TSTP Solution File: LAT019-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT019-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:31:45 EDT 2022
% Result : Unsatisfiable 73.03s 47.02s
% Output : Proof 73.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 76
% Syntax : Number of formulae : 247 ( 181 unt; 5 typ; 0 def)
% Number of atoms : 321 ( 311 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 116 ( 46 ~; 42 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 293 ( 272 !; 0 ?; 293 :)
% Comments :
%------------------------------------------------------------------------------
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_law) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(join(a,b),join(a,c)) = join(meet(join(a,b),a),meet(join(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
meet(join(a,b),join(a,c)) = join(meet(join(a,b),a),meet(join(a,b),c)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
join(meet(join(a,b),a),meet(join(a,b),c)) = meet(join(a,b),join(a,c)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(12,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)],[11]) ).
tff(13,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(14,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',commutativity_of_join) ).
tff(15,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,b),c),meet(join(a,b),a)) = join(meet(join(a,b),a),meet(join(a,b),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
join(meet(join(a,b),c),meet(join(a,b),a)) = join(meet(join(a,b),a),meet(join(a,b),c)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(21,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)],[20]) ).
tff(22,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(23,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',commutativity_of_meet) ).
tff(24,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,join(a,b)) = meet(join(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
meet(c,join(a,b)) = meet(join(a,b),c),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,a) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
join(b,a) = join(a,b),
inference(unit_resolution,[status(thm)],[29,17]) ).
tff(31,plain,
meet(c,join(b,a)) = meet(c,join(a,b)),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
<=> ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',quasi_lattice1) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(c,join(b,a)),meet(c,b)) = meet(c,join(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
join(meet(c,join(b,a)),meet(c,b)) = meet(c,join(b,a)),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,b) = meet(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
meet(c,b) = meet(b,c),
inference(unit_resolution,[status(thm)],[41,26]) ).
tff(43,plain,
meet(b,c) = meet(c,b),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
meet(c,join(a,b)) = meet(c,join(b,a)),
inference(symmetry,[status(thm)],[31]) ).
tff(45,plain,
meet(join(a,b),c) = meet(c,join(a,b)),
inference(symmetry,[status(thm)],[28]) ).
tff(46,plain,
meet(join(a,b),c) = meet(c,join(b,a)),
inference(transitivity,[status(thm)],[45,44]) ).
tff(47,plain,
join(meet(join(a,b),c),meet(b,c)) = join(meet(c,join(b,a)),meet(c,b)),
inference(monotonicity,[status(thm)],[46,43]) ).
tff(48,plain,
join(meet(join(a,b),c),meet(b,c)) = meet(join(a,b),c),
inference(transitivity,[status(thm)],[47,40,31,28]) ).
tff(49,plain,
join(join(meet(join(a,b),c),meet(b,c)),meet(join(a,b),a)) = join(meet(join(a,b),c),meet(join(a,b),a)),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,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(51,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)],[50]) ).
tff(52,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(53,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',associativity_of_join) ).
tff(54,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,b),c),meet(b,c)),meet(join(a,b),a)) = join(meet(join(a,b),c),join(meet(b,c),meet(join(a,b),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
join(join(meet(join(a,b),c),meet(b,c)),meet(join(a,b),a)) = join(meet(join(a,b),c),join(meet(b,c),meet(join(a,b),a))),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
join(meet(join(a,b),c),join(meet(b,c),meet(join(a,b),a))) = join(join(meet(join(a,b),c),meet(b,c)),meet(join(a,b),a)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,meet(join(a,b),a)) = join(meet(join(a,b),a),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
join(a,meet(join(a,b),a)) = join(meet(join(a,b),a),a),
inference(unit_resolution,[status(thm)],[60,17]) ).
tff(62,plain,
join(meet(join(a,b),a),a) = join(a,meet(join(a,b),a)),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
^ [X: $i] :
refl(
( ( meet(X,X) = X )
<=> ( meet(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
! [X: $i] : ( meet(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_of_meet) ).
tff(67,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(a,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
meet(a,a) = a,
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
a = meet(a,a),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,join(a,b)) = meet(join(a,b),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
meet(a,join(a,b)) = meet(join(a,b),a),
inference(unit_resolution,[status(thm)],[73,26]) ).
tff(75,plain,
meet(join(a,b),a) = meet(a,join(a,b)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
join(meet(join(a,b),a),a) = join(meet(a,join(a,b)),meet(a,a)),
inference(monotonicity,[status(thm)],[75,72]) ).
tff(77,plain,
join(meet(a,join(a,b)),meet(a,a)) = join(meet(join(a,b),a),a),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(a,join(a,b)),meet(a,a)) = meet(a,join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
join(meet(a,join(a,b)),meet(a,a)) = meet(a,join(a,b)),
inference(unit_resolution,[status(thm)],[78,38]) ).
tff(80,plain,
meet(a,join(a,b)) = join(meet(a,join(a,b)),meet(a,a)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
meet(join(a,b),a) = join(a,meet(join(a,b),a)),
inference(transitivity,[status(thm)],[75,80,77,62]) ).
tff(82,plain,
join(meet(b,c),meet(join(a,b),a)) = join(meet(b,c),join(a,meet(join(a,b),a))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
join(meet(b,c),join(a,meet(join(a,b),a))) = join(meet(b,c),meet(join(a,b),a)),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(b,c),a),meet(join(a,b),a)) = join(meet(b,c),join(a,meet(join(a,b),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
join(join(meet(b,c),a),meet(join(a,b),a)) = join(meet(b,c),join(a,meet(join(a,b),a))),
inference(unit_resolution,[status(thm)],[84,56]) ).
tff(86,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),join(a,meet(b,c))) = meet(join(a,meet(b,c)),join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
meet(join(a,b),join(a,meet(b,c))) = meet(join(a,meet(b,c)),join(a,b)),
inference(unit_resolution,[status(thm)],[86,26]) ).
tff(88,plain,
meet(join(a,meet(b,c)),join(a,b)) = meet(join(a,b),join(a,meet(b,c))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
<=> ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',quasi_lattice2) ).
tff(93,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
| ( meet(join(a,meet(b,c)),join(a,b)) = join(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
meet(join(a,meet(b,c)),join(a,b)) = join(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
join(a,meet(b,c)) = meet(join(a,meet(b,c)),join(a,b)),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(b,c),a) = join(a,meet(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
join(meet(b,c),a) = join(a,meet(b,c)),
inference(unit_resolution,[status(thm)],[99,17]) ).
tff(101,plain,
join(meet(b,c),a) = meet(join(a,b),join(a,meet(b,c))),
inference(transitivity,[status(thm)],[100,98,88]) ).
tff(102,plain,
join(join(meet(b,c),a),meet(join(a,b),a)) = join(meet(join(a,b),join(a,meet(b,c))),meet(join(a,b),a)),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
join(meet(join(a,b),join(a,meet(b,c))),meet(join(a,b),a)) = join(join(meet(b,c),a),meet(join(a,b),a)),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(join(a,b),join(a,meet(b,c))),meet(join(a,b),a)) = meet(join(a,b),join(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
join(meet(join(a,b),join(a,meet(b,c))),meet(join(a,b),a)) = meet(join(a,b),join(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[104,38]) ).
tff(106,plain,
meet(join(a,b),join(a,meet(b,c))) = join(meet(join(a,b),join(a,meet(b,c))),meet(join(a,b),a)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
join(meet(b,c),a) = join(meet(b,c),meet(join(a,b),a)),
inference(transitivity,[status(thm)],[100,98,88,106,103,85,83]) ).
tff(108,plain,
join(meet(join(a,b),c),join(meet(b,c),a)) = join(meet(join(a,b),c),join(meet(b,c),meet(join(a,b),a))),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,b),c),meet(b,c)),a) = join(meet(join(a,b),c),join(meet(b,c),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
join(join(meet(join(a,b),c),meet(b,c)),a) = join(meet(join(a,b),c),join(meet(b,c),a)),
inference(unit_resolution,[status(thm)],[109,56]) ).
tff(111,plain,
join(meet(c,join(b,a)),meet(c,b)) = join(meet(join(a,b),c),meet(b,c)),
inference(symmetry,[status(thm)],[47]) ).
tff(112,plain,
meet(c,join(b,a)) = join(meet(c,join(b,a)),meet(c,b)),
inference(symmetry,[status(thm)],[40]) ).
tff(113,plain,
meet(join(a,b),c) = join(meet(join(a,b),c),meet(b,c)),
inference(transitivity,[status(thm)],[45,44,112,111]) ).
tff(114,plain,
join(meet(join(a,b),c),a) = join(join(meet(join(a,b),c),meet(b,c)),a),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(c,join(a,b)),meet(c,a)) = meet(c,join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
join(meet(c,join(a,b)),meet(c,a)) = meet(c,join(a,b)),
inference(unit_resolution,[status(thm)],[115,38]) ).
tff(117,plain,
join(meet(join(a,b),c),meet(c,a)) = join(meet(c,join(a,b)),meet(c,a)),
inference(monotonicity,[status(thm)],[45]) ).
tff(118,plain,
join(meet(join(a,b),c),meet(c,a)) = meet(join(a,b),c),
inference(transitivity,[status(thm)],[117,116,28]) ).
tff(119,plain,
join(join(meet(join(a,b),c),meet(c,a)),a) = join(meet(join(a,b),c),a),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,b),c),meet(c,a)),a) = join(meet(join(a,b),c),join(meet(c,a),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
join(join(meet(join(a,b),c),meet(c,a)),a) = join(meet(join(a,b),c),join(meet(c,a),a)),
inference(unit_resolution,[status(thm)],[120,56]) ).
tff(122,plain,
join(meet(join(a,b),c),join(meet(c,a),a)) = join(join(meet(join(a,b),c),meet(c,a)),a),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,c) = meet(c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
meet(a,c) = meet(c,a),
inference(unit_resolution,[status(thm)],[123,26]) ).
tff(125,plain,
meet(c,a) = meet(a,c),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
join(meet(c,a),a) = join(meet(a,c),meet(a,a)),
inference(monotonicity,[status(thm)],[125,72]) ).
tff(127,plain,
join(meet(a,c),meet(a,a)) = join(meet(c,a),a),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(a,join(c,a)) = join(meet(a,c),meet(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
meet(a,join(c,a)) = join(meet(a,c),meet(a,a)),
inference(unit_resolution,[status(thm)],[128,7]) ).
tff(130,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(c,a) = join(a,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
join(c,a) = join(a,c),
inference(unit_resolution,[status(thm)],[130,17]) ).
tff(132,plain,
meet(a,join(c,a)) = meet(a,join(a,c)),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
meet(a,join(a,c)) = meet(a,join(c,a)),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,join(a,c)) = meet(join(a,c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
meet(a,join(a,c)) = meet(join(a,c),a),
inference(unit_resolution,[status(thm)],[134,26]) ).
tff(136,plain,
meet(join(a,c),a) = meet(a,join(a,c)),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
^ [X: $i] :
refl(
( ( join(X,X) = X )
<=> ( join(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(138,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(quant_intro,[status(thm)],[137]) ).
tff(139,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,axiom,
! [X: $i] : ( join(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_of_join) ).
tff(141,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [X: $i] : ( join(X,X) = X ),
inference(skolemize,[status(sab)],[141]) ).
tff(143,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[142,138]) ).
tff(144,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(meet(join(a,c),a),meet(join(a,c),a)) = meet(join(a,c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
join(meet(join(a,c),a),meet(join(a,c),a)) = meet(join(a,c),a),
inference(unit_resolution,[status(thm)],[144,143]) ).
tff(146,plain,
join(meet(join(a,c),a),meet(join(a,c),a)) = join(meet(c,a),a),
inference(transitivity,[status(thm)],[145,136,133,129,127]) ).
tff(147,plain,
join(meet(join(a,b),c),join(meet(join(a,c),a),meet(join(a,c),a))) = join(meet(join(a,b),c),join(meet(c,a),a)),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
meet(join(a,c),a) = join(meet(join(a,c),a),meet(join(a,c),a)),
inference(symmetry,[status(thm)],[145]) ).
tff(149,plain,
join(meet(join(a,b),c),meet(join(a,c),a)) = join(meet(join(a,b),c),join(meet(join(a,c),a),meet(join(a,c),a))),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,c),a),meet(join(a,b),c)) = join(meet(join(a,b),c),meet(join(a,c),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
join(meet(join(a,c),a),meet(join(a,b),c)) = join(meet(join(a,b),c),meet(join(a,c),a)),
inference(unit_resolution,[status(thm)],[150,17]) ).
tff(152,plain,
join(join(meet(join(a,c),a),meet(join(a,c),a)),meet(join(a,b),c)) = join(meet(join(a,c),a),meet(join(a,b),c)),
inference(monotonicity,[status(thm)],[145]) ).
tff(153,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(c,join(a,b)) = join(meet(c,a),meet(c,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
meet(c,join(a,b)) = join(meet(c,a),meet(c,b)),
inference(unit_resolution,[status(thm)],[153,7]) ).
tff(155,plain,
join(meet(c,a),meet(c,b)) = meet(c,join(a,b)),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
join(meet(c,a),meet(b,c)) = join(meet(c,a),meet(c,b)),
inference(monotonicity,[status(thm)],[43]) ).
tff(157,plain,
join(meet(c,a),meet(b,c)) = meet(join(a,b),c),
inference(transitivity,[status(thm)],[156,155,28]) ).
tff(158,plain,
join(meet(join(a,c),a),join(meet(c,a),meet(b,c))) = join(join(meet(join(a,c),a),meet(join(a,c),a)),meet(join(a,b),c)),
inference(monotonicity,[status(thm)],[148,157]) ).
tff(159,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(join(a,c),a),meet(c,a)),meet(b,c)) = join(meet(join(a,c),a),join(meet(c,a),meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
join(join(meet(join(a,c),a),meet(c,a)),meet(b,c)) = join(meet(join(a,c),a),join(meet(c,a),meet(b,c))),
inference(unit_resolution,[status(thm)],[159,56]) ).
tff(161,plain,
meet(join(a,c),a) = meet(a,join(c,a)),
inference(transitivity,[status(thm)],[136,133]) ).
tff(162,plain,
join(meet(join(a,c),a),meet(c,a)) = join(meet(a,join(c,a)),meet(a,c)),
inference(monotonicity,[status(thm)],[161,125]) ).
tff(163,plain,
join(meet(a,join(c,a)),meet(a,c)) = join(meet(join(a,c),a),meet(c,a)),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(a,join(c,a)),meet(a,c)) = meet(a,join(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
join(meet(a,join(c,a)),meet(a,c)) = meet(a,join(c,a)),
inference(unit_resolution,[status(thm)],[164,38]) ).
tff(166,plain,
meet(a,join(c,a)) = join(meet(a,join(c,a)),meet(a,c)),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
meet(join(a,c),a) = join(meet(join(a,c),a),meet(c,a)),
inference(transitivity,[status(thm)],[136,133,166,163]) ).
tff(168,plain,
join(meet(join(a,c),a),meet(b,c)) = join(join(meet(join(a,c),a),meet(c,a)),meet(b,c)),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(a,join(a,c)),meet(a,a)) = meet(a,join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
join(meet(a,join(a,c)),meet(a,a)) = meet(a,join(a,c)),
inference(unit_resolution,[status(thm)],[169,38]) ).
tff(171,plain,
join(meet(join(a,c),a),meet(a,a)) = join(meet(a,join(a,c)),meet(a,a)),
inference(monotonicity,[status(thm)],[136]) ).
tff(172,plain,
join(join(meet(join(a,c),a),meet(join(a,c),a)),a) = join(meet(join(a,c),a),meet(a,a)),
inference(monotonicity,[status(thm)],[145,72]) ).
tff(173,plain,
join(join(meet(join(a,c),a),meet(join(a,c),a)),a) = meet(join(a,c),a),
inference(transitivity,[status(thm)],[172,171,170,135]) ).
tff(174,plain,
join(join(join(meet(join(a,c),a),meet(join(a,c),a)),a),meet(b,c)) = join(meet(join(a,c),a),meet(b,c)),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(meet(join(a,c),a),meet(join(a,c),a)),a),meet(b,c)) = join(join(meet(join(a,c),a),meet(join(a,c),a)),join(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,plain,
join(join(join(meet(join(a,c),a),meet(join(a,c),a)),a),meet(b,c)) = join(join(meet(join(a,c),a),meet(join(a,c),a)),join(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[175,56]) ).
tff(177,plain,
join(join(meet(join(a,c),a),meet(join(a,c),a)),join(a,meet(b,c))) = join(join(join(meet(join(a,c),a),meet(join(a,c),a)),a),meet(b,c)),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
join(meet(join(a,c),a),join(a,meet(b,c))) = join(join(meet(join(a,c),a),meet(join(a,c),a)),join(a,meet(b,c))),
inference(monotonicity,[status(thm)],[148]) ).
tff(179,plain,
join(a,meet(b,c)) = join(a,meet(c,b)),
inference(monotonicity,[status(thm)],[43]) ).
tff(180,plain,
join(a,meet(c,b)) = join(a,meet(b,c)),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
| ( meet(join(a,meet(c,b)),join(a,c)) = join(a,meet(c,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
meet(join(a,meet(c,b)),join(a,c)) = join(a,meet(c,b)),
inference(unit_resolution,[status(thm)],[181,95]) ).
tff(183,plain,
meet(join(a,meet(c,b)),join(a,c)) = meet(join(a,meet(b,c)),join(a,c)),
inference(monotonicity,[status(thm)],[180]) ).
tff(184,plain,
meet(join(a,meet(b,c)),join(a,c)) = meet(join(a,meet(c,b)),join(a,c)),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
meet(join(a,meet(b,c)),join(a,c)) = join(a,meet(c,b)),
inference(transitivity,[status(thm)],[184,182]) ).
tff(186,plain,
meet(meet(join(a,meet(b,c)),join(a,c)),join(a,c)) = meet(join(a,meet(c,b)),join(a,c)),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,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(188,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)],[187]) ).
tff(189,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(190,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',associativity_of_meet) ).
tff(191,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[191]) ).
tff(193,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[192,188]) ).
tff(194,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,meet(b,c)),join(a,c)),join(a,c)) = meet(join(a,meet(b,c)),meet(join(a,c),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(195,plain,
meet(meet(join(a,meet(b,c)),join(a,c)),join(a,c)) = meet(join(a,meet(b,c)),meet(join(a,c),join(a,c))),
inference(unit_resolution,[status(thm)],[194,193]) ).
tff(196,plain,
meet(join(a,meet(b,c)),meet(join(a,c),join(a,c))) = meet(meet(join(a,meet(b,c)),join(a,c)),join(a,c)),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(join(a,c),join(a,c)),join(a,meet(b,c))) = meet(join(a,meet(b,c)),meet(join(a,c),join(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(198,plain,
meet(meet(join(a,c),join(a,c)),join(a,meet(b,c))) = meet(join(a,meet(b,c)),meet(join(a,c),join(a,c))),
inference(unit_resolution,[status(thm)],[197,26]) ).
tff(199,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(join(a,meet(b,c)),join(a,b)),meet(join(a,meet(b,c)),a)) = meet(join(a,meet(b,c)),join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(200,plain,
join(meet(join(a,meet(b,c)),join(a,b)),meet(join(a,meet(b,c)),a)) = meet(join(a,meet(b,c)),join(a,b)),
inference(unit_resolution,[status(thm)],[199,38]) ).
tff(201,plain,
join(meet(b,c),a) = meet(join(a,meet(b,c)),join(a,b)),
inference(transitivity,[status(thm)],[100,98]) ).
tff(202,plain,
join(join(meet(b,c),a),meet(join(a,meet(b,c)),a)) = join(meet(join(a,meet(b,c)),join(a,b)),meet(join(a,meet(b,c)),a)),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(b,c),a),meet(join(a,meet(b,c)),a)) = join(meet(b,c),join(a,meet(join(a,meet(b,c)),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
join(join(meet(b,c),a),meet(join(a,meet(b,c)),a)) = join(meet(b,c),join(a,meet(join(a,meet(b,c)),a))),
inference(unit_resolution,[status(thm)],[203,56]) ).
tff(205,plain,
join(meet(b,c),join(a,meet(join(a,meet(b,c)),a))) = join(join(meet(b,c),a),meet(join(a,meet(b,c)),a)),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(join(a,meet(b,c)),a),a) = join(a,meet(join(a,meet(b,c)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(207,plain,
join(meet(join(a,meet(b,c)),a),a) = join(a,meet(join(a,meet(b,c)),a)),
inference(unit_resolution,[status(thm)],[206,17]) ).
tff(208,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,join(a,meet(b,c))) = meet(join(a,meet(b,c)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(209,plain,
meet(a,join(a,meet(b,c))) = meet(join(a,meet(b,c)),a),
inference(unit_resolution,[status(thm)],[208,26]) ).
tff(210,plain,
meet(join(a,meet(b,c)),a) = meet(a,join(a,meet(b,c))),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
join(meet(join(a,meet(b,c)),a),a) = join(meet(a,join(a,meet(b,c))),meet(a,a)),
inference(monotonicity,[status(thm)],[210,72]) ).
tff(212,plain,
join(meet(a,join(a,meet(b,c))),meet(a,a)) = join(meet(join(a,meet(b,c)),a),a),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )
| ( join(meet(a,join(a,meet(b,c))),meet(a,a)) = meet(a,join(a,meet(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(214,plain,
join(meet(a,join(a,meet(b,c))),meet(a,a)) = meet(a,join(a,meet(b,c))),
inference(unit_resolution,[status(thm)],[213,38]) ).
tff(215,plain,
meet(a,join(a,meet(b,c))) = join(meet(a,join(a,meet(b,c))),meet(a,a)),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
meet(join(a,meet(b,c)),a) = join(a,meet(join(a,meet(b,c)),a)),
inference(transitivity,[status(thm)],[210,215,212,207]) ).
tff(217,plain,
join(meet(b,c),meet(join(a,meet(b,c)),a)) = join(meet(b,c),join(a,meet(join(a,meet(b,c)),a))),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
join(meet(b,c),meet(join(a,meet(b,c)),a)) = join(a,meet(b,c)),
inference(transitivity,[status(thm)],[217,205,202,200,97]) ).
tff(219,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(join(a,c),join(a,c)) = join(a,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(220,plain,
meet(join(a,c),join(a,c)) = join(a,c),
inference(unit_resolution,[status(thm)],[219,69]) ).
tff(221,plain,
join(a,c) = meet(join(a,c),join(a,c)),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
meet(join(a,c),join(meet(b,c),meet(join(a,meet(b,c)),a))) = meet(meet(join(a,c),join(a,c)),join(a,meet(b,c))),
inference(monotonicity,[status(thm)],[221,218]) ).
tff(223,plain,
meet(join(a,c),join(meet(b,c),meet(join(a,meet(b,c)),a))) = join(a,meet(b,c)),
inference(transitivity,[status(thm)],[222,198,196,186,182,180]) ).
tff(224,plain,
join(meet(join(a,c),a),meet(join(a,c),join(meet(b,c),meet(join(a,meet(b,c)),a)))) = join(meet(join(a,c),a),join(a,meet(b,c))),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(join(a,c),join(a,join(meet(b,c),meet(join(a,meet(b,c)),a)))) = join(meet(join(a,c),a),meet(join(a,c),join(meet(b,c),meet(join(a,meet(b,c)),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(226,plain,
meet(join(a,c),join(a,join(meet(b,c),meet(join(a,meet(b,c)),a)))) = join(meet(join(a,c),a),meet(join(a,c),join(meet(b,c),meet(join(a,meet(b,c)),a)))),
inference(unit_resolution,[status(thm)],[225,7]) ).
tff(227,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(a,meet(b,c)),meet(join(a,meet(b,c)),a)) = join(a,join(meet(b,c),meet(join(a,meet(b,c)),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
join(join(a,meet(b,c)),meet(join(a,meet(b,c)),a)) = join(a,join(meet(b,c),meet(join(a,meet(b,c)),a))),
inference(unit_resolution,[status(thm)],[227,56]) ).
tff(229,plain,
join(join(a,meet(b,c)),meet(join(a,meet(b,c)),a)) = join(meet(join(a,meet(b,c)),join(a,b)),meet(join(a,meet(b,c)),a)),
inference(monotonicity,[status(thm)],[98]) ).
tff(230,plain,
join(meet(join(a,meet(b,c)),join(a,b)),meet(join(a,meet(b,c)),a)) = join(join(a,meet(b,c)),meet(join(a,meet(b,c)),a)),
inference(symmetry,[status(thm)],[229]) ).
tff(231,plain,
meet(join(a,meet(b,c)),join(a,b)) = join(meet(join(a,meet(b,c)),join(a,b)),meet(join(a,meet(b,c)),a)),
inference(symmetry,[status(thm)],[200]) ).
tff(232,plain,
join(a,meet(b,c)) = join(a,join(meet(b,c),meet(join(a,meet(b,c)),a))),
inference(transitivity,[status(thm)],[98,231,230,228]) ).
tff(233,plain,
meet(join(a,c),join(a,meet(b,c))) = meet(join(a,c),join(a,join(meet(b,c),meet(join(a,meet(b,c)),a)))),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,c),join(a,meet(b,c))) = meet(join(a,meet(b,c)),join(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(235,plain,
meet(join(a,c),join(a,meet(b,c))) = meet(join(a,meet(b,c)),join(a,c)),
inference(unit_resolution,[status(thm)],[234,26]) ).
tff(236,plain,
meet(join(a,meet(b,c)),join(a,c)) = meet(join(a,c),join(a,meet(b,c))),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
join(a,meet(c,b)) = meet(join(a,meet(c,b)),join(a,c)),
inference(symmetry,[status(thm)],[182]) ).
tff(238,plain,
join(a,meet(b,c)) = meet(join(a,b),join(a,c)),
inference(transitivity,[status(thm)],[179,237,183,236,233,226,224,178,177,174,168,160,158,152,151,149,147,122,119,114,110,108,59,49,19,10]) ).
tff(239,plain,
( ( join(a,meet(b,c)) != meet(join(a,b),join(a,c)) )
<=> ( join(a,meet(b,c)) != meet(join(a,b),join(a,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(240,axiom,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_law_dual) ).
tff(241,plain,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
inference(modus_ponens,[status(thm)],[240,239]) ).
tff(242,plain,
$false,
inference(unit_resolution,[status(thm)],[241,238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT019-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n016.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 11:08:19 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.
% 73.03/47.02 % SZS status Unsatisfiable
% 73.03/47.02 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------