TSTP Solution File: LAT018-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT018-1 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 18:31:45 EDT 2022
% Result : Unsatisfiable 5.96s 4.04s
% Output : Proof 5.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 71
% Syntax : Number of formulae : 225 ( 162 unt; 6 typ; 0 def)
% Number of atoms : 288 ( 281 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 109 ( 46 ~; 42 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of FOOLs : 6 ( 6 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 210 ( 198 !; 0 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
tff(n1_type,type,
n1: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(a_type,type,
a: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( join(complement(X),X) = n1 )
<=> ( join(complement(X),X) = n1 ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( join(complement(X),X) = n1 )
<=> ! [X: $i] : ( join(complement(X),X) = n1 ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( join(complement(X),X) = n1 )
<=> ! [X: $i] : ( join(complement(X),X) = n1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( join(complement(X),X) = n1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT003-0.ax',top) ).
tff(5,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( join(complement(X),X) = n1 )
| ( join(complement(a),a) = n1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
join(complement(a),a) = n1,
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/sandbox2/benchmark/Axioms/LAT003-0.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),complement(b))) = complement(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
join(complement(a),meet(complement(a),complement(b))) = complement(a),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = complement(join(complement(X),complement(Y))) )
<=> ( meet(X,Y) = complement(join(complement(X),complement(Y))) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT003-0.ax',meet_complement) ).
tff(23,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) )
| ( meet(complement(a),complement(b)) = complement(join(complement(complement(a)),complement(complement(b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
meet(complement(a),complement(b)) = complement(join(complement(complement(a)),complement(complement(b)))),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
complement(join(complement(complement(a)),complement(complement(b)))) = meet(complement(a),complement(b)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
join(complement(a),complement(join(complement(complement(a)),complement(complement(b))))) = join(complement(a),meet(complement(a),complement(b))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
join(complement(a),complement(join(complement(complement(a)),complement(complement(b))))) = complement(a),
inference(transitivity,[status(thm)],[29,18]) ).
tff(31,plain,
join(join(complement(a),complement(join(complement(complement(a)),complement(complement(b))))),a) = join(complement(a),a),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,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(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(quant_intro,[status(thm)],[32]) ).
tff(34,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(35,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT003-0.ax',associativity_of_join) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(a),complement(join(complement(complement(a)),complement(complement(b))))),a) = join(complement(a),join(complement(join(complement(complement(a)),complement(complement(b)))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
join(join(complement(a),complement(join(complement(complement(a)),complement(complement(b))))),a) = join(complement(a),join(complement(join(complement(complement(a)),complement(complement(b)))),a)),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
join(complement(a),join(complement(join(complement(complement(a)),complement(complement(b)))),a)) = join(join(complement(a),complement(join(complement(complement(a)),complement(complement(b))))),a),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(a),meet(complement(a),b)) = complement(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
join(complement(a),meet(complement(a),b)) = complement(a),
inference(unit_resolution,[status(thm)],[42,16]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) )
| ( meet(complement(a),b) = complement(join(complement(complement(a)),complement(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
meet(complement(a),b) = complement(join(complement(complement(a)),complement(b))),
inference(unit_resolution,[status(thm)],[44,25]) ).
tff(46,plain,
complement(join(complement(complement(a)),complement(b))) = meet(complement(a),b),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
join(complement(a),complement(join(complement(complement(a)),complement(b)))) = join(complement(a),meet(complement(a),b)),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
join(complement(a),complement(join(complement(complement(a)),complement(b)))) = complement(a),
inference(transitivity,[status(thm)],[47,43]) ).
tff(49,plain,
join(join(complement(a),complement(join(complement(complement(a)),complement(b)))),complement(join(complement(complement(a)),complement(b)))) = join(complement(a),meet(complement(a),b)),
inference(monotonicity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(a),complement(join(complement(complement(a)),complement(b)))),complement(join(complement(complement(a)),complement(b)))) = join(complement(a),join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
join(join(complement(a),complement(join(complement(complement(a)),complement(b)))),complement(join(complement(complement(a)),complement(b)))) = join(complement(a),join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b))))),
inference(unit_resolution,[status(thm)],[50,38]) ).
tff(52,plain,
join(complement(a),join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b))))) = join(join(complement(a),complement(join(complement(complement(a)),complement(b)))),complement(join(complement(complement(a)),complement(b)))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
join(complement(a),join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b))))) = complement(a),
inference(transitivity,[status(thm)],[52,49,43]) ).
tff(54,plain,
join(join(complement(a),join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b))))),join(complement(join(complement(complement(a)),complement(complement(b)))),a)) = join(complement(a),join(complement(join(complement(complement(a)),complement(complement(b)))),a)),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(a),join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b))))),join(complement(join(complement(complement(a)),complement(complement(b)))),a)) = join(complement(a),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
join(join(complement(a),join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b))))),join(complement(join(complement(complement(a)),complement(complement(b)))),a)) = join(complement(a),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a))),
inference(unit_resolution,[status(thm)],[55,38]) ).
tff(57,plain,
join(complement(a),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a))) = join(join(complement(a),join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b))))),join(complement(join(complement(complement(a)),complement(complement(b)))),a)),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(a),meet(complement(a),join(complement(a),complement(join(complement(a),b))))) = complement(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
join(complement(a),meet(complement(a),join(complement(a),complement(join(complement(a),b))))) = complement(a),
inference(unit_resolution,[status(thm)],[58,16]) ).
tff(60,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) )
| ( meet(complement(a),join(complement(a),complement(join(complement(a),b)))) = complement(join(complement(complement(a)),complement(join(complement(a),complement(join(complement(a),b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
meet(complement(a),join(complement(a),complement(join(complement(a),b)))) = complement(join(complement(complement(a)),complement(join(complement(a),complement(join(complement(a),b)))))),
inference(unit_resolution,[status(thm)],[60,25]) ).
tff(62,plain,
complement(join(complement(complement(a)),complement(join(complement(a),complement(join(complement(a),b)))))) = meet(complement(a),join(complement(a),complement(join(complement(a),b)))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(a,meet(a,join(complement(a),b))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
join(a,meet(a,join(complement(a),b))) = a,
inference(unit_resolution,[status(thm)],[63,16]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = complement(join(complement(X),complement(Y))) )
| ( meet(a,join(complement(a),b)) = complement(join(complement(a),complement(join(complement(a),b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
meet(a,join(complement(a),b)) = complement(join(complement(a),complement(join(complement(a),b)))),
inference(unit_resolution,[status(thm)],[65,25]) ).
tff(67,plain,
complement(join(complement(a),complement(join(complement(a),b)))) = meet(a,join(complement(a),b)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
( ! [X: $i] : ( complement(complement(X)) = X )
<=> ! [X: $i] : ( complement(complement(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ! [X: $i] : ( complement(complement(X)) = X )
<=> ! [X: $i] : ( complement(complement(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,axiom,
! [X: $i] : ( complement(complement(X)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT003-0.ax',complement_involution) ).
tff(71,plain,
! [X: $i] : ( complement(complement(X)) = X ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [X: $i] : ( complement(complement(X)) = X ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [X: $i] : ( complement(complement(X)) = X ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( ~ ! [X: $i] : ( complement(complement(X)) = X )
| ( complement(complement(a)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
complement(complement(a)) = a,
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
join(complement(complement(a)),complement(join(complement(a),complement(join(complement(a),b))))) = join(a,meet(a,join(complement(a),b))),
inference(monotonicity,[status(thm)],[75,67]) ).
tff(77,plain,
join(complement(complement(a)),complement(join(complement(a),complement(join(complement(a),b))))) = a,
inference(transitivity,[status(thm)],[76,64]) ).
tff(78,plain,
complement(join(complement(complement(a)),complement(join(complement(a),complement(join(complement(a),b)))))) = complement(a),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
complement(a) = complement(join(complement(complement(a)),complement(join(complement(a),complement(join(complement(a),b)))))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
complement(a) = meet(complement(a),join(complement(a),complement(join(complement(a),b)))),
inference(transitivity,[status(thm)],[79,62]) ).
tff(81,plain,
join(complement(a),complement(a)) = join(complement(a),meet(complement(a),join(complement(a),complement(join(complement(a),b))))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
join(complement(a),complement(a)) = complement(a),
inference(transitivity,[status(thm)],[81,59]) ).
tff(83,plain,
join(join(complement(a),complement(a)),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a))) = join(complement(a),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a))),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(a),complement(a)),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a))) = join(complement(a),join(complement(a),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
join(join(complement(a),complement(a)),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a))) = join(complement(a),join(complement(a),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a)))),
inference(unit_resolution,[status(thm)],[84,38]) ).
tff(86,plain,
join(complement(a),join(complement(a),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a)))) = join(join(complement(a),complement(a)),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
join(complement(a),join(complement(join(complement(complement(a)),complement(complement(b)))),a)) = join(join(complement(a),join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b))))),join(complement(join(complement(complement(a)),complement(complement(b)))),a)),
inference(symmetry,[status(thm)],[54]) ).
tff(88,plain,
join(complement(a),a) = join(join(complement(a),complement(join(complement(complement(a)),complement(complement(b))))),a),
inference(symmetry,[status(thm)],[31]) ).
tff(89,plain,
n1 = join(complement(a),a),
inference(symmetry,[status(thm)],[9]) ).
tff(90,plain,
( ~ ! [X: $i] : ( join(complement(X),X) = n1 )
| ( join(complement(join(b,complement(a))),join(b,complement(a))) = n1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
join(complement(join(b,complement(a))),join(b,complement(a))) = n1,
inference(unit_resolution,[status(thm)],[90,7]) ).
tff(92,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(b,complement(a)),meet(join(b,complement(a)),a)) = join(b,complement(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
join(join(b,complement(a)),meet(join(b,complement(a)),a)) = join(b,complement(a)),
inference(unit_resolution,[status(thm)],[92,16]) ).
tff(94,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(95,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)],[94]) ).
tff(96,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(97,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT003-0.ax',commutativity_of_join) ).
tff(98,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(complement(a),b) = join(b,complement(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
join(complement(a),b) = join(b,complement(a)),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
join(b,complement(a)) = join(complement(a),b),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
meet(join(b,complement(a)),a) = meet(join(complement(a),b),a),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
meet(join(complement(a),b),a) = meet(join(b,complement(a)),a),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(107,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)],[106]) ).
tff(108,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(109,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT003-0.ax',commutativity_of_meet) ).
tff(110,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(complement(a),b),a) = meet(a,join(complement(a),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
meet(join(complement(a),b),a) = meet(a,join(complement(a),b)),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
meet(a,join(complement(a),b)) = meet(join(complement(a),b),a),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
complement(join(complement(a),complement(join(complement(a),b)))) = meet(join(b,complement(a)),a),
inference(transitivity,[status(thm)],[67,115,105]) ).
tff(117,plain,
join(join(b,complement(a)),complement(join(complement(a),complement(join(complement(a),b))))) = join(join(b,complement(a)),meet(join(b,complement(a)),a)),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(b,complement(a)),complement(join(complement(a),complement(join(complement(a),b))))) = join(complement(join(complement(a),complement(join(complement(a),b)))),join(b,complement(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
join(join(b,complement(a)),complement(join(complement(a),complement(join(complement(a),b))))) = join(complement(join(complement(a),complement(join(complement(a),b)))),join(b,complement(a))),
inference(unit_resolution,[status(thm)],[118,100]) ).
tff(120,plain,
join(complement(join(complement(a),complement(join(complement(a),b)))),join(b,complement(a))) = join(join(b,complement(a)),complement(join(complement(a),complement(join(complement(a),b))))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
join(complement(join(complement(a),complement(join(complement(a),b)))),join(b,complement(a))) = join(b,complement(a)),
inference(transitivity,[status(thm)],[120,117,93]) ).
tff(122,plain,
complement(join(b,complement(a))) = complement(join(complement(a),b)),
inference(monotonicity,[status(thm)],[103]) ).
tff(123,plain,
complement(join(complement(a),b)) = complement(join(b,complement(a))),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
join(complement(join(complement(a),b)),join(complement(join(complement(a),complement(join(complement(a),b)))),join(b,complement(a)))) = join(complement(join(b,complement(a))),join(b,complement(a))),
inference(monotonicity,[status(thm)],[123,121]) ).
tff(125,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b))))),join(b,complement(a))) = join(complement(join(complement(a),b)),join(complement(join(complement(a),complement(join(complement(a),b)))),join(b,complement(a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
join(join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b))))),join(b,complement(a))) = join(complement(join(complement(a),b)),join(complement(join(complement(a),complement(join(complement(a),b)))),join(b,complement(a)))),
inference(unit_resolution,[status(thm)],[125,38]) ).
tff(127,plain,
join(join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b))))),join(b,complement(a))) = join(complement(a),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a))),
inference(transitivity,[status(thm)],[126,124,91,89,88,40,87,56]) ).
tff(128,plain,
join(complement(a),join(join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b))))),join(b,complement(a)))) = join(complement(a),join(complement(a),join(join(complement(join(complement(complement(a)),complement(b))),complement(join(complement(complement(a)),complement(b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),a)))),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(a),join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b)))))),join(b,complement(a))) = join(complement(a),join(join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b))))),join(b,complement(a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
join(join(complement(a),join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b)))))),join(b,complement(a))) = join(complement(a),join(join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b))))),join(b,complement(a)))),
inference(unit_resolution,[status(thm)],[129,38]) ).
tff(131,plain,
join(b,join(complement(a),complement(join(complement(complement(a)),complement(complement(b)))))) = join(b,complement(a)),
inference(monotonicity,[status(thm)],[30]) ).
tff(132,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(b,complement(a)),complement(join(complement(complement(a)),complement(complement(b))))) = join(b,join(complement(a),complement(join(complement(complement(a)),complement(complement(b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
join(join(b,complement(a)),complement(join(complement(complement(a)),complement(complement(b))))) = join(b,join(complement(a),complement(join(complement(complement(a)),complement(complement(b)))))),
inference(unit_resolution,[status(thm)],[132,38]) ).
tff(134,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(b,complement(a)),complement(join(complement(complement(a)),complement(complement(b))))) = join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
join(join(b,complement(a)),complement(join(complement(complement(a)),complement(complement(b))))) = join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(a))),
inference(unit_resolution,[status(thm)],[134,100]) ).
tff(136,plain,
join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(a))) = join(join(b,complement(a)),complement(join(complement(complement(a)),complement(complement(b))))),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(complement(a),complement(join(complement(complement(a)),complement(complement(b))))) = join(complement(join(complement(complement(a)),complement(complement(b)))),complement(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
join(complement(a),complement(join(complement(complement(a)),complement(complement(b))))) = join(complement(join(complement(complement(a)),complement(complement(b)))),complement(a)),
inference(unit_resolution,[status(thm)],[137,100]) ).
tff(139,plain,
join(complement(join(complement(complement(a)),complement(complement(b)))),complement(a)) = join(complement(a),complement(join(complement(complement(a)),complement(complement(b))))),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
join(complement(join(complement(complement(a)),complement(complement(b)))),complement(a)) = complement(a),
inference(transitivity,[status(thm)],[139,29,18]) ).
tff(141,plain,
join(b,join(complement(join(complement(complement(a)),complement(complement(b)))),complement(a))) = join(b,complement(a)),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(b,complement(join(complement(complement(a)),complement(complement(b))))),complement(a)) = join(b,join(complement(join(complement(complement(a)),complement(complement(b)))),complement(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
join(join(b,complement(join(complement(complement(a)),complement(complement(b))))),complement(a)) = join(b,join(complement(join(complement(complement(a)),complement(complement(b)))),complement(a))),
inference(unit_resolution,[status(thm)],[142,38]) ).
tff(144,plain,
join(join(b,complement(join(complement(complement(a)),complement(complement(b))))),complement(a)) = join(b,complement(a)),
inference(transitivity,[status(thm)],[143,141]) ).
tff(145,plain,
join(complement(join(complement(complement(a)),complement(complement(b)))),join(join(b,complement(join(complement(complement(a)),complement(complement(b))))),complement(a))) = join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(a))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(join(complement(complement(a)),complement(complement(b)))))),complement(a)) = join(complement(join(complement(complement(a)),complement(complement(b)))),join(join(b,complement(join(complement(complement(a)),complement(complement(b))))),complement(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
join(join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(join(complement(complement(a)),complement(complement(b)))))),complement(a)) = join(complement(join(complement(complement(a)),complement(complement(b)))),join(join(b,complement(join(complement(complement(a)),complement(complement(b))))),complement(a))),
inference(unit_resolution,[status(thm)],[146,38]) ).
tff(148,plain,
join(join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(join(complement(complement(a)),complement(complement(b)))))),complement(a)) = join(b,complement(a)),
inference(transitivity,[status(thm)],[147,145,136,133,131]) ).
tff(149,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(a),complement(join(complement(a),b))),complement(join(complement(a),complement(join(complement(a),b))))) = join(complement(a),join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
join(join(complement(a),complement(join(complement(a),b))),complement(join(complement(a),complement(join(complement(a),b))))) = join(complement(a),join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b)))))),
inference(unit_resolution,[status(thm)],[149,38]) ).
tff(151,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(complement(join(complement(a),complement(join(complement(a),b)))),join(complement(a),complement(join(complement(a),b)))) = join(join(complement(a),complement(join(complement(a),b))),complement(join(complement(a),complement(join(complement(a),b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
join(complement(join(complement(a),complement(join(complement(a),b)))),join(complement(a),complement(join(complement(a),b)))) = join(join(complement(a),complement(join(complement(a),b))),complement(join(complement(a),complement(join(complement(a),b))))),
inference(unit_resolution,[status(thm)],[151,100]) ).
tff(153,plain,
( ~ ! [X: $i] : ( join(complement(X),X) = n1 )
| ( join(complement(join(complement(a),complement(join(complement(a),b)))),join(complement(a),complement(join(complement(a),b)))) = n1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
join(complement(join(complement(a),complement(join(complement(a),b)))),join(complement(a),complement(join(complement(a),b)))) = n1,
inference(unit_resolution,[status(thm)],[153,7]) ).
tff(155,plain,
n1 = join(complement(join(complement(a),complement(join(complement(a),b)))),join(complement(a),complement(join(complement(a),b)))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
n1 = join(complement(a),join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b)))))),
inference(transitivity,[status(thm)],[155,152,150]) ).
tff(157,plain,
join(n1,join(join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(join(complement(complement(a)),complement(complement(b)))))),complement(a))) = join(join(complement(a),join(complement(join(complement(a),b)),complement(join(complement(a),complement(join(complement(a),b)))))),join(b,complement(a))),
inference(monotonicity,[status(thm)],[156,148]) ).
tff(158,plain,
join(complement(join(complement(complement(a)),complement(complement(b)))),join(join(b,complement(join(complement(complement(a)),complement(complement(b))))),complement(a))) = join(join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(join(complement(complement(a)),complement(complement(b)))))),complement(a)),
inference(symmetry,[status(thm)],[147]) ).
tff(159,plain,
join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(a))) = join(complement(join(complement(complement(a)),complement(complement(b)))),join(join(b,complement(join(complement(complement(a)),complement(complement(b))))),complement(a))),
inference(symmetry,[status(thm)],[145]) ).
tff(160,plain,
join(b,join(complement(a),complement(join(complement(complement(a)),complement(complement(b)))))) = join(join(b,complement(a)),complement(join(complement(complement(a)),complement(complement(b))))),
inference(symmetry,[status(thm)],[133]) ).
tff(161,plain,
join(b,complement(a)) = join(b,join(complement(a),complement(join(complement(complement(a)),complement(complement(b)))))),
inference(symmetry,[status(thm)],[131]) ).
tff(162,plain,
join(b,complement(a)) = join(join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(join(complement(complement(a)),complement(complement(b)))))),complement(a)),
inference(transitivity,[status(thm)],[161,160,135,159,158]) ).
tff(163,plain,
join(n1,join(b,complement(a))) = join(n1,join(join(complement(join(complement(complement(a)),complement(complement(b)))),join(b,complement(join(complement(complement(a)),complement(complement(b)))))),complement(a))),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(b,complement(a)),n1) = join(n1,join(b,complement(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
join(join(b,complement(a)),n1) = join(n1,join(b,complement(a))),
inference(unit_resolution,[status(thm)],[164,100]) ).
tff(166,plain,
( ~ ! [X: $i] : ( join(complement(X),X) = n1 )
| ( join(complement(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))) = n1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
join(complement(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))) = n1,
inference(unit_resolution,[status(thm)],[166,7]) ).
tff(168,plain,
( ~ ! [X: $i] : ( complement(complement(X)) = X )
| ( complement(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))) = join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(169,plain,
complement(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))) = join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))),
inference(unit_resolution,[status(thm)],[168,73]) ).
tff(170,plain,
join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))) = complement(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))) = join(meet(a,join(complement(a),b)),join(meet(complement(a),b),meet(complement(a),complement(b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(172,plain,
join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))) = join(meet(a,join(complement(a),b)),join(meet(complement(a),b),meet(complement(a),complement(b)))),
inference(unit_resolution,[status(thm)],[171,100]) ).
tff(173,plain,
join(meet(a,join(complement(a),b)),join(meet(complement(a),b),meet(complement(a),complement(b)))) = join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(complement(a),b),meet(complement(a),complement(b))) = join(meet(complement(a),complement(b)),meet(complement(a),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
join(meet(complement(a),b),meet(complement(a),complement(b))) = join(meet(complement(a),complement(b)),meet(complement(a),b)),
inference(unit_resolution,[status(thm)],[174,100]) ).
tff(176,plain,
join(meet(complement(a),complement(b)),meet(complement(a),b)) = join(meet(complement(a),b),meet(complement(a),complement(b))),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(complement(a)),complement(b)))) = join(meet(complement(a),complement(b)),meet(complement(a),b)),
inference(monotonicity,[status(thm)],[28,46]) ).
tff(178,plain,
join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(complement(a)),complement(b)))) = join(meet(complement(a),b),meet(complement(a),complement(b))),
inference(transitivity,[status(thm)],[177,176]) ).
tff(179,plain,
join(complement(join(complement(a),complement(join(complement(a),b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(complement(a)),complement(b))))) = join(meet(a,join(complement(a),b)),join(meet(complement(a),b),meet(complement(a),complement(b)))),
inference(monotonicity,[status(thm)],[67,178]) ).
tff(180,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),complement(join(complement(complement(a)),complement(b)))) = join(complement(join(complement(a),complement(join(complement(a),b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(complement(a)),complement(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),complement(join(complement(complement(a)),complement(b)))) = join(complement(join(complement(a),complement(join(complement(a),b)))),join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(complement(a)),complement(b))))),
inference(unit_resolution,[status(thm)],[180,38]) ).
tff(182,plain,
join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),complement(join(complement(complement(a)),complement(b)))) = complement(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))),
inference(transitivity,[status(thm)],[181,179,173,170]) ).
tff(183,plain,
join(join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),complement(join(complement(complement(a)),complement(b)))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))) = join(complement(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),complement(join(complement(complement(a)),complement(b)))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))) = join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
join(join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),complement(join(complement(complement(a)),complement(b)))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))) = join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))))),
inference(unit_resolution,[status(thm)],[184,38]) ).
tff(186,plain,
join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))))) = join(join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),complement(join(complement(complement(a)),complement(b)))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))))) = n1,
inference(transitivity,[status(thm)],[186,183,167]) ).
tff(188,plain,
join(join(b,complement(a)),join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))))) = join(join(b,complement(a)),n1),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(b,complement(a)),join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b)))))),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))))) = join(join(b,complement(a)),join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(190,plain,
join(join(join(b,complement(a)),join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b)))))),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))))) = join(join(b,complement(a)),join(join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))))),
inference(unit_resolution,[status(thm)],[189,38]) ).
tff(191,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(a),complement(join(complement(a),b))))) = join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(192,plain,
join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(a),complement(join(complement(a),b))))) = join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))),
inference(unit_resolution,[status(thm)],[191,100]) ).
tff(193,plain,
join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b))))) = join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(a),complement(join(complement(a),b))))),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
join(join(b,complement(a)),join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b)))))) = join(join(b,complement(a)),join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(a),complement(join(complement(a),b)))))),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
join(join(b,complement(a)),join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(a),complement(join(complement(a),b)))))) = join(join(b,complement(a)),join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b)))))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(b,complement(a)),complement(join(complement(complement(a)),complement(complement(b))))),complement(join(complement(a),complement(join(complement(a),b))))) = join(join(b,complement(a)),join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(a),complement(join(complement(a),b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(197,plain,
join(join(join(b,complement(a)),complement(join(complement(complement(a)),complement(complement(b))))),complement(join(complement(a),complement(join(complement(a),b))))) = join(join(b,complement(a)),join(complement(join(complement(complement(a)),complement(complement(b)))),complement(join(complement(a),complement(join(complement(a),b)))))),
inference(unit_resolution,[status(thm)],[196,38]) ).
tff(198,plain,
join(join(b,complement(a)),complement(join(complement(complement(a)),complement(complement(b))))) = join(b,complement(a)),
inference(transitivity,[status(thm)],[133,131]) ).
tff(199,plain,
join(join(join(b,complement(a)),complement(join(complement(complement(a)),complement(complement(b))))),complement(join(complement(a),complement(join(complement(a),b))))) = join(join(b,complement(a)),meet(join(b,complement(a)),a)),
inference(monotonicity,[status(thm)],[198,116]) ).
tff(200,plain,
join(join(b,complement(a)),meet(join(b,complement(a)),a)) = join(join(join(b,complement(a)),complement(join(complement(complement(a)),complement(complement(b))))),complement(join(complement(a),complement(join(complement(a),b))))),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
join(b,complement(a)) = join(join(b,complement(a)),meet(join(b,complement(a)),a)),
inference(symmetry,[status(thm)],[93]) ).
tff(202,plain,
join(b,complement(a)) = join(join(b,complement(a)),join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b)))))),
inference(transitivity,[status(thm)],[201,200,197,195]) ).
tff(203,plain,
join(join(b,complement(a)),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))))) = join(join(join(b,complement(a)),join(complement(join(complement(a),complement(join(complement(a),b)))),complement(join(complement(complement(a)),complement(complement(b)))))),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))))),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(b,complement(a)),complement(join(complement(complement(a)),complement(b)))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))) = join(join(b,complement(a)),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
join(join(join(b,complement(a)),complement(join(complement(complement(a)),complement(b)))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))) = join(join(b,complement(a)),join(complement(join(complement(complement(a)),complement(b))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))))),
inference(unit_resolution,[status(thm)],[204,38]) ).
tff(206,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(b,complement(a)),complement(join(complement(complement(a)),complement(b)))) = join(b,join(complement(a),complement(join(complement(complement(a)),complement(b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(207,plain,
join(join(b,complement(a)),complement(join(complement(complement(a)),complement(b)))) = join(b,join(complement(a),complement(join(complement(complement(a)),complement(b))))),
inference(unit_resolution,[status(thm)],[206,38]) ).
tff(208,plain,
join(b,join(complement(a),complement(join(complement(complement(a)),complement(b))))) = join(join(b,complement(a)),complement(join(complement(complement(a)),complement(b)))),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
join(b,join(complement(a),complement(join(complement(complement(a)),complement(b))))) = join(b,complement(a)),
inference(monotonicity,[status(thm)],[48]) ).
tff(210,plain,
join(b,complement(a)) = join(b,join(complement(a),complement(join(complement(complement(a)),complement(b))))),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
join(complement(a),b) = join(join(b,complement(a)),complement(join(complement(complement(a)),complement(b)))),
inference(transitivity,[status(thm)],[102,210,208]) ).
tff(212,plain,
join(join(complement(a),b),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))) = join(join(join(b,complement(a)),complement(join(complement(complement(a)),complement(b)))),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))),join(complement(a),b)) = join(join(complement(a),b),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(214,plain,
join(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))),join(complement(a),b)) = join(join(complement(a),b),complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b))))),
inference(unit_resolution,[status(thm)],[213,100]) ).
tff(215,plain,
join(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))),join(complement(a),b)) = n1,
inference(transitivity,[status(thm)],[214,212,205,203,190,188,165,163,157,130,128,86,83,57,54,41,31,9]) ).
tff(216,plain,
( ( join(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))),join(complement(a),b)) != n1 )
<=> ( join(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))),join(complement(a),b)) != n1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(217,axiom,
join(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))),join(complement(a),b)) != n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_e3) ).
tff(218,plain,
join(complement(join(join(meet(complement(a),b),meet(complement(a),complement(b))),meet(a,join(complement(a),b)))),join(complement(a),b)) != n1,
inference(modus_ponens,[status(thm)],[217,216]) ).
tff(219,plain,
$false,
inference(unit_resolution,[status(thm)],[218,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : LAT018-1 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.04/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 10:46:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 5.96/4.04 % SZS status Unsatisfiable
% 5.96/4.04 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------