%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT044-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.57s 0.71s
% Output : Proof 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 55
% Syntax : Number of formulae : 162 ( 117 unt; 0 typ; 0 def)
% Number of atoms : 225 ( 215 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 84 ( 30 ~; 26 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 9 ( 9 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 : 220 ( 202 !; 0 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
tff(n1_type,type,
n1: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( join(complement(X),X) = n1 )
<=> ( join(complement(X),X) = n1 ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( join(complement(X),X) = n1 )
<=> ! [X: $i] : ( join(complement(X),X) = n1 ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( join(complement(X),X) = n1 )
<=> ! [X: $i] : ( join(complement(X),X) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( join(complement(X),X) = n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',invertability1) ).
tff(5,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( join(complement(X),X) = n1 )
| ( join(complement(meet(a,b)),meet(a,b)) = n1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
join(complement(meet(a,b)),meet(a,b)) = n1,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility2) ).
tff(14,plain,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
| ( complement(meet(a,b)) = join(complement(a),complement(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
complement(meet(a,b)) = join(complement(a),complement(b)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
join(complement(a),complement(b)) = complement(meet(a,b)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(21,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)],[20]) ).
tff(22,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(23,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(24,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(a),meet(complement(a),join(a,b))) = complement(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
join(complement(a),meet(complement(a),join(a,b))) = complement(a),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
join(join(complement(a),meet(complement(a),join(a,b))),complement(b)) = join(complement(a),complement(b)),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(a),meet(complement(a),join(a,b))),complement(b)) = join(complement(a),join(meet(complement(a),join(a,b)),complement(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
join(join(complement(a),meet(complement(a),join(a,b))),complement(b)) = join(complement(a),join(meet(complement(a),join(a,b)),complement(b))),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
join(complement(a),join(meet(complement(a),join(a,b)),complement(b))) = join(join(complement(a),meet(complement(a),join(a,b))),complement(b)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
join(complement(a),join(meet(complement(a),join(a,b)),complement(b))) = complement(meet(a,b)),
inference(transitivity,[status(thm)],[39,29,19]) ).
tff(41,plain,
join(join(complement(a),join(meet(complement(a),join(a,b)),complement(b))),meet(a,b)) = join(complement(meet(a,b)),meet(a,b)),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(a),join(meet(complement(a),join(a,b)),complement(b))),meet(a,b)) = join(complement(a),join(join(meet(complement(a),join(a,b)),complement(b)),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
join(join(complement(a),join(meet(complement(a),join(a,b)),complement(b))),meet(a,b)) = join(complement(a),join(join(meet(complement(a),join(a,b)),complement(b)),meet(a,b))),
inference(unit_resolution,[status(thm)],[42,36]) ).
tff(44,plain,
join(complement(a),join(join(meet(complement(a),join(a,b)),complement(b)),meet(a,b))) = join(join(complement(a),join(meet(complement(a),join(a,b)),complement(b))),meet(a,b)),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(complement(a),join(a,b)),complement(b)),meet(a,b)) = join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
join(join(meet(complement(a),join(a,b)),complement(b)),meet(a,b)) = join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))),
inference(unit_resolution,[status(thm)],[45,36]) ).
tff(47,plain,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) = join(join(meet(complement(a),join(a,b)),complement(b)),meet(a,b)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(49,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)],[48]) ).
tff(50,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(51,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(52,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(complement(a),join(a,b)),complement(a)) = join(complement(a),meet(complement(a),join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
join(meet(complement(a),join(a,b)),complement(a)) = join(complement(a),meet(complement(a),join(a,b))),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
<=> ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
<=> ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
<=> ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',orthomodular_law) ).
tff(61,plain,
! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
| ( join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a)))) = join(meet(complement(a),join(a,b)),complement(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a)))) = join(meet(complement(a),join(a,b)),complement(a)),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
join(meet(complement(a),join(a,b)),complement(a)) = complement(a),
inference(transitivity,[status(thm)],[56,28]) ).
tff(67,plain,
meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a))) = meet(complement(meet(complement(a),join(a,b))),complement(a)),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
meet(complement(meet(complement(a),join(a,b))),complement(a)) = meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,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(70,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)],[69]) ).
tff(71,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(72,axiom,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility1) ).
tff(73,plain,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ~ ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) )
| ( complement(join(meet(complement(a),join(a,b)),a)) = meet(complement(meet(complement(a),join(a,b))),complement(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
complement(join(meet(complement(a),join(a,b)),a)) = meet(complement(meet(complement(a),join(a,b))),complement(a)),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
| ( join(a,meet(complement(a),join(a,b))) = join(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
join(a,meet(complement(a),join(a,b))) = join(a,b),
inference(unit_resolution,[status(thm)],[78,63]) ).
tff(80,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(complement(a),join(a,b)),a) = join(a,meet(complement(a),join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
join(meet(complement(a),join(a,b)),a) = join(a,meet(complement(a),join(a,b))),
inference(unit_resolution,[status(thm)],[80,54]) ).
tff(82,plain,
join(meet(complement(a),join(a,b)),a) = join(a,b),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
complement(join(meet(complement(a),join(a,b)),a)) = complement(join(a,b)),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
complement(join(a,b)) = complement(join(meet(complement(a),join(a,b)),a)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,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(86,plain,
complement(join(a,b)) = meet(complement(a),complement(b)),
inference(unit_resolution,[status(thm)],[85,75]) ).
tff(87,plain,
meet(complement(a),complement(b)) = complement(join(a,b)),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
meet(complement(a),complement(b)) = meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a))),
inference(transitivity,[status(thm)],[87,84,77,68]) ).
tff(89,plain,
join(meet(complement(a),join(a,b)),meet(complement(a),complement(b))) = join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a)))),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
join(meet(complement(a),join(a,b)),meet(complement(a),complement(b))) = complement(a),
inference(transitivity,[status(thm)],[89,65,56,28]) ).
tff(91,plain,
join(join(meet(complement(a),join(a,b)),meet(complement(a),complement(b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))) = join(complement(a),join(join(meet(complement(a),join(a,b)),complement(b)),meet(a,b))),
inference(monotonicity,[status(thm)],[90,47]) ).
tff(92,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(complement(a),join(a,b)),meet(complement(a),complement(b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))) = join(meet(complement(a),join(a,b)),join(meet(complement(a),complement(b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
join(join(meet(complement(a),join(a,b)),meet(complement(a),complement(b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))) = join(meet(complement(a),join(a,b)),join(meet(complement(a),complement(b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))),
inference(unit_resolution,[status(thm)],[92,36]) ).
tff(94,plain,
join(meet(complement(a),join(a,b)),join(meet(complement(a),complement(b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))) = join(join(meet(complement(a),join(a,b)),meet(complement(a),complement(b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(b),meet(a,b)),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))))) = join(complement(b),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
join(join(complement(b),meet(a,b)),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))))) = join(complement(b),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b)))))),
inference(unit_resolution,[status(thm)],[95,36]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
| ( join(join(complement(b),meet(a,b)),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))))) = join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
join(join(complement(b),meet(a,b)),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))))) = join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))),
inference(unit_resolution,[status(thm)],[97,63]) ).
tff(99,plain,
join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))) = join(join(complement(b),meet(a,b)),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))) = join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))) = join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))),
inference(unit_resolution,[status(thm)],[100,54]) ).
tff(102,plain,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) = join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) = join(complement(b),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b)))))),
inference(transitivity,[status(thm)],[102,99,96]) ).
tff(104,plain,
join(meet(complement(a),complement(b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))) = join(meet(complement(a),complement(b)),join(complement(b),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))))))),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
join(meet(complement(a),complement(b)),join(complement(b),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))))))) = join(meet(complement(a),complement(b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(complement(a),complement(b)),complement(b)),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b)))))) = join(meet(complement(a),complement(b)),join(complement(b),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
join(join(meet(complement(a),complement(b)),complement(b)),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b)))))) = join(meet(complement(a),complement(b)),join(complement(b),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))))))),
inference(unit_resolution,[status(thm)],[106,36]) ).
tff(108,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(b),meet(complement(b),complement(a))) = complement(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
join(complement(b),meet(complement(b),complement(a))) = complement(b),
inference(unit_resolution,[status(thm)],[108,26]) ).
tff(110,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(111,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)],[110]) ).
tff(112,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(113,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(114,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[114]) ).
tff(116,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(complement(b),complement(a)) = meet(complement(a),complement(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
meet(complement(b),complement(a)) = meet(complement(a),complement(b)),
inference(unit_resolution,[status(thm)],[117,116]) ).
tff(119,plain,
meet(complement(a),complement(b)) = meet(complement(b),complement(a)),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
complement(join(a,b)) = meet(complement(b),complement(a)),
inference(transitivity,[status(thm)],[86,119]) ).
tff(121,plain,
join(complement(b),complement(join(a,b))) = join(complement(b),meet(complement(b),complement(a))),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
| ( complement(meet(b,join(a,b))) = join(complement(b),complement(join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
complement(meet(b,join(a,b))) = join(complement(b),complement(join(a,b))),
inference(unit_resolution,[status(thm)],[122,16]) ).
tff(124,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),b) = meet(b,join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
meet(join(a,b),b) = meet(b,join(a,b)),
inference(unit_resolution,[status(thm)],[124,116]) ).
tff(126,plain,
complement(meet(join(a,b),b)) = complement(meet(b,join(a,b))),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
| ( complement(meet(join(a,b),b)) = join(complement(join(a,b)),complement(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
complement(meet(join(a,b),b)) = join(complement(join(a,b)),complement(b)),
inference(unit_resolution,[status(thm)],[127,16]) ).
tff(129,plain,
join(complement(join(a,b)),complement(b)) = complement(meet(join(a,b),b)),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
join(meet(complement(a),complement(b)),complement(b)) = join(complement(join(a,b)),complement(b)),
inference(monotonicity,[status(thm)],[87]) ).
tff(131,plain,
join(meet(complement(a),complement(b)),complement(b)) = complement(b),
inference(transitivity,[status(thm)],[130,129,126,123,121,109]) ).
tff(132,plain,
join(join(meet(complement(a),complement(b)),complement(b)),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b)))))) = join(complement(b),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b)))))),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
join(complement(b),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b)))))) = join(join(meet(complement(a),complement(b)),complement(b)),join(meet(a,b),meet(complement(join(complement(b),meet(a,b))),join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b)))))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
| ( join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))) = join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))) = join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))),
inference(unit_resolution,[status(thm)],[134,63]) ).
tff(136,plain,
join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))) = join(meet(complement(a),complement(b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))),
inference(transitivity,[status(thm)],[135,102,99,96,133,107,105]) ).
tff(137,plain,
join(meet(complement(a),join(a,b)),join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))))) = join(meet(complement(a),join(a,b)),join(meet(complement(a),complement(b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(complement(a),join(a,b)),meet(complement(a),join(a,b))),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))) = join(meet(complement(a),join(a,b)),join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
join(join(meet(complement(a),join(a,b)),meet(complement(a),join(a,b))),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))) = join(meet(complement(a),join(a,b)),join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))))),
inference(unit_resolution,[status(thm)],[138,36]) ).
tff(140,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(141,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)],[140]) ).
tff(142,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(143,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(144,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[144]) ).
tff(146,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[145,141]) ).
tff(147,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(complement(a),join(a,b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))) = meet(complement(a),join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
meet(meet(complement(a),join(a,b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))) = meet(complement(a),join(a,b)),
inference(unit_resolution,[status(thm)],[147,146]) ).
tff(149,plain,
meet(complement(a),join(a,b)) = meet(meet(complement(a),join(a,b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b)))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
join(meet(complement(a),join(a,b)),meet(complement(a),join(a,b))) = join(meet(complement(a),join(a,b)),meet(meet(complement(a),join(a,b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
join(meet(complement(a),join(a,b)),meet(meet(complement(a),join(a,b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))) = join(meet(complement(a),join(a,b)),meet(complement(a),join(a,b))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(complement(a),join(a,b)),meet(meet(complement(a),join(a,b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))) = meet(complement(a),join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
join(meet(complement(a),join(a,b)),meet(meet(complement(a),join(a,b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))) = meet(complement(a),join(a,b)),
inference(unit_resolution,[status(thm)],[152,26]) ).
tff(154,plain,
meet(complement(a),join(a,b)) = join(meet(complement(a),join(a,b)),meet(meet(complement(a),join(a,b)),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
meet(complement(a),join(a,b)) = join(meet(complement(a),join(a,b)),meet(complement(a),join(a,b))),
inference(transitivity,[status(thm)],[154,151]) ).
tff(156,plain,
join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))) = join(join(meet(complement(a),join(a,b)),meet(complement(a),join(a,b))),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) = join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))))),
inference(symmetry,[status(thm)],[135]) ).
tff(158,plain,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) = n1,
inference(transitivity,[status(thm)],[157,156,139,137,94,91,44,41,9]) ).
tff(159,plain,
( ( join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1 )
<=> ( join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,axiom,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_orthomodular_law) ).
tff(161,plain,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1,
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
$false,
inference(unit_resolution,[status(thm)],[161,158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LAT044-1 : TPTP v9.0.0. Released v2.5.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 19:28:20 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.57/0.71 % SZS status Unsatisfiable
% 0.57/0.71 % SZS output start Proof
% See solution above
% 0.57/0.73 % E exiting
%------------------------------------------------------------------------------