%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT237-1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:14:01 AM UTC 2025
% Result : Unsatisfiable 4.95s 5.15s
% Output : Proof 4.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 52
% Syntax : Number of formulae : 150 ( 100 unt; 0 typ; 0 def)
% Number of atoms : 283 ( 269 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 205 ( 88 ~; 79 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 221 ( 200 !; 0 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_type,type,
zero: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(one_type,type,
one: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( meet(X,complement(X)) = zero )
<=> ( meet(X,complement(X)) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( meet(X,complement(X)) = zero )
<=> ! [X: $i] : ( meet(X,complement(X)) = zero ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( meet(X,complement(X)) = zero )
<=> ! [X: $i] : ( meet(X,complement(X)) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( meet(X,complement(X)) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
tff(5,plain,
! [X: $i] : ( meet(X,complement(X)) = zero ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( meet(X,complement(X)) = zero ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( meet(X,complement(X)) = zero ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( meet(X,complement(X)) = zero )
| ( meet(a,complement(a)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
meet(a,complement(a)) = zero,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(14,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(a),meet(complement(a),a)) = complement(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
join(complement(a),meet(complement(a),a)) = complement(a),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(20,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)],[19]) ).
tff(21,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(22,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(23,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(complement(a),a) = meet(a,complement(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
meet(complement(a),a) = meet(a,complement(a)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
meet(a,complement(a)) = meet(complement(a),a),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
zero = meet(a,complement(a)),
inference(symmetry,[status(thm)],[9]) ).
tff(30,plain,
( ~ ! [X: $i] : ( meet(X,complement(X)) = zero )
| ( meet(b,complement(b)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
meet(b,complement(b)) = zero,
inference(unit_resolution,[status(thm)],[30,7]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(complement(b),b) = meet(b,complement(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
meet(complement(b),b) = meet(b,complement(b)),
inference(unit_resolution,[status(thm)],[32,25]) ).
tff(34,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(b,meet(b,a)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
join(b,meet(b,a)) = b,
inference(unit_resolution,[status(thm)],[34,16]) ).
tff(36,plain,
( ( meet(b,a) = a )
<=> ( meet(b,a) = a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
tff(38,plain,
meet(b,a) = a,
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
a = meet(b,a),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
join(b,a) = join(b,meet(b,a)),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(42,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)],[41]) ).
tff(43,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(44,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(45,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,b) = join(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
join(a,b) = join(b,a),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
join(a,b) = b,
inference(transitivity,[status(thm)],[49,40,35]) ).
tff(51,plain,
meet(complement(b),join(a,b)) = meet(complement(b),b),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
meet(complement(b),join(a,b)) = meet(complement(a),a),
inference(transitivity,[status(thm)],[51,33,31,29,28]) ).
tff(53,plain,
join(complement(a),meet(complement(b),join(a,b))) = join(complement(a),meet(complement(a),a)),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
join(complement(a),meet(complement(b),join(a,b))) = complement(a),
inference(transitivity,[status(thm)],[53,18]) ).
tff(55,plain,
meet(a,join(complement(a),meet(complement(b),join(a,b)))) = meet(a,complement(a)),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
^ [Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))) )
<=> ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))) )
<=> ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))) )
<=> ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H40) ).
tff(60,plain,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( ~ ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))) )
| ( meet(a,join(complement(a),meet(complement(b),join(a,b)))) = meet(a,join(complement(a),meet(complement(b),join(b,meet(complement(b),join(a,complement(a))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
meet(a,join(complement(a),meet(complement(b),join(a,b)))) = meet(a,join(complement(a),meet(complement(b),join(b,meet(complement(b),join(a,complement(a))))))),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
meet(a,join(complement(a),meet(complement(b),join(b,meet(complement(b),join(a,complement(a))))))) = meet(a,join(complement(a),meet(complement(b),join(a,b)))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(67,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)],[66]) ).
tff(68,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(69,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(70,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(complement(b),join(complement(b),b)) = complement(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
meet(complement(b),join(complement(b),b)) = complement(b),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(complement(b),b) = join(b,complement(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
join(complement(b),b) = join(b,complement(b)),
inference(unit_resolution,[status(thm)],[75,47]) ).
tff(77,plain,
join(b,complement(b)) = join(complement(b),b),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
^ [X: $i] :
refl(( ( join(X,complement(X)) = one )
<=> ( join(X,complement(X)) = one ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [X: $i] : ( join(X,complement(X)) = one )
<=> ! [X: $i] : ( join(X,complement(X)) = one ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [X: $i] : ( join(X,complement(X)) = one )
<=> ! [X: $i] : ( join(X,complement(X)) = one ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,axiom,
! [X: $i] : ( join(X,complement(X)) = one ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_join) ).
tff(82,plain,
! [X: $i] : ( join(X,complement(X)) = one ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [X: $i] : ( join(X,complement(X)) = one ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i] : ( join(X,complement(X)) = one ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ~ ! [X: $i] : ( join(X,complement(X)) = one )
| ( join(b,complement(b)) = one ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
join(b,complement(b)) = one,
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
one = join(b,complement(b)),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ~ ! [X: $i] : ( join(X,complement(X)) = one )
| ( join(a,complement(a)) = one ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
join(a,complement(a)) = one,
inference(unit_resolution,[status(thm)],[88,84]) ).
tff(90,plain,
join(a,complement(a)) = join(complement(b),b),
inference(transitivity,[status(thm)],[89,87,77]) ).
tff(91,plain,
meet(complement(b),join(a,complement(a))) = meet(complement(b),join(complement(b),b)),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
meet(complement(b),join(a,complement(a))) = complement(b),
inference(transitivity,[status(thm)],[91,74]) ).
tff(93,plain,
join(b,meet(complement(b),join(a,complement(a)))) = join(b,complement(b)),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
join(b,meet(complement(b),join(a,complement(a)))) = join(complement(b),b),
inference(transitivity,[status(thm)],[93,77]) ).
tff(95,plain,
meet(complement(b),join(b,meet(complement(b),join(a,complement(a))))) = meet(complement(b),join(complement(b),b)),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
meet(complement(b),join(b,meet(complement(b),join(a,complement(a))))) = complement(b),
inference(transitivity,[status(thm)],[95,74]) ).
tff(97,plain,
join(complement(a),meet(complement(b),join(b,meet(complement(b),join(a,complement(a)))))) = join(complement(a),complement(b)),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
join(complement(a),complement(b)) = join(complement(a),meet(complement(b),join(b,meet(complement(b),join(a,complement(a)))))),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(complement(a),complement(b)) = join(complement(b),complement(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
join(complement(a),complement(b)) = join(complement(b),complement(a)),
inference(unit_resolution,[status(thm)],[99,47]) ).
tff(101,plain,
join(complement(b),complement(a)) = join(complement(a),complement(b)),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
join(complement(b),complement(a)) = join(complement(a),meet(complement(b),join(b,meet(complement(b),join(a,complement(a)))))),
inference(transitivity,[status(thm)],[101,98]) ).
tff(103,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(a),meet(complement(b),join(b,meet(complement(b),join(a,complement(a))))))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(transitivity,[status(thm)],[103,65,55,9]) ).
tff(105,plain,
( ( complement(a) = join(complement(b),complement(a)) )
<=> ( join(complement(b),complement(a)) = complement(a) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(106,plain,
( ( join(complement(b),complement(a)) = complement(a) )
<=> ( complement(a) = join(complement(b),complement(a)) ) ),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ( join(complement(b),complement(a)) != complement(a) )
<=> ( complement(a) != join(complement(b),complement(a)) ) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ( join(complement(b),complement(a)) != complement(a) )
<=> ( join(complement(b),complement(a)) != complement(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,axiom,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
tff(110,plain,
join(complement(b),complement(a)) != complement(a),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
complement(a) != join(complement(b),complement(a)),
inference(modus_ponens,[status(thm)],[110,107]) ).
tff(112,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(b),meet(complement(b),join(complement(b),complement(a)))) = complement(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
join(complement(b),meet(complement(b),join(complement(b),complement(a)))) = complement(b),
inference(unit_resolution,[status(thm)],[112,16]) ).
tff(114,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(complement(b),join(complement(b),complement(a))) = complement(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
meet(complement(b),join(complement(b),complement(a))) = complement(b),
inference(unit_resolution,[status(thm)],[114,72]) ).
tff(116,plain,
complement(b) = meet(complement(b),join(complement(b),complement(a))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
join(complement(b),complement(b)) = join(complement(b),meet(complement(b),join(complement(b),complement(a)))),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
join(complement(b),complement(b)) = complement(b),
inference(transitivity,[status(thm)],[117,113]) ).
tff(119,plain,
join(b,join(complement(b),complement(b))) = join(b,complement(b)),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,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(121,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)],[120]) ).
tff(122,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(123,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
tff(124,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(b,complement(b)),complement(b)) = join(b,join(complement(b),complement(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
join(join(b,complement(b)),complement(b)) = join(b,join(complement(b),complement(b))),
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
join(a,complement(a)) = join(b,complement(b)),
inference(transitivity,[status(thm)],[89,87]) ).
tff(130,plain,
join(join(a,complement(a)),complement(b)) = join(join(b,complement(b)),complement(b)),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(a,complement(a)),complement(b)) = join(a,join(complement(a),complement(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
join(join(a,complement(a)),complement(b)) = join(a,join(complement(a),complement(b))),
inference(unit_resolution,[status(thm)],[131,126]) ).
tff(133,plain,
join(a,join(complement(a),complement(b))) = join(join(a,complement(a)),complement(b)),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
join(a,join(complement(b),complement(a))) = join(a,join(complement(a),complement(b))),
inference(monotonicity,[status(thm)],[101]) ).
tff(135,plain,
join(a,join(complement(b),complement(a))) = one,
inference(transitivity,[status(thm)],[134,133,130,128,119,86]) ).
tff(136,plain,
^ [Y: $i,X: $i] :
refl(( ( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
<=> ( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) )),
inference(bind,[status(th)],[]) ).
tff(137,plain,
( ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
<=> ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
( ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
<=> ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ( meet(X,Y) != zero )
| ( join(X,Y) != one ) )
<=> ( ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) )),
( ( ( meet(X,Y) != zero )
| ( join(X,Y) != one )
| ( complement(X) = Y ) )
<=> ( ( join(X,Y) != one )
| ( meet(X,Y) != zero )
| ( complement(X) = Y ) ) )),
rewrite(( ( ( join(X,Y) != one )
| ( meet(X,Y) != zero )
| ( complement(X) = Y ) )
<=> ( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) )),
( ( ( meet(X,Y) != zero )
| ( join(X,Y) != one )
| ( complement(X) = Y ) )
<=> ( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) )),
inference(bind,[status(th)],[]) ).
tff(140,plain,
( ! [Y: $i,X: $i] :
( ( meet(X,Y) != zero )
| ( join(X,Y) != one )
| ( complement(X) = Y ) )
<=> ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,axiom,
! [Y: $i,X: $i] :
( ( meet(X,Y) != zero )
| ( join(X,Y) != one )
| ( complement(X) = Y ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
tff(142,plain,
! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[142,138]) ).
tff(144,plain,
! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ),
inference(skolemize,[status(sab)],[143]) ).
tff(145,plain,
! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[144,137]) ).
tff(146,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
| ( complement(a) = join(complement(b),complement(a)) )
| ( join(a,join(complement(b),complement(a))) != one )
| ( meet(a,join(complement(b),complement(a))) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
| ( complement(a) = join(complement(b),complement(a)) )
| ( join(a,join(complement(b),complement(a))) != one )
| ( meet(a,join(complement(b),complement(a))) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
( ~ ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
| ( complement(a) = join(complement(b),complement(a)) )
| ( join(a,join(complement(b),complement(a))) != one )
| ( meet(a,join(complement(b),complement(a))) != zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
( ~ ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
| ( complement(a) = join(complement(b),complement(a)) )
| ( join(a,join(complement(b),complement(a))) != one )
| ( meet(a,join(complement(b),complement(a))) != zero ) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
( ( complement(a) = join(complement(b),complement(a)) )
| ( join(a,join(complement(b),complement(a))) != one )
| ( meet(a,join(complement(b),complement(a))) != zero ) ),
inference(unit_resolution,[status(thm)],[148,145]) ).
tff(150,plain,
$false,
inference(unit_resolution,[status(thm)],[149,135,111,104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : LAT237-1 : TPTP v9.0.0. Released v3.1.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Jun 19 19:55:47 EDT 2025
% 0.15/0.36 % CPUTime :
% 4.95/5.15 % SZS status Unsatisfiable
% 4.95/5.15 % SZS output start Proof
% See solution above
% 4.95/5.16 % E exiting
%------------------------------------------------------------------------------