%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT005-4 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:13:43 AM UTC 2025
% Result : Unsatisfiable 1.91s 2.08s
% Output : Proof 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 58
% Syntax : Number of formulae : 182 ( 127 unt; 0 typ; 0 def)
% Number of atoms : 275 ( 268 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 153 ( 66 ~; 62 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 212 ( 198 !; 0 ?; 212 :)
% Comments :
%------------------------------------------------------------------------------
tff(r1_type,type,
r1: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(b2_type,type,
b2: $i ).
tff(a2_type,type,
a2: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(r2_type,type,
r2: $i ).
tff(n0_type,type,
n0: $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/sandbox2/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(r1,meet(r1,join(a,b))) = r1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
join(r1,meet(r1,join(a,b))) = r1,
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/sandbox2/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(join(a,b),r1) = meet(r1,join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
meet(join(a,b),r1) = meet(r1,join(a,b)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(20,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)],[19]) ).
tff(21,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(22,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(23,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(r1,join(r1,meet(a,r2))) = r1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
meet(r1,join(r1,meet(a,r2))) = r1,
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
( ( join(r1,meet(a,r2)) = b2 )
<=> ( join(r1,meet(a,r2)) = b2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
join(r1,meet(a,r2)) = b2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',define_b2) ).
tff(30,plain,
join(r1,meet(a,r2)) = b2,
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
b2 = join(r1,meet(a,r2)),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
meet(r1,b2) = meet(r1,join(r1,meet(a,r2))),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
meet(r1,b2) = r1,
inference(transitivity,[status(thm)],[32,27]) ).
tff(34,plain,
meet(join(a,b),meet(r1,b2)) = meet(join(a,b),r1),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
tff(39,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,b),r1),b2) = meet(join(a,b),meet(r1,b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
meet(meet(join(a,b),r1),b2) = meet(join(a,b),meet(r1,b2)),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
meet(r1,join(a,b)) = meet(join(a,b),r1),
inference(symmetry,[status(thm)],[18]) ).
tff(45,plain,
( ( meet(r1,join(a,b)) = n0 )
<=> ( meet(r1,join(a,b)) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
meet(r1,join(a,b)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1_complement_join_a_b_2) ).
tff(47,plain,
meet(r1,join(a,b)) = n0,
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
n0 = meet(r1,join(a,b)),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ( meet(r2,meet(a,b)) = n0 )
<=> ( meet(r2,meet(a,b)) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
meet(r2,meet(a,b)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_complement_meet_a_b_2) ).
tff(51,plain,
meet(r2,meet(a,b)) = n0,
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,a) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
meet(b,a) = meet(a,b),
inference(unit_resolution,[status(thm)],[52,16]) ).
tff(54,plain,
meet(r2,meet(b,a)) = meet(r2,meet(a,b)),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,b),a) = meet(r2,meet(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
meet(meet(r2,b),a) = meet(r2,meet(b,a)),
inference(unit_resolution,[status(thm)],[55,41]) ).
tff(57,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(r2,b) = meet(b,r2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
meet(r2,b) = meet(b,r2),
inference(unit_resolution,[status(thm)],[57,16]) ).
tff(59,plain,
meet(b,r2) = meet(r2,b),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
meet(meet(b,r2),a) = meet(meet(r2,b),a),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
meet(meet(b,r2),a) = meet(join(a,b),r1),
inference(transitivity,[status(thm)],[60,56,54,51,48,44]) ).
tff(62,plain,
meet(meet(meet(b,r2),a),b2) = meet(meet(join(a,b),r1),b2),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(b,r2),a),b2) = meet(meet(b,r2),meet(a,b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
meet(meet(meet(b,r2),a),b2) = meet(meet(b,r2),meet(a,b2)),
inference(unit_resolution,[status(thm)],[63,41]) ).
tff(65,plain,
meet(meet(b,r2),meet(a,b2)) = meet(meet(meet(b,r2),a),b2),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(r2,join(r2,n0)) = r2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
meet(r2,join(r2,n0)) = r2,
inference(unit_resolution,[status(thm)],[66,25]) ).
tff(68,plain,
n0 = meet(r2,meet(a,b)),
inference(symmetry,[status(thm)],[51]) ).
tff(69,plain,
join(r2,n0) = join(r2,meet(r2,meet(a,b))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
join(r2,meet(r2,meet(a,b))) = join(r2,n0),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(r2,meet(r2,meet(a,b))) = r2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
join(r2,meet(r2,meet(a,b))) = r2,
inference(unit_resolution,[status(thm)],[71,7]) ).
tff(73,plain,
r2 = join(r2,meet(r2,meet(a,b))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
r2 = join(r2,n0),
inference(transitivity,[status(thm)],[73,70]) ).
tff(75,plain,
meet(r2,r2) = meet(r2,join(r2,n0)),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
meet(r2,r2) = r2,
inference(transitivity,[status(thm)],[75,67]) ).
tff(77,plain,
meet(b,meet(r2,r2)) = meet(b,r2),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(b,r2),r2) = meet(b,meet(r2,r2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
meet(meet(b,r2),r2) = meet(b,meet(r2,r2)),
inference(unit_resolution,[status(thm)],[78,41]) ).
tff(80,plain,
meet(meet(b,r2),r2) = meet(b,r2),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
meet(meet(meet(b,r2),r2),meet(a,b2)) = meet(meet(b,r2),meet(a,b2)),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(b,r2),r2),meet(a,b2)) = meet(meet(b,r2),meet(r2,meet(a,b2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
meet(meet(meet(b,r2),r2),meet(a,b2)) = meet(meet(b,r2),meet(r2,meet(a,b2))),
inference(unit_resolution,[status(thm)],[82,41]) ).
tff(84,plain,
meet(meet(b,r2),meet(r2,meet(a,b2))) = meet(meet(meet(b,r2),r2),meet(a,b2)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,a),b2) = meet(r2,meet(a,b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
meet(meet(r2,a),b2) = meet(r2,meet(a,b2)),
inference(unit_resolution,[status(thm)],[85,41]) ).
tff(87,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(r2,a) = meet(a,r2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
meet(r2,a) = meet(a,r2),
inference(unit_resolution,[status(thm)],[87,16]) ).
tff(89,plain,
meet(meet(r2,a),b2) = meet(meet(a,r2),b2),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
meet(meet(a,r2),b2) = meet(meet(r2,a),b2),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(92,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)],[91]) ).
tff(93,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(94,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(95,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,r2),r1) = join(r1,meet(a,r2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
join(meet(a,r2),r1) = join(r1,meet(a,r2)),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
join(r1,meet(a,r2)) = join(meet(a,r2),r1),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
b2 = join(meet(a,r2),r1),
inference(transitivity,[status(thm)],[31,100]) ).
tff(102,plain,
meet(meet(a,r2),b2) = meet(meet(a,r2),join(meet(a,r2),r1)),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
meet(meet(a,r2),join(meet(a,r2),r1)) = meet(meet(a,r2),b2),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(a,r2),join(meet(a,r2),r1)) = meet(a,r2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
meet(meet(a,r2),join(meet(a,r2),r1)) = meet(a,r2),
inference(unit_resolution,[status(thm)],[104,25]) ).
tff(106,plain,
meet(a,r2) = meet(meet(a,r2),join(meet(a,r2),r1)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
meet(a,r2) = meet(r2,meet(a,b2)),
inference(transitivity,[status(thm)],[106,103,90,86]) ).
tff(108,plain,
meet(meet(b,r2),meet(a,r2)) = meet(meet(b,r2),meet(r2,meet(a,b2))),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(a,r2),meet(meet(a,r2),b)) = meet(a,r2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
join(meet(a,r2),meet(meet(a,r2),b)) = meet(a,r2),
inference(unit_resolution,[status(thm)],[109,7]) ).
tff(111,plain,
meet(a,r2) = meet(r2,a),
inference(symmetry,[status(thm)],[88]) ).
tff(112,plain,
meet(meet(a,r2),b) = meet(meet(r2,a),b),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
meet(meet(r2,a),b) = meet(meet(a,r2),b),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,a),b) = meet(r2,meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
meet(meet(r2,a),b) = meet(r2,meet(a,b)),
inference(unit_resolution,[status(thm)],[114,41]) ).
tff(116,plain,
meet(r2,meet(a,b)) = meet(meet(r2,a),b),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
meet(r1,join(a,b)) = meet(meet(a,r2),b),
inference(transitivity,[status(thm)],[47,68,116,113]) ).
tff(118,plain,
join(meet(a,r2),meet(r1,join(a,b))) = join(meet(a,r2),meet(meet(a,r2),b)),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,b)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
meet(a,join(a,b)) = a,
inference(unit_resolution,[status(thm)],[119,25]) ).
tff(121,plain,
meet(r2,meet(a,join(a,b))) = meet(r2,a),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,a),join(a,b)) = meet(r2,meet(a,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
meet(meet(r2,a),join(a,b)) = meet(r2,meet(a,join(a,b))),
inference(unit_resolution,[status(thm)],[122,41]) ).
tff(124,plain,
meet(meet(a,r2),join(a,b)) = meet(meet(r2,a),join(a,b)),
inference(monotonicity,[status(thm)],[111]) ).
tff(125,plain,
meet(meet(a,r2),join(a,b)) = meet(a,r2),
inference(transitivity,[status(thm)],[124,123,121,88]) ).
tff(126,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
<=> ( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-1.ax',modular) ).
tff(130,plain,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(skolemize,[status(sab)],[130]) ).
tff(132,plain,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,r2),join(a,b)) != meet(a,r2) )
| ( meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),meet(r1,join(a,b))) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,r2),join(a,b)) != meet(a,r2) )
| ( meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),meet(r1,join(a,b))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,r2),join(a,b)) != meet(a,r2) )
| ( meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),meet(r1,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(a,r2),join(a,b)) != meet(a,r2) )
| ( meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),meet(r1,join(a,b))) ) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
( ( meet(meet(a,r2),join(a,b)) != meet(a,r2) )
| ( meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),meet(r1,join(a,b))) ) ),
inference(unit_resolution,[status(thm)],[135,132]) ).
tff(137,plain,
meet(join(a,b),join(meet(a,r2),r1)) = join(meet(a,r2),meet(r1,join(a,b))),
inference(unit_resolution,[status(thm)],[136,125]) ).
tff(138,plain,
meet(join(a,b),b2) = meet(join(a,b),join(meet(a,r2),r1)),
inference(monotonicity,[status(thm)],[101]) ).
tff(139,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),b2) = meet(b2,join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
meet(join(a,b),b2) = meet(b2,join(a,b)),
inference(unit_resolution,[status(thm)],[139,16]) ).
tff(141,plain,
meet(b2,join(a,b)) = meet(join(a,b),b2),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
meet(b2,join(a,b)) = meet(a,r2),
inference(transitivity,[status(thm)],[141,138,137,118,110]) ).
tff(143,plain,
meet(meet(b,r2),meet(b2,join(a,b))) = meet(meet(b,r2),meet(a,r2)),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
meet(meet(b,r2),meet(join(a,b),b2)) = meet(meet(b,r2),meet(b2,join(a,b))),
inference(monotonicity,[status(thm)],[140]) ).
tff(145,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(b,r2),join(a,b)),b2) = meet(meet(b,r2),meet(join(a,b),b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
meet(meet(meet(b,r2),join(a,b)),b2) = meet(meet(b,r2),meet(join(a,b),b2)),
inference(unit_resolution,[status(thm)],[145,41]) ).
tff(147,plain,
meet(meet(b,r2),join(a,b)) = meet(meet(r2,b),join(a,b)),
inference(monotonicity,[status(thm)],[59]) ).
tff(148,plain,
meet(meet(r2,b),join(a,b)) = meet(meet(b,r2),join(a,b)),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,b),join(a,b)) = meet(r2,meet(b,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
meet(meet(r2,b),join(a,b)) = meet(r2,meet(b,join(a,b))),
inference(unit_resolution,[status(thm)],[149,41]) ).
tff(151,plain,
meet(r2,meet(b,join(a,b))) = meet(meet(r2,b),join(a,b)),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(b,join(b,a)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
meet(b,join(b,a)) = b,
inference(unit_resolution,[status(thm)],[152,25]) ).
tff(154,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,a) = join(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
join(b,a) = join(a,b),
inference(unit_resolution,[status(thm)],[154,97]) ).
tff(156,plain,
join(a,b) = join(b,a),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
meet(b,join(a,b)) = meet(b,join(b,a)),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
meet(b,join(a,b)) = b,
inference(transitivity,[status(thm)],[157,153]) ).
tff(159,plain,
meet(r2,meet(b,join(a,b))) = meet(r2,b),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
meet(r2,b) = meet(r2,meet(b,join(a,b))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
meet(b,r2) = meet(meet(b,r2),join(a,b)),
inference(transitivity,[status(thm)],[59,160,151,148]) ).
tff(162,plain,
meet(meet(b,r2),b2) = meet(meet(meet(b,r2),join(a,b)),b2),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
meet(meet(b,r2),b2) = meet(r1,join(a,b)),
inference(transitivity,[status(thm)],[162,146,144,143,108,84,81,65,62,43,34,18]) ).
tff(164,plain,
join(r1,meet(meet(b,r2),b2)) = join(r1,meet(r1,join(a,b))),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,b2) != r1 )
| ( meet(b2,join(r1,meet(b,r2))) = join(r1,meet(meet(b,r2),b2)) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,b2) != r1 )
| ( meet(b2,join(r1,meet(b,r2))) = join(r1,meet(meet(b,r2),b2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,b2) != r1 )
| ( meet(b2,join(r1,meet(b,r2))) = join(r1,meet(meet(b,r2),b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,b2) != r1 )
| ( meet(b2,join(r1,meet(b,r2))) = join(r1,meet(meet(b,r2),b2)) ) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
( ( meet(r1,b2) != r1 )
| ( meet(b2,join(r1,meet(b,r2))) = join(r1,meet(meet(b,r2),b2)) ) ),
inference(unit_resolution,[status(thm)],[167,132]) ).
tff(169,plain,
meet(b2,join(r1,meet(b,r2))) = join(r1,meet(meet(b,r2),b2)),
inference(unit_resolution,[status(thm)],[168,33]) ).
tff(170,plain,
( ( join(r1,meet(b,r2)) = a2 )
<=> ( join(r1,meet(b,r2)) = a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,axiom,
join(r1,meet(b,r2)) = a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',define_a2) ).
tff(172,plain,
join(r1,meet(b,r2)) = a2,
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
a2 = join(r1,meet(b,r2)),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
meet(b2,a2) = meet(b2,join(r1,meet(b,r2))),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b2,a2) = meet(a2,b2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
meet(b2,a2) = meet(a2,b2),
inference(unit_resolution,[status(thm)],[175,16]) ).
tff(177,plain,
meet(a2,b2) = meet(b2,a2),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
meet(a2,b2) = r1,
inference(transitivity,[status(thm)],[177,174,169,164,9]) ).
tff(179,plain,
( ( meet(a2,b2) != r1 )
<=> ( meet(a2,b2) != r1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,axiom,
meet(a2,b2) != r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_SAMs_lemma) ).
tff(181,plain,
meet(a2,b2) != r1,
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
$false,
inference(unit_resolution,[status(thm)],[181,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT005-4 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 19:23:08 EDT 2025
% 0.18/0.33 % CPUTime :
% 1.91/2.08 % SZS status Unsatisfiable
% 1.91/2.08 % SZS output start Proof
% See solution above
% 1.91/2.09 % E exiting
%------------------------------------------------------------------------------