(thm)],[157,30]) ).
tff(159,plain,
meet(b,r2) = meet(r2,b),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
meet(meet(b,r2),a) = meet(meet(r2,b),a),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
meet(meet(r2,b),a) = meet(meet(b,r2),a),
inference(symmetry,[status(thm)],[160]) ).
tff(162,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(163,plain,
meet(meet(r2,b),a) = meet(r2,meet(b,a)),
inference(unit_resolution,[status(thm)],[162,60]) ).
tff(164,plain,
meet(r2,meet(b,a)) = meet(meet(r2,b),a),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,a) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
meet(b,a) = meet(a,b),
inference(unit_resolution,[status(thm)],[165,30]) ).
tff(167,plain,
meet(r2,meet(b,a)) = meet(r2,meet(a,b)),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
meet(r2,meet(a,b)) = meet(r2,meet(b,a)),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
meet(r1,join(a,b)) = meet(meet(b,r2),a),
inference(transitivity,[status(thm)],[85,168,164,161]) ).
tff(170,plain,
join(meet(b,r2),meet(r1,join(a,b))) = join(meet(b,r2),meet(meet(b,r2),a)),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(b,join(b,a)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(172,plain,
meet(b,join(b,a)) = b,
inference(unit_resolution,[status(thm)],[171,40]) ).
tff(173,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,a) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
join(b,a) = join(a,b),
inference(unit_resolution,[status(thm)],[173,7]) ).
tff(175,plain,
join(a,b) = join(b,a),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
meet(b,join(a,b)) = meet(b,join(b,a)),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
meet(b,join(a,b)) = b,
inference(transitivity,[status(thm)],[176,172]) ).
tff(178,plain,
meet(r2,meet(b,join(a,b))) = meet(r2,b),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,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(180,plain,
meet(meet(r2,b),join(a,b)) = meet(r2,meet(b,join(a,b))),
inference(unit_resolution,[status(thm)],[179,60]) ).
tff(181,plain,
meet(meet(b,r2),join(a,b)) = meet(meet(r2,b),join(a,b)),
inference(monotonicity,[status(thm)],[159]) ).
tff(182,plain,
meet(meet(b,r2),join(a,b)) = meet(b,r2),
inference(transitivity,[status(thm)],[181,180,178,158]) ).
tff(183,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(b,r2),join(a,b)) != meet(b,r2) )
| ( meet(join(a,b),join(meet(b,r2),r1)) = join(meet(b,r2),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(b,r2),join(a,b)) != meet(b,r2) )
| ( meet(join(a,b),join(meet(b,r2),r1)) = join(meet(b,r2),meet(r1,join(a,b))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(b,r2),join(a,b)) != meet(b,r2) )
| ( meet(join(a,b),join(meet(b,r2),r1)) = join(meet(b,r2),meet(r1,join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(b,r2),join(a,b)) != meet(b,r2) )
| ( meet(join(a,b),join(meet(b,r2),r1)) = join(meet(b,r2),meet(r1,join(a,b))) ) ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
meet(join(a,b),join(meet(b,r2),r1)) = join(meet(b,r2),meet(r1,join(a,b))),
inference(unit_resolution,[status(thm)],[185,135,182]) ).
tff(187,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,r2),r1) = join(r1,meet(b,r2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
join(meet(b,r2),r1) = join(r1,meet(b,r2)),
inference(unit_resolution,[status(thm)],[187,7]) ).
tff(189,plain,
join(r1,meet(b,r2)) = join(meet(b,r2),r1),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
meet(join(a,b),join(r1,meet(b,r2))) = meet(join(a,b),join(meet(b,r2),r1)),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
meet(join(r1,meet(b,r2)),join(a,b)) = meet(b,r2),
inference(transitivity,[status(thm)],[100,190,186,170,156]) ).
tff(192,plain,
meet(meet(join(r1,meet(b,r2)),join(a,b)),join(r1,meet(a,r2))) = meet(meet(b,r2),join(r1,meet(a,r2))),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
meet(meet(b,r2),join(r1,meet(a,r2))) = meet(meet(join(r1,meet(b,r2)),join(a,b)),join(r1,meet(a,r2))),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
meet(meet(r2,b),join(a,b)) = meet(meet(b,r2),join(a,b)),
inference(symmetry,[status(thm)],[181]) ).
tff(195,plain,
meet(r2,meet(b,join(a,b))) = meet(meet(r2,b),join(a,b)),
inference(symmetry,[status(thm)],[180]) ).
tff(196,plain,
meet(r2,b) = meet(r2,meet(b,join(a,b))),
inference(symmetry,[status(thm)],[178]) ).
tff(197,plain,
meet(b,r2) = meet(meet(b,r2),join(a,b)),
inference(transitivity,[status(thm)],[159,196,195,194]) ).
tff(198,plain,
meet(meet(b,r2),join(r1,meet(a,r2))) = meet(meet(meet(b,r2),join(a,b)),join(r1,meet(a,r2))),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
meet(meet(meet(b,r2),join(a,b)),join(r1,meet(a,r2))) = meet(meet(b,r2),join(r1,meet(a,r2))),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(b,r2),join(a,b)),join(r1,meet(a,r2))) = meet(meet(b,r2),meet(join(a,b),join(r1,meet(a,r2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(201,plain,
meet(meet(meet(b,r2),join(a,b)),join(r1,meet(a,r2))) = meet(meet(b,r2),meet(join(a,b),join(r1,meet(a,r2)))),
inference(unit_resolution,[status(thm)],[200,60]) ).
tff(202,plain,
meet(meet(b,r2),meet(join(a,b),join(r1,meet(a,r2)))) = meet(meet(meet(b,r2),join(a,b)),join(r1,meet(a,r2))),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
meet(meet(b,r2),meet(join(a,b),join(r1,meet(a,r2)))) = meet(meet(b,r2),meet(join(r1,meet(a,r2)),join(a,b))),
inference(monotonicity,[status(thm)],[123]) ).
tff(204,plain,
meet(meet(b,r2),meet(join(r1,meet(a,r2)),join(a,b))) = meet(meet(b,r2),meet(join(a,b),join(r1,meet(a,r2)))),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
meet(join(r1,meet(a,r2)),join(a,b)) = meet(a,r2),
inference(transitivity,[status(thm)],[150,127,140,143,75]) ).
tff(206,plain,
meet(meet(b,r2),meet(join(r1,meet(a,r2)),join(a,b))) = meet(meet(b,r2),meet(a,r2)),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
meet(meet(b,r2),meet(a,r2)) = meet(meet(b,r2),meet(join(r1,meet(a,r2)),join(a,b))),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,a),join(r1,meet(a,r2))) = meet(r2,meet(a,join(r1,meet(a,r2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(209,plain,
meet(meet(r2,a),join(r1,meet(a,r2))) = meet(r2,meet(a,join(r1,meet(a,r2)))),
inference(unit_resolution,[status(thm)],[208,60]) ).
tff(210,plain,
meet(meet(r2,a),join(r1,meet(a,r2))) = meet(meet(a,r2),join(r1,meet(a,r2))),
inference(monotonicity,[status(thm)],[50]) ).
tff(211,plain,
meet(meet(a,r2),join(r1,meet(a,r2))) = meet(meet(r2,a),join(r1,meet(a,r2))),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
meet(meet(a,r2),join(r1,meet(a,r2))) = meet(meet(a,r2),join(meet(a,r2),r1)),
inference(monotonicity,[status(thm)],[126]) ).
tff(213,plain,
meet(meet(a,r2),join(meet(a,r2),r1)) = meet(meet(a,r2),join(r1,meet(a,r2))),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(a,r2),join(meet(a,r2),r1)) = meet(a,r2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(215,plain,
meet(meet(a,r2),join(meet(a,r2),r1)) = meet(a,r2),
inference(unit_resolution,[status(thm)],[214,40]) ).
tff(216,plain,
meet(a,r2) = meet(meet(a,r2),join(meet(a,r2),r1)),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
meet(a,r2) = meet(r2,meet(a,join(r1,meet(a,r2)))),
inference(transitivity,[status(thm)],[216,213,211,209]) ).
tff(218,plain,
meet(meet(b,r2),meet(a,r2)) = meet(meet(b,r2),meet(r2,meet(a,join(r1,meet(a,r2))))),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
meet(meet(b,r2),meet(r2,meet(a,join(r1,meet(a,r2))))) = meet(meet(b,r2),meet(a,r2)),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(b,r2),r2),meet(a,join(r1,meet(a,r2)))) = meet(meet(b,r2),meet(r2,meet(a,join(r1,meet(a,r2))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(221,plain,
meet(meet(meet(b,r2),r2),meet(a,join(r1,meet(a,r2)))) = meet(meet(b,r2),meet(r2,meet(a,join(r1,meet(a,r2))))),
inference(unit_resolution,[status(thm)],[220,60]) ).
tff(222,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(r2,join(r2,meet(r2,meet(a,b)))) = r2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(223,plain,
meet(r2,join(r2,meet(r2,meet(a,b)))) = r2,
inference(unit_resolution,[status(thm)],[222,40]) ).
tff(224,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(r2,meet(r2,meet(a,b))) = r2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(225,plain,
join(r2,meet(r2,meet(a,b))) = r2,
inference(unit_resolution,[status(thm)],[224,73]) ).
tff(226,plain,
r2 = join(r2,meet(r2,meet(a,b))),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
meet(r2,r2) = meet(r2,join(r2,meet(r2,meet(a,b)))),
inference(monotonicity,[status(thm)],[226]) ).
tff(228,plain,
meet(r2,r2) = r2,
inference(transitivity,[status(thm)],[227,223]) ).
tff(229,plain,
meet(b,meet(r2,r2)) = meet(b,r2),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(b,r2),r2) = meet(b,meet(r2,r2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(231,plain,
meet(meet(b,r2),r2) = meet(b,meet(r2,r2)),
inference(unit_resolution,[status(thm)],[230,60]) ).
tff(232,plain,
meet(meet(b,r2),r2) = meet(b,r2),
inference(transitivity,[status(thm)],[231,229]) ).
tff(233,plain,
meet(meet(meet(b,r2),r2),meet(a,join(r1,meet(a,r2)))) = meet(meet(b,r2),meet(a,join(r1,meet(a,r2)))),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
meet(meet(b,r2),meet(a,join(r1,meet(a,r2)))) = meet(meet(meet(b,r2),r2),meet(a,join(r1,meet(a,r2)))),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(b,r2),a),join(r1,meet(a,r2))) = meet(meet(b,r2),meet(a,join(r1,meet(a,r2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(236,plain,
meet(meet(meet(b,r2),a),join(r1,meet(a,r2))) = meet(meet(b,r2),meet(a,join(r1,meet(a,r2)))),
inference(unit_resolution,[status(thm)],[235,60]) ).
tff(237,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),r1) = meet(r1,join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(238,plain,
meet(join(a,b),r1) = meet(r1,join(a,b)),
inference(unit_resolution,[status(thm)],[237,30]) ).
tff(239,plain,
meet(r1,join(a,b)) = meet(join(a,b),r1),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
meet(r2,meet(a,b)) = meet(r1,join(a,b)),
inference(symmetry,[status(thm)],[85]) ).
tff(241,plain,
meet(meet(b,r2),a) = meet(join(a,b),r1),
inference(transitivity,[status(thm)],[160,163,167,240,239]) ).
tff(242,plain,
meet(meet(meet(b,r2),a),join(r1,meet(a,r2))) = meet(meet(join(a,b),r1),join(r1,meet(a,r2))),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
meet(meet(join(a,b),r1),join(r1,meet(a,r2))) = meet(meet(meet(b,r2),a),join(r1,meet(a,r2))),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,b),r1),join(r1,meet(a,r2))) = meet(join(a,b),meet(r1,join(r1,meet(a,r2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(245,plain,
meet(meet(join(a,b),r1),join(r1,meet(a,r2))) = meet(join(a,b),meet(r1,join(r1,meet(a,r2)))),
inference(unit_resolution,[status(thm)],[244,60]) ).
tff(246,plain,
meet(join(a,b),meet(r1,join(r1,meet(a,r2)))) = meet(meet(join(a,b),r1),join(r1,meet(a,r2))),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(r1,join(r1,meet(a,r2))) = r1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(248,plain,
meet(r1,join(r1,meet(a,r2))) = r1,
inference(unit_resolution,[status(thm)],[247,40]) ).
tff(249,plain,
meet(join(a,b),meet(r1,join(r1,meet(a,r2)))) = meet(join(a,b),r1),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
meet(join(a,b),r1) = meet(join(a,b),meet(r1,join(r1,meet(a,r2)))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
meet(join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))),meet(r2,meet(a,b))) = join(meet(r2,meet(a,b)),meet(a,meet(r2,join(r1,meet(b,r2))))),
inference(transitivity,[status(thm)],[32,42,240,239,250,246,243,236,234,221,219,207,204,202,199,193,154,152,149,147,115,22,9]) ).
tff(252,plain,
meet(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) = meet(a,meet(r2,join(r1,meet(b,r2)))),
inference(modus_ponens,[status(thm)],[251,121]) ).
tff(253,plain,
( ( r1 = meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) )
<=> ( meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) = r1 ) ),
inference(commutativity,[status(thm)],]) ).
tff(254,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,join(r1,meet(b,r2))) != r1 )
| ( meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) = join(r1,meet(meet(a,r2),join(r1,meet(b,r2)))) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,join(r1,meet(b,r2))) != r1 )
| ( meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) = join(r1,meet(meet(a,r2),join(r1,meet(b,r2)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(255,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,join(r1,meet(b,r2))) != r1 )
| ( meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) = join(r1,meet(meet(a,r2),join(r1,meet(b,r2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(256,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,join(r1,meet(b,r2))) != r1 )
| ( meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) = join(r1,meet(meet(a,r2),join(r1,meet(b,r2)))) ) ),
inference(modus_ponens,[status(thm)],[255,254]) ).
tff(257,plain,
( ( meet(r1,join(r1,meet(b,r2))) != r1 )
| ( meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) = join(r1,meet(meet(a,r2),join(r1,meet(b,r2)))) ) ),
inference(unit_resolution,[status(thm)],[256,135]) ).
tff(258,plain,
meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) = join(r1,meet(meet(a,r2),join(r1,meet(b,r2)))),
inference(unit_resolution,[status(thm)],[257,87]) ).
tff(259,plain,
join(r1,meet(meet(a,r2),join(r1,meet(b,r2)))) = meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(meet(a,r2),join(r1,meet(b,r2))),r1) = join(r1,meet(meet(a,r2),join(r1,meet(b,r2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(261,plain,
join(meet(meet(a,r2),join(r1,meet(b,r2))),r1) = join(r1,meet(meet(a,r2),join(r1,meet(b,r2)))),
inference(unit_resolution,[status(thm)],[260,7]) ).
tff(262,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(r1,join(r1,meet(r2,meet(a,b)))) = r1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
meet(r1,join(r1,meet(r2,meet(a,b)))) = r1,
inference(unit_resolution,[status(thm)],[262,40]) ).
tff(264,plain,
join(r1,meet(r2,meet(a,b))) = join(r1,meet(r1,join(a,b))),
inference(monotonicity,[status(thm)],[240]) ).
tff(265,plain,
join(r1,meet(r1,join(a,b))) = join(r1,meet(r2,meet(a,b))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(r1,meet(r1,join(a,b))) = r1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(267,plain,
join(r1,meet(r1,join(a,b))) = r1,
inference(unit_resolution,[status(thm)],[266,73]) ).
tff(268,plain,
r1 = join(r1,meet(r1,join(a,b))),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
r1 = join(r1,meet(r2,meet(a,b))),
inference(transitivity,[status(thm)],[268,265]) ).
tff(270,plain,
meet(r1,r1) = meet(r1,join(r1,meet(r2,meet(a,b)))),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
meet(r1,r1) = r1,
inference(transitivity,[status(thm)],[270,263]) ).
tff(272,plain,
join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)) = join(meet(meet(a,r2),join(r1,meet(b,r2))),r1),
inference(monotonicity,[status(thm)],[116,271]) ).
tff(273,plain,
join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)) = meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))),
inference(transitivity,[status(thm)],[272,261,259]) ).
tff(274,plain,
meet(meet(r1,join(r1,meet(a,r2))),join(r1,meet(b,r2))) = meet(r1,join(r1,meet(b,r2))),
inference(monotonicity,[status(thm)],[248]) ).
tff(275,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r1,join(r1,meet(a,r2))),join(r1,meet(b,r2))) = meet(r1,meet(join(r1,meet(a,r2)),join(r1,meet(b,r2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(276,plain,
meet(meet(r1,join(r1,meet(a,r2))),join(r1,meet(b,r2))) = meet(r1,meet(join(r1,meet(a,r2)),join(r1,meet(b,r2)))),
inference(unit_resolution,[status(thm)],[275,60]) ).
tff(277,plain,
meet(r1,meet(join(r1,meet(a,r2)),join(r1,meet(b,r2)))) = meet(meet(r1,join(r1,meet(a,r2))),join(r1,meet(b,r2))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(r1,meet(a,r2)),join(r1,meet(b,r2))) = meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(279,plain,
meet(join(r1,meet(a,r2)),join(r1,meet(b,r2))) = meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))),
inference(unit_resolution,[status(thm)],[278,30]) ).
tff(280,plain,
meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) = meet(join(r1,meet(a,r2)),join(r1,meet(b,r2))),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) = join(meet(meet(a,r2),join(r1,meet(b,r2))),r1),
inference(monotonicity,[status(thm)],[116]) ).
tff(282,plain,
join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) = meet(join(r1,meet(a,r2)),join(r1,meet(b,r2))),
inference(transitivity,[status(thm)],[281,261,259,280]) ).
tff(283,plain,
meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) = meet(r1,meet(join(r1,meet(a,r2)),join(r1,meet(b,r2)))),
inference(monotonicity,[status(thm)],[282]) ).
tff(284,plain,
meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) = r1,
inference(transitivity,[status(thm)],[283,277,274,87]) ).
tff(285,plain,
( ( meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) = join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)) )
<=> ( r1 = meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) ) ),
inference(monotonicity,[status(thm)],[284,273]) ).
tff(286,plain,
( ( meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) = join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)) )
<=> ( meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) = r1 ) ),
inference(transitivity,[status(thm)],[285,253]) ).
tff(287,plain,
( ( meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) = r1 )
<=> ( meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) = join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)) ) ),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
( ( meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) != r1 )
<=> ( meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) != join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)) ) ),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
( ( meet(a2,b2) != r1 )
<=> ( meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) != r1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(290,plain,
( ( meet(a2,b2) != r1 )
<=> ( meet(a2,b2) != r1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(291,axiom,
meet(a2,b2) != r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_SAMs_lemma) ).
tff(292,plain,
meet(a2,b2) != r1,
inference(modus_ponens,[status(thm)],[291,290]) ).
tff(293,plain,
meet(join(r1,meet(b,r2)),join(r1,meet(a,r2))) != r1,
inference(modus_ponens,[status(thm)],[292,289]) ).
tff(294,plain,
meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) != join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)),
inference(modus_ponens,[status(thm)],[293,288]) ).
tff(295,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) != meet(a,meet(r2,join(r1,meet(b,r2)))) )
| ( meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) = join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) != meet(a,meet(r2,join(r1,meet(b,r2)))) )
| ( meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) = join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(296,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) != meet(a,meet(r2,join(r1,meet(b,r2)))) )
| ( meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) = join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(297,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) != meet(a,meet(r2,join(r1,meet(b,r2)))) )
| ( meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) = join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)) ) ),
inference(modus_ponens,[status(thm)],[296,295]) ).
tff(298,plain,
( ( meet(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) != meet(a,meet(r2,join(r1,meet(b,r2)))) )
| ( meet(r1,join(meet(a,meet(r2,join(r1,meet(b,r2)))),r1)) = join(meet(a,meet(r2,join(r1,meet(b,r2)))),meet(r1,r1)) ) ),
inference(unit_resolution,[status(thm)],[297,135]) ).
tff(299,plain,
meet(meet(a,meet(r2,join(r1,meet(b,r2)))),r1) != meet(a,meet(r2,join(r1,meet(b,r2)))),
inference(unit_resolution,[status(thm)],[298,294]) ).
tff(300,plain,
$false,
inference(unit_resolution,[status(thm)],[299,252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT005-4 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 10:42:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 3.60/2.58 % SZS status Unsatisfiable
% 3.60/2.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------