%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT032-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:13:46 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 28
% Syntax : Number of formulae : 75 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 101 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 42 ( 15 ~; 11 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 5 ( 5 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 : 124 ( 113 !; 0 ?; 124 :)
% Comments :
%------------------------------------------------------------------------------
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(zz_type,type,
zz: $i ).
tff(xx_type,type,
xx: $i ).
tff(yy_type,type,
yy: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
<=> ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_join) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
| ( join(meet(xx,yy),meet(xx,zz)) = meet(join(meet(xx,yy),xx),join(meet(xx,yy),zz)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
join(meet(xx,yy),meet(xx,zz)) = meet(join(meet(xx,yy),xx),join(meet(xx,yy),zz)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
meet(join(meet(xx,yy),xx),join(meet(xx,yy),zz)) = join(meet(xx,yy),meet(xx,zz)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(12,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)],[11]) ).
tff(13,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(14,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(15,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(zz,meet(xx,yy)) = join(meet(xx,yy),zz) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
join(zz,meet(xx,yy)) = join(meet(xx,yy),zz),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
| ( join(zz,meet(xx,yy)) = meet(join(zz,xx),join(zz,yy)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
join(zz,meet(xx,yy)) = meet(join(zz,xx),join(zz,yy)),
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,plain,
meet(join(zz,xx),join(zz,yy)) = join(zz,meet(xx,yy)),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(zz,yy) = join(yy,zz) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
join(zz,yy) = join(yy,zz),
inference(unit_resolution,[status(thm)],[23,17]) ).
tff(25,plain,
join(yy,zz) = join(zz,yy),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(zz,xx) = join(xx,zz) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
join(zz,xx) = join(xx,zz),
inference(unit_resolution,[status(thm)],[26,17]) ).
tff(28,plain,
join(xx,zz) = join(zz,xx),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
meet(join(xx,zz),join(yy,zz)) = meet(join(zz,xx),join(zz,yy)),
inference(monotonicity,[status(thm)],[28,25]) ).
tff(30,plain,
meet(join(xx,zz),join(yy,zz)) = join(meet(xx,yy),zz),
inference(transitivity,[status(thm)],[29,22,19]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(xx,yy),xx) = join(xx,meet(xx,yy)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
join(meet(xx,yy),xx) = join(xx,meet(xx,yy)),
inference(unit_resolution,[status(thm)],[31,17]) ).
tff(33,plain,
join(xx,meet(xx,yy)) = join(meet(xx,yy),xx),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(35,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)],[34]) ).
tff(36,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(37,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(38,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(xx,meet(xx,yy)) = xx ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
join(xx,meet(xx,yy)) = xx,
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
xx = join(xx,meet(xx,yy)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
^ [X: $i] :
refl(( ( join(X,X) = X )
<=> ( join(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [X: $i] : ( join(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
tff(48,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [X: $i] : ( join(X,X) = X ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(xx,xx) = xx ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
join(xx,xx) = xx,
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
join(xx,xx) = join(meet(xx,yy),xx),
inference(transitivity,[status(thm)],[52,43,33]) ).
tff(54,plain,
meet(join(xx,xx),meet(join(xx,zz),join(yy,zz))) = meet(join(meet(xx,yy),xx),join(meet(xx,yy),zz)),
inference(monotonicity,[status(thm)],[53,30]) ).
tff(55,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(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(quant_intro,[status(thm)],[55]) ).
tff(57,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(58,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(59,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(xx,xx),join(xx,zz)),join(yy,zz)) = meet(join(xx,xx),meet(join(xx,zz),join(yy,zz))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
meet(meet(join(xx,xx),join(xx,zz)),join(yy,zz)) = meet(join(xx,xx),meet(join(xx,zz),join(yy,zz))),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
| ( join(xx,meet(xx,zz)) = meet(join(xx,xx),join(xx,zz)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
join(xx,meet(xx,zz)) = meet(join(xx,xx),join(xx,zz)),
inference(unit_resolution,[status(thm)],[64,7]) ).
tff(66,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(xx,meet(xx,zz)) = xx ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
join(xx,meet(xx,zz)) = xx,
inference(unit_resolution,[status(thm)],[66,40]) ).
tff(68,plain,
xx = join(xx,meet(xx,zz)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
xx = meet(join(xx,xx),join(xx,zz)),
inference(transitivity,[status(thm)],[68,65]) ).
tff(70,plain,
meet(xx,join(yy,zz)) = meet(meet(join(xx,xx),join(xx,zz)),join(yy,zz)),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
meet(xx,join(yy,zz)) = join(meet(xx,yy),meet(xx,zz)),
inference(transitivity,[status(thm)],[70,63,54,10]) ).
tff(72,plain,
( ( meet(xx,join(yy,zz)) != join(meet(xx,yy),meet(xx,zz)) )
<=> ( meet(xx,join(yy,zz)) != join(meet(xx,yy),meet(xx,zz)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
meet(xx,join(yy,zz)) != join(meet(xx,yy),meet(xx,zz)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_meet) ).
tff(74,plain,
meet(xx,join(yy,zz)) != join(meet(xx,yy),meet(xx,zz)),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
$false,
inference(unit_resolution,[status(thm)],[74,71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT032-1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:29:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------