%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT038-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 30
% Syntax : Number of formulae : 79 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 105 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 13 ~; 9 |; 0 &)
% ( 18 <=>; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 130 ( 118 !; 0 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(dd_type,type,
dd: $i ).
tff(cc_type,type,
cc: $i ).
tff(aa_type,type,
aa: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(bb_type,type,
bb: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(5,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(f(cc,dd),meet(f(cc,dd),f(bb,dd))) = f(cc,dd) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
join(f(cc,dd),meet(f(cc,dd),f(bb,dd))) = f(cc,dd),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(14,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(f(bb,dd),f(aa,dd)) = meet(f(aa,dd),f(bb,dd)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
meet(f(bb,dd),f(aa,dd)) = meet(f(aa,dd),f(bb,dd)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
meet(f(aa,dd),f(bb,dd)) = meet(f(bb,dd),f(aa,dd)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ( meet(f(aa,dd),f(bb,dd)) = meet(f(cc,dd),f(bb,dd)) )
<=> ( meet(f(aa,dd),f(bb,dd)) = meet(f(cc,dd),f(bb,dd)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
meet(f(aa,dd),f(bb,dd)) = meet(f(cc,dd),f(bb,dd)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs2) ).
tff(22,plain,
meet(f(aa,dd),f(bb,dd)) = meet(f(cc,dd),f(bb,dd)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
meet(f(cc,dd),f(bb,dd)) = meet(f(aa,dd),f(bb,dd)),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
meet(f(cc,dd),f(bb,dd)) = meet(f(bb,dd),f(aa,dd)),
inference(transitivity,[status(thm)],[23,19]) ).
tff(25,plain,
join(f(cc,dd),meet(f(cc,dd),f(bb,dd))) = join(f(cc,dd),meet(f(bb,dd),f(aa,dd))),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
join(f(cc,dd),meet(f(bb,dd),f(aa,dd))) = join(f(cc,dd),meet(f(cc,dd),f(bb,dd))),
inference(symmetry,[status(thm)],[25]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(30,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(31,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
| ( join(f(cc,dd),meet(f(bb,dd),f(aa,dd))) = meet(join(f(cc,dd),f(bb,dd)),join(f(cc,dd),f(aa,dd))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
join(f(cc,dd),meet(f(bb,dd),f(aa,dd))) = meet(join(f(cc,dd),f(bb,dd)),join(f(cc,dd),f(aa,dd))),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
meet(join(f(cc,dd),f(bb,dd)),join(f(cc,dd),f(aa,dd))) = join(f(cc,dd),meet(f(bb,dd),f(aa,dd))),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(38,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)],[37]) ).
tff(39,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(40,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(41,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(f(cc,dd),f(aa,dd)) = join(f(aa,dd),f(cc,dd)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
join(f(cc,dd),f(aa,dd)) = join(f(aa,dd),f(cc,dd)),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( f(join(U,V),W) = join(f(U,W),f(V,W)) )
<=> ( f(join(U,V),W) = join(f(U,W),f(V,W)) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [W: $i,V: $i,U: $i] : ( f(join(U,V),W) = join(f(U,W),f(V,W)) )
<=> ! [W: $i,V: $i,U: $i] : ( f(join(U,V),W) = join(f(U,W),f(V,W)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [W: $i,V: $i,U: $i] : ( f(join(U,V),W) = join(f(U,W),f(V,W)) )
<=> ! [W: $i,V: $i,U: $i] : ( f(join(U,V),W) = join(f(U,W),f(V,W)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [W: $i,V: $i,U: $i] : ( f(join(U,V),W) = join(f(U,W),f(V,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_on_left_join) ).
tff(50,plain,
! [W: $i,V: $i,U: $i] : ( f(join(U,V),W) = join(f(U,W),f(V,W)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [W: $i,V: $i,U: $i] : ( f(join(U,V),W) = join(f(U,W),f(V,W)) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [W: $i,V: $i,U: $i] : ( f(join(U,V),W) = join(f(U,W),f(V,W)) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [W: $i,V: $i,U: $i] : ( f(join(U,V),W) = join(f(U,W),f(V,W)) )
| ( f(join(aa,bb),dd) = join(f(aa,dd),f(bb,dd)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
f(join(aa,bb),dd) = join(f(aa,dd),f(bb,dd)),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( ( f(join(aa,bb),dd) = f(join(cc,bb),dd) )
<=> ( f(join(aa,bb),dd) = f(join(cc,bb),dd) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
f(join(aa,bb),dd) = f(join(cc,bb),dd),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs1) ).
tff(57,plain,
f(join(aa,bb),dd) = f(join(cc,bb),dd),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
f(join(cc,bb),dd) = f(join(aa,bb),dd),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
( ~ ! [W: $i,V: $i,U: $i] : ( f(join(U,V),W) = join(f(U,W),f(V,W)) )
| ( f(join(cc,bb),dd) = join(f(cc,dd),f(bb,dd)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
f(join(cc,bb),dd) = join(f(cc,dd),f(bb,dd)),
inference(unit_resolution,[status(thm)],[59,52]) ).
tff(61,plain,
join(f(cc,dd),f(bb,dd)) = f(join(cc,bb),dd),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
join(f(cc,dd),f(bb,dd)) = join(f(aa,dd),f(bb,dd)),
inference(transitivity,[status(thm)],[61,58,54]) ).
tff(63,plain,
meet(join(f(cc,dd),f(bb,dd)),join(f(cc,dd),f(aa,dd))) = meet(join(f(aa,dd),f(bb,dd)),join(f(aa,dd),f(cc,dd))),
inference(monotonicity,[status(thm)],[62,45]) ).
tff(64,plain,
meet(join(f(aa,dd),f(bb,dd)),join(f(aa,dd),f(cc,dd))) = meet(join(f(cc,dd),f(bb,dd)),join(f(cc,dd),f(aa,dd))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
| ( join(f(aa,dd),meet(f(bb,dd),f(cc,dd))) = meet(join(f(aa,dd),f(bb,dd)),join(f(aa,dd),f(cc,dd))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
join(f(aa,dd),meet(f(bb,dd),f(cc,dd))) = meet(join(f(aa,dd),f(bb,dd)),join(f(aa,dd),f(cc,dd))),
inference(unit_resolution,[status(thm)],[65,33]) ).
tff(67,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(f(bb,dd),f(cc,dd)) = meet(f(cc,dd),f(bb,dd)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
meet(f(bb,dd),f(cc,dd)) = meet(f(cc,dd),f(bb,dd)),
inference(unit_resolution,[status(thm)],[67,16]) ).
tff(69,plain,
meet(f(bb,dd),f(cc,dd)) = meet(f(aa,dd),f(bb,dd)),
inference(transitivity,[status(thm)],[68,23]) ).
tff(70,plain,
join(f(aa,dd),meet(f(bb,dd),f(cc,dd))) = join(f(aa,dd),meet(f(aa,dd),f(bb,dd))),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
join(f(aa,dd),meet(f(aa,dd),f(bb,dd))) = join(f(aa,dd),meet(f(bb,dd),f(cc,dd))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(f(aa,dd),meet(f(aa,dd),f(bb,dd))) = f(aa,dd) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
join(f(aa,dd),meet(f(aa,dd),f(bb,dd))) = f(aa,dd),
inference(unit_resolution,[status(thm)],[72,7]) ).
tff(74,plain,
f(aa,dd) = join(f(aa,dd),meet(f(aa,dd),f(bb,dd))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
f(aa,dd) = f(cc,dd),
inference(transitivity,[status(thm)],[74,71,66,64,36,26,9]) ).
tff(76,plain,
( ( f(aa,dd) != f(cc,dd) )
<=> ( f(aa,dd) != f(cc,dd) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
f(aa,dd) != f(cc,dd),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rhs) ).
tff(78,plain,
f(aa,dd) != f(cc,dd),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT038-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 19:28:18 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% See solution above
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------