TSTP Solution File: LAT043-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT043-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 Sep 17 18:31:51 EDT 2022
% Result : Unsatisfiable 0.74s 0.74s
% Output : Proof 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 85
% Syntax : Number of formulae : 273 ( 199 unt; 7 typ; 0 def)
% Number of atoms : 353 ( 342 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 127 ( 50 ~; 46 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 284 ( 264 !; 0 ?; 284 :)
% Comments :
%------------------------------------------------------------------------------
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(d_type,type,
d: $i ).
tff(c_type,type,
c: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n0_type,type,
n0: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(5,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(complement(d),complement(c)) = meet(complement(c),complement(d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
meet(complement(d),complement(c)) = meet(complement(c),complement(d)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
<=> ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(complement(c),join(join(complement(join(c,d)),c),d)) = join(meet(complement(c),join(complement(join(c,d)),c)),meet(complement(c),d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
meet(complement(c),join(join(complement(join(c,d)),c),d)) = join(meet(complement(c),join(complement(join(c,d)),c)),meet(complement(c),d)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X: $i] :
refl(
( ( join(complement(X),X) = n1 )
<=> ( join(complement(X),X) = n1 ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X: $i] : ( join(complement(X),X) = n1 )
<=> ! [X: $i] : ( join(complement(X),X) = n1 ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] : ( join(complement(X),X) = n1 )
<=> ! [X: $i] : ( join(complement(X),X) = n1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [X: $i] : ( join(complement(X),X) = n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',invertability1) ).
tff(23,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [X: $i] : ( join(complement(X),X) = n1 )
| ( join(complement(c),c) = n1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
join(complement(c),c) = n1,
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
n1 = join(complement(c),c),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ~ ! [X: $i] : ( join(complement(X),X) = n1 )
| ( join(complement(join(c,d)),join(c,d)) = n1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
join(complement(join(c,d)),join(c,d)) = n1,
inference(unit_resolution,[status(thm)],[29,25]) ).
tff(31,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(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(quant_intro,[status(thm)],[31]) ).
tff(33,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(34,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(35,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(join(c,d)),c),d) = join(complement(join(c,d)),join(c,d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
join(join(complement(join(c,d)),c),d) = join(complement(join(c,d)),join(c,d)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
join(join(complement(join(c,d)),c),d) = join(complement(c),c),
inference(transitivity,[status(thm)],[39,30,28]) ).
tff(41,plain,
meet(complement(c),join(join(complement(join(c,d)),c),d)) = meet(complement(c),join(complement(c),c)),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
meet(complement(c),join(complement(c),c)) = meet(complement(c),join(join(complement(join(c,d)),c),d)),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(44,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)],[43]) ).
tff(45,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(46,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(47,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(complement(c),join(complement(c),c)) = complement(c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
meet(complement(c),join(complement(c),c)) = complement(c),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
complement(c) = meet(complement(c),join(complement(c),c)),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
complement(c) = join(meet(complement(c),join(complement(join(c,d)),c)),meet(complement(c),d)),
inference(transitivity,[status(thm)],[52,42,18]) ).
tff(54,plain,
meet(complement(d),complement(c)) = meet(complement(d),join(meet(complement(c),join(complement(join(c,d)),c)),meet(complement(c),d))),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
meet(complement(d),join(meet(complement(c),join(complement(join(c,d)),c)),meet(complement(c),d))) = meet(complement(d),complement(c)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(complement(d),join(meet(complement(c),join(complement(join(c,d)),c)),meet(complement(c),d))) = join(meet(complement(d),meet(complement(c),join(complement(join(c,d)),c))),meet(complement(d),meet(complement(c),d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
meet(complement(d),join(meet(complement(c),join(complement(join(c,d)),c)),meet(complement(c),d))) = join(meet(complement(d),meet(complement(c),join(complement(join(c,d)),c))),meet(complement(d),meet(complement(c),d))),
inference(unit_resolution,[status(thm)],[56,16]) ).
tff(58,plain,
join(meet(complement(d),meet(complement(c),join(complement(join(c,d)),c))),meet(complement(d),meet(complement(c),d))) = meet(complement(d),join(meet(complement(c),join(complement(join(c,d)),c)),meet(complement(c),d))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
^ [X: $i] :
refl(
( ( meet(complement(X),X) = n0 )
<=> ( meet(complement(X),X) = n0 ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [X: $i] : ( meet(complement(X),X) = n0 )
<=> ! [X: $i] : ( meet(complement(X),X) = n0 ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [X: $i] : ( meet(complement(X),X) = n0 )
<=> ! [X: $i] : ( meet(complement(X),X) = n0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
! [X: $i] : ( meet(complement(X),X) = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',invertability2) ).
tff(63,plain,
! [X: $i] : ( meet(complement(X),X) = n0 ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [X: $i] : ( meet(complement(X),X) = n0 ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [X: $i] : ( meet(complement(X),X) = n0 ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ~ ! [X: $i] : ( meet(complement(X),X) = n0 )
| ( meet(complement(c),c) = n0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
meet(complement(c),c) = n0,
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(c,join(c,d)) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
meet(c,join(c,d)) = c,
inference(unit_resolution,[status(thm)],[68,49]) ).
tff(70,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(c,d),c) = meet(c,join(c,d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
meet(join(c,d),c) = meet(c,join(c,d)),
inference(unit_resolution,[status(thm)],[70,7]) ).
tff(72,plain,
meet(join(c,d),c) = c,
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
meet(complement(c),meet(join(c,d),c)) = meet(complement(c),c),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,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(75,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)],[74]) ).
tff(76,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(77,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(78,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(complement(c),join(c,d)),c) = meet(complement(c),meet(join(c,d),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
meet(meet(complement(c),join(c,d)),c) = meet(complement(c),meet(join(c,d),c)),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
^ [X: $i] :
refl(
( ( meet(X,X) = X )
<=> ( meet(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,axiom,
! [X: $i] : ( meet(X,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
tff(87,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(c,c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
meet(c,c) = c,
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
meet(meet(complement(c),join(c,d)),meet(c,c)) = meet(meet(complement(c),join(c,d)),c),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(complement(c),join(c,d)),c),c) = meet(meet(complement(c),join(c,d)),meet(c,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
meet(meet(meet(complement(c),join(c,d)),c),c) = meet(meet(complement(c),join(c,d)),meet(c,c)),
inference(unit_resolution,[status(thm)],[93,80]) ).
tff(95,plain,
meet(complement(c),meet(join(c,d),c)) = meet(meet(complement(c),join(c,d)),c),
inference(symmetry,[status(thm)],[82]) ).
tff(96,plain,
meet(complement(c),c) = meet(complement(c),meet(join(c,d),c)),
inference(symmetry,[status(thm)],[73]) ).
tff(97,plain,
n0 = meet(complement(c),c),
inference(symmetry,[status(thm)],[67]) ).
tff(98,plain,
( ~ ! [X: $i] : ( meet(complement(X),X) = n0 )
| ( meet(complement(join(c,d)),join(c,d)) = n0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
meet(complement(join(c,d)),join(c,d)) = n0,
inference(unit_resolution,[status(thm)],[98,65]) ).
tff(100,plain,
meet(complement(join(c,d)),join(c,d)) = meet(meet(complement(c),join(c,d)),c),
inference(transitivity,[status(thm)],[99,97,96,95]) ).
tff(101,plain,
meet(meet(complement(join(c,d)),join(c,d)),c) = meet(meet(meet(complement(c),join(c,d)),c),c),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(complement(join(c,d)),join(c,d)),c) = meet(complement(join(c,d)),meet(join(c,d),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
meet(meet(complement(join(c,d)),join(c,d)),c) = meet(complement(join(c,d)),meet(join(c,d),c)),
inference(unit_resolution,[status(thm)],[102,80]) ).
tff(104,plain,
meet(complement(join(c,d)),meet(join(c,d),c)) = meet(meet(complement(join(c,d)),join(c,d)),c),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
meet(c,join(c,d)) = meet(join(c,d),c),
inference(symmetry,[status(thm)],[71]) ).
tff(106,plain,
c = meet(c,join(c,d)),
inference(symmetry,[status(thm)],[69]) ).
tff(107,plain,
c = meet(join(c,d),c),
inference(transitivity,[status(thm)],[106,105]) ).
tff(108,plain,
meet(complement(join(c,d)),c) = meet(complement(join(c,d)),meet(join(c,d),c)),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
meet(complement(join(c,d)),c) = n0,
inference(transitivity,[status(thm)],[108,104,101,94,92,82,73,67]) ).
tff(110,plain,
meet(complement(d),meet(complement(join(c,d)),c)) = meet(complement(d),n0),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
meet(complement(d),n0) = meet(complement(d),meet(complement(join(c,d)),c)),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(n0,complement(d)) = meet(complement(d),n0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
meet(n0,complement(d)) = meet(complement(d),n0),
inference(unit_resolution,[status(thm)],[112,7]) ).
tff(114,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(115,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)],[114]) ).
tff(116,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(117,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(118,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(n0,complement(d)) = join(complement(d),n0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
join(n0,complement(d)) = join(complement(d),n0),
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
join(complement(d),n0) = join(n0,complement(d)),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [X: $i] : ( meet(complement(X),X) = n0 )
| ( meet(complement(d),d) = n0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
meet(complement(d),d) = n0,
inference(unit_resolution,[status(thm)],[124,65]) ).
tff(126,plain,
n0 = meet(complement(d),d),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
join(complement(d),n0) = join(complement(d),meet(complement(d),d)),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
join(complement(d),meet(complement(d),d)) = join(complement(d),n0),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(130,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)],[129]) ).
tff(131,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(132,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(133,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(d),meet(complement(d),d)) = complement(d) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
join(complement(d),meet(complement(d),d)) = complement(d),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
complement(d) = join(complement(d),meet(complement(d),d)),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
complement(d) = join(n0,complement(d)),
inference(transitivity,[status(thm)],[138,128,123]) ).
tff(140,plain,
meet(n0,complement(d)) = meet(n0,join(n0,complement(d))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
meet(n0,join(n0,complement(d))) = meet(n0,complement(d)),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(n0,join(n0,complement(d))) = n0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
meet(n0,join(n0,complement(d))) = n0,
inference(unit_resolution,[status(thm)],[142,49]) ).
tff(144,plain,
n0 = meet(n0,join(n0,complement(d))),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,complement(c)) = meet(complement(c),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
meet(c,complement(c)) = meet(complement(c),c),
inference(unit_resolution,[status(thm)],[145,7]) ).
tff(147,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(complement(c),join(complement(c),meet(complement(c),complement(d)))) = complement(c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
meet(complement(c),join(complement(c),meet(complement(c),complement(d)))) = complement(c),
inference(unit_resolution,[status(thm)],[147,49]) ).
tff(149,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(c),meet(complement(c),complement(d))) = complement(c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
join(complement(c),meet(complement(c),complement(d))) = complement(c),
inference(unit_resolution,[status(thm)],[149,135]) ).
tff(151,plain,
complement(c) = join(complement(c),meet(complement(c),complement(d))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
meet(complement(c),complement(c)) = meet(complement(c),join(complement(c),meet(complement(c),complement(d)))),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
meet(complement(c),complement(c)) = complement(c),
inference(transitivity,[status(thm)],[152,148]) ).
tff(154,plain,
meet(c,meet(complement(c),complement(c))) = meet(c,complement(c)),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(c,complement(c)),complement(c)) = meet(c,meet(complement(c),complement(c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
meet(meet(c,complement(c)),complement(c)) = meet(c,meet(complement(c),complement(c))),
inference(unit_resolution,[status(thm)],[155,80]) ).
tff(157,plain,
meet(complement(c),c) = meet(c,complement(c)),
inference(symmetry,[status(thm)],[146]) ).
tff(158,plain,
meet(complement(d),d) = meet(c,complement(c)),
inference(transitivity,[status(thm)],[125,97,157]) ).
tff(159,plain,
meet(meet(complement(d),d),complement(c)) = meet(meet(c,complement(c)),complement(c)),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(complement(d),d),complement(c)) = meet(complement(d),meet(d,complement(c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
meet(meet(complement(d),d),complement(c)) = meet(complement(d),meet(d,complement(c))),
inference(unit_resolution,[status(thm)],[160,80]) ).
tff(162,plain,
meet(complement(d),meet(d,complement(c))) = meet(meet(complement(d),d),complement(c)),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(d,complement(c)) = meet(complement(c),d) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
meet(d,complement(c)) = meet(complement(c),d),
inference(unit_resolution,[status(thm)],[163,7]) ).
tff(165,plain,
meet(complement(c),d) = meet(d,complement(c)),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
meet(complement(d),meet(complement(c),d)) = meet(complement(d),meet(d,complement(c))),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
meet(complement(d),meet(complement(c),d)) = meet(complement(d),meet(complement(join(c,d)),c)),
inference(transitivity,[status(thm)],[166,162,159,156,154,146,67,144,141,113,111]) ).
tff(168,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(complement(c),complement(join(c,d))) = meet(complement(join(c,d)),complement(c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(169,plain,
meet(complement(c),complement(join(c,d))) = meet(complement(join(c,d)),complement(c)),
inference(unit_resolution,[status(thm)],[168,7]) ).
tff(170,plain,
n0 = meet(complement(join(c,d)),join(c,d)),
inference(symmetry,[status(thm)],[99]) ).
tff(171,plain,
join(complement(join(c,d)),n0) = join(complement(join(c,d)),meet(complement(join(c,d)),join(c,d))),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
join(complement(join(c,d)),meet(complement(join(c,d)),join(c,d))) = join(complement(join(c,d)),n0),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(join(c,d)),meet(complement(join(c,d)),join(c,d))) = complement(join(c,d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
join(complement(join(c,d)),meet(complement(join(c,d)),join(c,d))) = complement(join(c,d)),
inference(unit_resolution,[status(thm)],[173,135]) ).
tff(175,plain,
complement(join(c,d)) = join(complement(join(c,d)),meet(complement(join(c,d)),join(c,d))),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
complement(join(c,d)) = join(complement(join(c,d)),n0),
inference(transitivity,[status(thm)],[175,172]) ).
tff(177,plain,
meet(complement(c),complement(join(c,d))) = meet(complement(c),join(complement(join(c,d)),n0)),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
meet(complement(c),join(complement(join(c,d)),n0)) = meet(complement(c),complement(join(c,d))),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(complement(c),join(complement(join(c,d)),n0)) = join(meet(complement(c),complement(join(c,d))),meet(complement(c),n0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(180,plain,
meet(complement(c),join(complement(join(c,d)),n0)) = join(meet(complement(c),complement(join(c,d))),meet(complement(c),n0)),
inference(unit_resolution,[status(thm)],[179,16]) ).
tff(181,plain,
join(meet(complement(c),complement(join(c,d))),meet(complement(c),n0)) = meet(complement(c),join(complement(join(c,d)),n0)),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
meet(complement(c),n0) = meet(complement(c),meet(complement(c),c)),
inference(monotonicity,[status(thm)],[97]) ).
tff(183,plain,
meet(complement(c),meet(complement(c),c)) = meet(complement(c),n0),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(complement(c),complement(c)),c) = meet(complement(c),meet(complement(c),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
meet(meet(complement(c),complement(c)),c) = meet(complement(c),meet(complement(c),c)),
inference(unit_resolution,[status(thm)],[184,80]) ).
tff(186,plain,
meet(meet(complement(c),complement(c)),c) = meet(complement(c),c),
inference(monotonicity,[status(thm)],[153]) ).
tff(187,plain,
meet(complement(c),c) = meet(meet(complement(c),complement(c)),c),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
meet(complement(c),c) = meet(complement(c),n0),
inference(transitivity,[status(thm)],[187,185,183]) ).
tff(189,plain,
join(meet(complement(c),complement(join(c,d))),meet(complement(c),c)) = join(meet(complement(c),complement(join(c,d))),meet(complement(c),n0)),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(complement(c),join(complement(join(c,d)),c)) = join(meet(complement(c),complement(join(c,d))),meet(complement(c),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
meet(complement(c),join(complement(join(c,d)),c)) = join(meet(complement(c),complement(join(c,d))),meet(complement(c),c)),
inference(unit_resolution,[status(thm)],[190,16]) ).
tff(192,plain,
meet(complement(c),join(complement(join(c,d)),c)) = meet(complement(join(c,d)),complement(c)),
inference(transitivity,[status(thm)],[191,189,181,178,169]) ).
tff(193,plain,
meet(complement(d),meet(complement(c),join(complement(join(c,d)),c))) = meet(complement(d),meet(complement(join(c,d)),complement(c))),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
join(meet(complement(d),meet(complement(c),join(complement(join(c,d)),c))),meet(complement(d),meet(complement(c),d))) = join(meet(complement(d),meet(complement(join(c,d)),complement(c))),meet(complement(d),meet(complement(join(c,d)),c))),
inference(monotonicity,[status(thm)],[193,167]) ).
tff(195,plain,
join(meet(complement(d),meet(complement(join(c,d)),complement(c))),meet(complement(d),meet(complement(join(c,d)),c))) = join(meet(complement(d),meet(complement(c),join(complement(join(c,d)),c))),meet(complement(d),meet(complement(c),d))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(complement(d),join(meet(complement(join(c,d)),complement(c)),meet(complement(join(c,d)),c))) = join(meet(complement(d),meet(complement(join(c,d)),complement(c))),meet(complement(d),meet(complement(join(c,d)),c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(197,plain,
meet(complement(d),join(meet(complement(join(c,d)),complement(c)),meet(complement(join(c,d)),c))) = join(meet(complement(d),meet(complement(join(c,d)),complement(c))),meet(complement(d),meet(complement(join(c,d)),c))),
inference(unit_resolution,[status(thm)],[196,16]) ).
tff(198,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(complement(join(c,d)),join(complement(join(c,d)),join(c,d))) = complement(join(c,d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(199,plain,
meet(complement(join(c,d)),join(complement(join(c,d)),join(c,d))) = complement(join(c,d)),
inference(unit_resolution,[status(thm)],[198,49]) ).
tff(200,plain,
n1 = join(complement(join(c,d)),join(c,d)),
inference(symmetry,[status(thm)],[30]) ).
tff(201,plain,
join(complement(c),c) = join(complement(join(c,d)),join(c,d)),
inference(transitivity,[status(thm)],[27,200]) ).
tff(202,plain,
meet(complement(join(c,d)),join(complement(c),c)) = meet(complement(join(c,d)),join(complement(join(c,d)),join(c,d))),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(complement(join(c,d)),join(complement(c),c)) = join(meet(complement(join(c,d)),complement(c)),meet(complement(join(c,d)),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
meet(complement(join(c,d)),join(complement(c),c)) = join(meet(complement(join(c,d)),complement(c)),meet(complement(join(c,d)),c)),
inference(unit_resolution,[status(thm)],[203,16]) ).
tff(205,plain,
join(meet(complement(join(c,d)),complement(c)),meet(complement(join(c,d)),c)) = meet(complement(join(c,d)),join(complement(c),c)),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
join(meet(complement(join(c,d)),complement(c)),meet(complement(join(c,d)),c)) = complement(join(c,d)),
inference(transitivity,[status(thm)],[205,202,199]) ).
tff(207,plain,
meet(complement(d),join(meet(complement(join(c,d)),complement(c)),meet(complement(join(c,d)),c))) = meet(complement(d),complement(join(c,d))),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
meet(complement(d),complement(join(c,d))) = meet(complement(d),join(meet(complement(join(c,d)),complement(c)),meet(complement(join(c,d)),c))),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(n0,complement(join(c,d))) = join(complement(join(c,d)),n0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(210,plain,
join(n0,complement(join(c,d))) = join(complement(join(c,d)),n0),
inference(unit_resolution,[status(thm)],[209,120]) ).
tff(211,plain,
join(complement(join(c,d)),n0) = join(n0,complement(join(c,d))),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
complement(join(c,d)) = join(n0,complement(join(c,d))),
inference(transitivity,[status(thm)],[175,172,211]) ).
tff(213,plain,
meet(complement(d),complement(join(c,d))) = meet(complement(d),join(n0,complement(join(c,d)))),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
meet(complement(d),join(n0,complement(join(c,d)))) = meet(complement(d),complement(join(c,d))),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(complement(d),join(n0,complement(join(c,d)))) = join(meet(complement(d),n0),meet(complement(d),complement(join(c,d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(216,plain,
meet(complement(d),join(n0,complement(join(c,d)))) = join(meet(complement(d),n0),meet(complement(d),complement(join(c,d)))),
inference(unit_resolution,[status(thm)],[215,16]) ).
tff(217,plain,
join(meet(complement(d),n0),meet(complement(d),complement(join(c,d)))) = meet(complement(d),join(n0,complement(join(c,d)))),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(complement(d),complement(join(c,d))) = meet(complement(join(c,d)),complement(d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(219,plain,
meet(complement(d),complement(join(c,d))) = meet(complement(join(c,d)),complement(d)),
inference(unit_resolution,[status(thm)],[218,7]) ).
tff(220,plain,
meet(complement(d),n0) = meet(n0,complement(d)),
inference(symmetry,[status(thm)],[113]) ).
tff(221,plain,
meet(complement(d),n0) = n0,
inference(transitivity,[status(thm)],[220,140,143]) ).
tff(222,plain,
join(meet(complement(d),n0),meet(complement(d),complement(join(c,d)))) = join(n0,meet(complement(join(c,d)),complement(d))),
inference(monotonicity,[status(thm)],[221,219]) ).
tff(223,plain,
join(n0,meet(complement(join(c,d)),complement(d))) = join(meet(complement(d),n0),meet(complement(d),complement(join(c,d)))),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
meet(complement(join(c,d)),complement(d)) = meet(complement(d),complement(join(c,d))),
inference(symmetry,[status(thm)],[219]) ).
tff(225,plain,
join(n0,meet(complement(join(c,d)),complement(d))) = join(n0,meet(complement(d),complement(join(c,d)))),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
join(n0,meet(complement(d),complement(join(c,d)))) = join(n0,meet(complement(join(c,d)),complement(d))),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
join(n0,meet(complement(d),complement(join(c,d)))) = join(meet(complement(d),d),meet(complement(d),complement(join(c,d)))),
inference(monotonicity,[status(thm)],[126]) ).
tff(228,plain,
join(meet(complement(d),d),meet(complement(d),complement(join(c,d)))) = join(n0,meet(complement(d),complement(join(c,d)))),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(complement(d),join(d,complement(join(c,d)))) = join(meet(complement(d),d),meet(complement(d),complement(join(c,d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(230,plain,
meet(complement(d),join(d,complement(join(c,d)))) = join(meet(complement(d),d),meet(complement(d),complement(join(c,d)))),
inference(unit_resolution,[status(thm)],[229,16]) ).
tff(231,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(d,complement(join(c,d))) = join(complement(join(c,d)),d) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(232,plain,
join(d,complement(join(c,d))) = join(complement(join(c,d)),d),
inference(unit_resolution,[status(thm)],[231,120]) ).
tff(233,plain,
meet(complement(d),join(d,complement(join(c,d)))) = meet(complement(d),join(complement(join(c,d)),d)),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
meet(complement(d),join(complement(join(c,d)),d)) = meet(complement(d),join(d,complement(join(c,d)))),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(complement(d),join(complement(join(c,d)),d)) = join(meet(complement(d),complement(join(c,d))),meet(complement(d),d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(236,plain,
meet(complement(d),join(complement(join(c,d)),d)) = join(meet(complement(d),complement(join(c,d))),meet(complement(d),d)),
inference(unit_resolution,[status(thm)],[235,16]) ).
tff(237,plain,
join(meet(complement(d),complement(join(c,d))),meet(complement(d),d)) = meet(complement(d),join(complement(join(c,d)),d)),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(complement(join(c,d)),join(d,c)) = join(meet(complement(join(c,d)),d),meet(complement(join(c,d)),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(239,plain,
meet(complement(join(c,d)),join(d,c)) = join(meet(complement(join(c,d)),d),meet(complement(join(c,d)),c)),
inference(unit_resolution,[status(thm)],[238,16]) ).
tff(240,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(d,c) = join(c,d) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(241,plain,
join(d,c) = join(c,d),
inference(unit_resolution,[status(thm)],[240,120]) ).
tff(242,plain,
meet(complement(join(c,d)),join(d,c)) = meet(complement(join(c,d)),join(c,d)),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
meet(complement(join(c,d)),join(c,d)) = meet(complement(join(c,d)),join(d,c)),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
meet(complement(d),d) = join(meet(complement(join(c,d)),d),meet(complement(join(c,d)),c)),
inference(transitivity,[status(thm)],[125,170,243,239]) ).
tff(245,plain,
join(meet(complement(d),complement(join(c,d))),meet(complement(d),d)) = join(meet(complement(join(c,d)),complement(d)),join(meet(complement(join(c,d)),d),meet(complement(join(c,d)),c))),
inference(monotonicity,[status(thm)],[219,244]) ).
tff(246,plain,
join(meet(complement(join(c,d)),complement(d)),join(meet(complement(join(c,d)),d),meet(complement(join(c,d)),c))) = join(meet(complement(d),complement(join(c,d))),meet(complement(d),d)),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(complement(join(c,d)),complement(d)),meet(complement(join(c,d)),d)),meet(complement(join(c,d)),c)) = join(meet(complement(join(c,d)),complement(d)),join(meet(complement(join(c,d)),d),meet(complement(join(c,d)),c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(248,plain,
join(join(meet(complement(join(c,d)),complement(d)),meet(complement(join(c,d)),d)),meet(complement(join(c,d)),c)) = join(meet(complement(join(c,d)),complement(d)),join(meet(complement(join(c,d)),d),meet(complement(join(c,d)),c))),
inference(unit_resolution,[status(thm)],[247,37]) ).
tff(249,plain,
( ~ ! [X: $i] : ( join(complement(X),X) = n1 )
| ( join(complement(d),d) = n1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(250,plain,
join(complement(d),d) = n1,
inference(unit_resolution,[status(thm)],[249,25]) ).
tff(251,plain,
join(complement(d),d) = join(complement(join(c,d)),join(c,d)),
inference(transitivity,[status(thm)],[250,200]) ).
tff(252,plain,
meet(complement(join(c,d)),join(complement(d),d)) = meet(complement(join(c,d)),join(complement(join(c,d)),join(c,d))),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(complement(join(c,d)),join(complement(d),d)) = join(meet(complement(join(c,d)),complement(d)),meet(complement(join(c,d)),d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(254,plain,
meet(complement(join(c,d)),join(complement(d),d)) = join(meet(complement(join(c,d)),complement(d)),meet(complement(join(c,d)),d)),
inference(unit_resolution,[status(thm)],[253,16]) ).
tff(255,plain,
join(meet(complement(join(c,d)),complement(d)),meet(complement(join(c,d)),d)) = meet(complement(join(c,d)),join(complement(d),d)),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
join(meet(complement(join(c,d)),complement(d)),meet(complement(join(c,d)),d)) = complement(join(c,d)),
inference(transitivity,[status(thm)],[255,252,199]) ).
tff(257,plain,
join(join(meet(complement(join(c,d)),complement(d)),meet(complement(join(c,d)),d)),meet(complement(join(c,d)),c)) = join(complement(join(c,d)),meet(complement(join(c,d)),c)),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
join(complement(join(c,d)),meet(complement(join(c,d)),c)) = join(join(meet(complement(join(c,d)),complement(d)),meet(complement(join(c,d)),d)),meet(complement(join(c,d)),c)),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(join(c,d)),meet(complement(join(c,d)),c)) = complement(join(c,d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(260,plain,
join(complement(join(c,d)),meet(complement(join(c,d)),c)) = complement(join(c,d)),
inference(unit_resolution,[status(thm)],[259,135]) ).
tff(261,plain,
complement(join(c,d)) = join(complement(join(c,d)),meet(complement(join(c,d)),c)),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
complement(join(c,d)) = meet(complement(c),complement(d)),
inference(transitivity,[status(thm)],[261,258,248,246,237,234,230,228,226,223,217,214,208,197,195,58,55,9]) ).
tff(263,plain,
( ( complement(join(c,d)) != meet(complement(c),complement(d)) )
<=> ( complement(join(c,d)) != meet(complement(c),complement(d)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(264,axiom,
complement(join(c,d)) != meet(complement(c),complement(d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compatability_law) ).
tff(265,plain,
complement(join(c,d)) != meet(complement(c),complement(d)),
inference(modus_ponens,[status(thm)],[264,263]) ).
tff(266,plain,
$false,
inference(unit_resolution,[status(thm)],[265,262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT043-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 11:02:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.74/0.74 % SZS status Unsatisfiable
% 0.74/0.74 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------