%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT014-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:44 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 25 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 2 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 2 ( 2 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 54 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( meet(X,join(Y,join(X,Z))) = X )
<=> ( meet(X,join(Y,join(X,Z))) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mckenzie2) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(join(meet(a,join(a,b)),meet(join(a,b),join(b,join(join(a,b),b)))),join(a,b))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
meet(a,join(join(meet(a,join(a,b)),meet(join(a,b),join(b,join(join(a,b),b)))),join(a,b))) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
<=> ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mckenzie3) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(meet(X,Y),meet(Y,Z)),Y) = Y )
| ( join(join(meet(a,join(a,b)),meet(join(a,b),join(b,join(join(a,b),b)))),join(a,b)) = join(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
join(join(meet(a,join(a,b)),meet(join(a,b),join(b,join(join(a,b),b)))),join(a,b)) = join(a,b),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
join(a,b) = join(join(meet(a,join(a,b)),meet(join(a,b),join(b,join(join(a,b),b)))),join(a,b)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
meet(a,join(a,b)) = meet(a,join(join(meet(a,join(a,b)),meet(join(a,b),join(b,join(join(a,b),b)))),join(a,b))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
meet(a,join(a,b)) = a,
inference(transitivity,[status(thm)],[20,9]) ).
tff(22,plain,
( ( meet(a,join(a,b)) != a )
<=> ( meet(a,join(a,b)) != a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
meet(a,join(a,b)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_absorbtion) ).
tff(24,plain,
meet(a,join(a,b)) != a,
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
$false,
inference(unit_resolution,[status(thm)],[24,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT014-1 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:28:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------