%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT045-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:13:47 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 34
% Syntax : Number of formulae : 93 ( 67 unt; 0 typ; 0 def)
% Number of atoms : 131 ( 124 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 47 ( 15 ~; 11 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 6 ( 6 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 134 ( 122 !; 0 ?; 134 :)
% Comments :
%------------------------------------------------------------------------------
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(n0_type,type,
n0: $i ).
tff(1,plain,
( ! [X: $i] : ( complement(complement(X)) = X )
<=> ! [X: $i] : ( complement(complement(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ! [X: $i] : ( complement(complement(X)) = X )
<=> ! [X: $i] : ( complement(complement(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
! [X: $i] : ( complement(complement(X)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',invertability3) ).
tff(4,plain,
! [X: $i] : ( complement(complement(X)) = X ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
! [X: $i] : ( complement(complement(X)) = X ),
inference(skolemize,[status(sab)],[4]) ).
tff(6,plain,
! [X: $i] : ( complement(complement(X)) = X ),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ~ ! [X: $i] : ( complement(complement(X)) = X )
| ( complement(complement(join(a,b))) = join(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(8,plain,
complement(complement(join(a,b))) = join(a,b),
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
^ [Y: $i,X: $i] :
refl(( ( complement(join(X,Y)) = meet(complement(X),complement(Y)) )
<=> ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) )
<=> ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) )
<=> ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility1) ).
tff(13,plain,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ~ ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) )
| ( complement(join(a,b)) = meet(complement(a),complement(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
complement(join(a,b)) = meet(complement(a),complement(b)),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
complement(complement(join(a,b))) = complement(meet(complement(a),complement(b))),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
complement(meet(complement(a),complement(b))) = complement(complement(join(a,b))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(( ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
<=> ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
<=> ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
<=> ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility2) ).
tff(24,plain,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
| ( complement(meet(join(a,complement(a)),join(a,b))) = join(complement(join(a,complement(a))),complement(join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
complement(meet(join(a,complement(a)),join(a,b))) = join(complement(join(a,complement(a))),complement(join(a,b))),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
join(complement(join(a,complement(a))),complement(join(a,b))) = complement(meet(join(a,complement(a)),join(a,b))),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
meet(complement(a),complement(b)) = complement(join(a,b)),
inference(symmetry,[status(thm)],[17]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) )
| ( complement(join(a,complement(a))) = meet(complement(a),complement(complement(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
complement(join(a,complement(a))) = meet(complement(a),complement(complement(a))),
inference(unit_resolution,[status(thm)],[31,15]) ).
tff(33,plain,
meet(complement(a),complement(complement(a))) = complement(join(a,complement(a))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ~ ! [X: $i] : ( complement(complement(X)) = X )
| ( complement(complement(a)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
complement(complement(a)) = a,
inference(unit_resolution,[status(thm)],[34,6]) ).
tff(36,plain,
meet(complement(a),complement(complement(a))) = meet(complement(a),a),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
meet(complement(a),a) = meet(complement(a),complement(complement(a))),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
^ [X: $i] :
refl(( ( meet(complement(X),X) = n0 )
<=> ( meet(complement(X),X) = n0 ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i] : ( meet(complement(X),X) = n0 )
<=> ! [X: $i] : ( meet(complement(X),X) = n0 ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] : ( meet(complement(X),X) = n0 )
<=> ! [X: $i] : ( meet(complement(X),X) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [X: $i] : ( meet(complement(X),X) = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',invertability2) ).
tff(42,plain,
! [X: $i] : ( meet(complement(X),X) = n0 ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X: $i] : ( meet(complement(X),X) = n0 ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i] : ( meet(complement(X),X) = n0 ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [X: $i] : ( meet(complement(X),X) = n0 )
| ( meet(complement(a),a) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
meet(complement(a),a) = n0,
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
n0 = meet(complement(a),a),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
n0 = complement(join(a,complement(a))),
inference(transitivity,[status(thm)],[47,37,33]) ).
tff(49,plain,
join(n0,meet(complement(a),complement(b))) = join(complement(join(a,complement(a))),complement(join(a,b))),
inference(monotonicity,[status(thm)],[48,30]) ).
tff(50,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(51,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)],[50]) ).
tff(52,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(53,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(54,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(complement(a),complement(b)),n0) = join(n0,meet(complement(a),complement(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
join(meet(complement(a),complement(b)),n0) = join(n0,meet(complement(a),complement(b))),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
( ~ ! [X: $i] : ( meet(complement(X),X) = n0 )
| ( meet(complement(join(a,b)),join(a,b)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
meet(complement(join(a,b)),join(a,b)) = n0,
inference(unit_resolution,[status(thm)],[59,44]) ).
tff(61,plain,
meet(meet(complement(a),complement(b)),join(a,b)) = meet(complement(join(a,b)),join(a,b)),
inference(monotonicity,[status(thm)],[30]) ).
tff(62,plain,
meet(meet(complement(a),complement(b)),join(a,b)) = n0,
inference(transitivity,[status(thm)],[61,60]) ).
tff(63,plain,
join(meet(complement(a),complement(b)),meet(meet(complement(a),complement(b)),join(a,b))) = join(meet(complement(a),complement(b)),n0),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(65,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)],[64]) ).
tff(66,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(67,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(68,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(complement(a),complement(b)),meet(meet(complement(a),complement(b)),join(a,b))) = meet(complement(a),complement(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
join(meet(complement(a),complement(b)),meet(meet(complement(a),complement(b)),join(a,b))) = meet(complement(a),complement(b)),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
meet(complement(a),complement(b)) = join(meet(complement(a),complement(b)),meet(meet(complement(a),complement(b)),join(a,b))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
meet(complement(a),complement(b)) = complement(meet(join(a,complement(a)),join(a,b))),
inference(transitivity,[status(thm)],[73,63,58,49,29]) ).
tff(75,plain,
complement(meet(complement(a),complement(b))) = complement(complement(meet(join(a,complement(a)),join(a,b)))),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
complement(complement(meet(join(a,complement(a)),join(a,b)))) = complement(meet(complement(a),complement(b))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [X: $i] : ( complement(complement(X)) = X )
| ( complement(complement(meet(join(a,complement(a)),join(a,b)))) = meet(join(a,complement(a)),join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
complement(complement(meet(join(a,complement(a)),join(a,b)))) = meet(join(a,complement(a)),join(a,b)),
inference(unit_resolution,[status(thm)],[77,6]) ).
tff(79,plain,
meet(join(a,complement(a)),join(a,b)) = complement(complement(meet(join(a,complement(a)),join(a,b)))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) )
<=> ( join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law) ).
tff(84,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) )
| ( join(a,meet(complement(a),join(a,b))) = meet(join(a,complement(a)),join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
join(a,meet(complement(a),join(a,b))) = meet(join(a,complement(a)),join(a,b)),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
join(a,meet(complement(a),join(a,b))) = join(a,b),
inference(transitivity,[status(thm)],[88,79,76,19,8]) ).
tff(90,plain,
( ( join(a,meet(complement(a),join(a,b))) != join(a,b) )
<=> ( join(a,meet(complement(a),join(a,b))) != join(a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
join(a,meet(complement(a),join(a,b))) != join(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_orthomodular_law) ).
tff(92,plain,
join(a,meet(complement(a),join(a,b))) != join(a,b),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
$false,
inference(unit_resolution,[status(thm)],[92,89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT045-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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 19:28:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------