TSTP Solution File: LAT011-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT011-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 18:31:42 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 60
% Syntax : Number of formulae : 159 ( 110 unt; 5 typ; 0 def)
% Number of atoms : 218 ( 207 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 81 ( 27 ~; 23 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 258 ( 235 !; 0 ?; 258 :)
% Comments :
%------------------------------------------------------------------------------
tff(meet2_type,type,
meet2: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet2(X,join(X,Y)) = X )
<=> ( meet2(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( meet2(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet2(X,join(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( meet2(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet2(X,join(X,Y)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( meet2(X,join(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1_2) ).
tff(5,plain,
! [Y: $i,X: $i] : ( meet2(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( meet2(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( meet2(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( meet2(X,join(X,Y)) = X )
| ( meet2(meet2(a,b),join(meet2(a,b),meet(a,b))) = meet2(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
meet2(meet2(a,b),join(meet2(a,b),meet(a,b))) = meet2(a,b),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) )
<=> ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet2) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) )
| ( meet2(meet2(a,b),join(meet2(a,b),meet(a,b))) = meet2(a,meet2(b,join(meet2(a,b),meet(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
meet2(meet2(a,b),join(meet2(a,b),meet(a,b))) = meet2(a,meet2(b,join(meet2(a,b),meet(a,b)))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
meet2(a,meet2(b,join(meet2(a,b),meet(a,b)))) = meet2(meet2(a,b),join(meet2(a,b),meet(a,b))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet2(X,Y) = meet2(Y,X) )
<=> ( meet2(X,Y) = meet2(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [Y: $i,X: $i] : ( meet2(X,Y) = meet2(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet2(X,Y) = meet2(Y,X) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : ( meet2(X,Y) = meet2(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet2(X,Y) = meet2(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [Y: $i,X: $i] : ( meet2(X,Y) = meet2(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet2) ).
tff(24,plain,
! [Y: $i,X: $i] : ( meet2(X,Y) = meet2(Y,X) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( meet2(X,Y) = meet2(Y,X) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( meet2(X,Y) = meet2(Y,X) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( meet2(X,Y) = meet2(Y,X) )
| ( meet2(meet2(b,join(meet2(a,b),meet(a,b))),a) = meet2(a,meet2(b,join(meet2(a,b),meet(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
meet2(meet2(b,join(meet2(a,b),meet(a,b))),a) = meet2(a,meet2(b,join(meet2(a,b),meet(a,b)))),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) )
| ( meet2(meet2(b,join(meet2(a,b),meet(a,b))),a) = meet2(b,meet2(join(meet2(a,b),meet(a,b)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
meet2(meet2(b,join(meet2(a,b),meet(a,b))),a) = meet2(b,meet2(join(meet2(a,b),meet(a,b)),a)),
inference(unit_resolution,[status(thm)],[29,16]) ).
tff(31,plain,
meet2(b,meet2(join(meet2(a,b),meet(a,b)),a)) = meet2(meet2(b,join(meet2(a,b),meet(a,b))),a),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] : ( meet2(X,join(X,Y)) = X )
| ( meet2(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),a)) = join(meet2(a,b),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
meet2(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),a)) = join(meet2(a,b),meet(a,b)),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(35,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)],[34]) ).
tff(36,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(37,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(38,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(meet2(a,b),meet(a,b)),a) = join(a,join(meet2(a,b),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
join(join(meet2(a,b),meet(a,b)),a) = join(a,join(meet2(a,b),meet(a,b))),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
join(a,join(meet2(a,b),meet(a,b))) = join(join(meet2(a,b),meet(a,b)),a),
inference(symmetry,[status(thm)],[42]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
tff(48,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(a,meet2(a,b)),meet(a,b)) = join(a,join(meet2(a,b),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
join(join(a,meet2(a,b)),meet(a,b)) = join(a,join(meet2(a,b),meet(a,b))),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet2(X,Y)) = X )
<=> ( join(X,meet2(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [Y: $i,X: $i] : ( join(X,meet2(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( join(X,meet2(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [Y: $i,X: $i] : ( join(X,meet2(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( join(X,meet2(X,Y)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
! [Y: $i,X: $i] : ( join(X,meet2(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2_2) ).
tff(57,plain,
! [Y: $i,X: $i] : ( join(X,meet2(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [Y: $i,X: $i] : ( join(X,meet2(X,Y)) = X ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [Y: $i,X: $i] : ( join(X,meet2(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet2(X,Y)) = X )
| ( join(a,meet2(a,b)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
join(a,meet2(a,b)) = a,
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
join(join(a,meet2(a,b)),meet(a,b)) = join(a,meet(a,b)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
join(a,meet(a,b)) = join(join(a,meet2(a,b)),meet(a,b)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(65,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)],[64]) ).
tff(66,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(67,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(68,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(a,meet(a,b)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
join(a,meet(a,b)) = a,
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
a = join(a,meet(a,b)),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
a = join(join(meet2(a,b),meet(a,b)),a),
inference(transitivity,[status(thm)],[73,63,52,43]) ).
tff(75,plain,
meet2(join(meet2(a,b),meet(a,b)),a) = meet2(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),a)),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
meet2(join(meet2(a,b),meet(a,b)),a) = join(meet2(a,b),meet(a,b)),
inference(transitivity,[status(thm)],[75,33]) ).
tff(77,plain,
meet2(b,meet2(join(meet2(a,b),meet(a,b)),a)) = meet2(b,join(meet2(a,b),meet(a,b))),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
meet2(b,join(meet2(a,b),meet(a,b))) = meet2(b,meet2(join(meet2(a,b),meet(a,b)),a)),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
( ~ ! [Y: $i,X: $i] : ( meet2(X,Y) = meet2(Y,X) )
| ( meet2(join(meet2(a,b),meet(a,b)),b) = meet2(b,join(meet2(a,b),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
meet2(join(meet2(a,b),meet(a,b)),b) = meet2(b,join(meet2(a,b),meet(a,b))),
inference(unit_resolution,[status(thm)],[79,26]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(meet2(a,b),meet(a,b)),b) = join(b,join(meet2(a,b),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
join(join(meet2(a,b),meet(a,b)),b) = join(b,join(meet2(a,b),meet(a,b))),
inference(unit_resolution,[status(thm)],[81,40]) ).
tff(83,plain,
join(b,join(meet2(a,b),meet(a,b))) = join(join(meet2(a,b),meet(a,b)),b),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),meet2(a,b)) = join(meet2(a,b),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
join(meet(a,b),meet2(a,b)) = join(meet2(a,b),meet(a,b)),
inference(unit_resolution,[status(thm)],[84,40]) ).
tff(86,plain,
join(meet2(a,b),meet(a,b)) = join(meet(a,b),meet2(a,b)),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
join(b,join(meet2(a,b),meet(a,b))) = join(b,join(meet(a,b),meet2(a,b))),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
join(b,join(meet(a,b),meet2(a,b))) = join(b,join(meet2(a,b),meet(a,b))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(b,meet(a,b)),meet2(a,b)) = join(b,join(meet(a,b),meet2(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
join(join(b,meet(a,b)),meet2(a,b)) = join(b,join(meet(a,b),meet2(a,b))),
inference(unit_resolution,[status(thm)],[89,50]) ).
tff(91,plain,
( ~ ! [Y: $i,X: $i] : ( meet2(X,Y) = meet2(Y,X) )
| ( meet2(b,a) = meet2(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
meet2(b,a) = meet2(a,b),
inference(unit_resolution,[status(thm)],[91,26]) ).
tff(93,plain,
meet2(a,b) = meet2(b,a),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(b,meet(b,a)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
join(b,meet(b,a)) = b,
inference(unit_resolution,[status(thm)],[94,70]) ).
tff(96,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(97,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)],[96]) ).
tff(98,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(99,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(100,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,a) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
meet(b,a) = meet(a,b),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
meet(a,b) = meet(b,a),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
join(b,meet(a,b)) = join(b,meet(b,a)),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
join(b,meet(a,b)) = b,
inference(transitivity,[status(thm)],[106,95]) ).
tff(108,plain,
join(join(b,meet(a,b)),meet2(a,b)) = join(b,meet2(b,a)),
inference(monotonicity,[status(thm)],[107,93]) ).
tff(109,plain,
join(b,meet2(b,a)) = join(join(b,meet(a,b)),meet2(a,b)),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet2(X,Y)) = X )
| ( join(b,meet2(b,a)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
join(b,meet2(b,a)) = b,
inference(unit_resolution,[status(thm)],[110,59]) ).
tff(112,plain,
b = join(b,meet2(b,a)),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
b = join(join(meet2(a,b),meet(a,b)),b),
inference(transitivity,[status(thm)],[112,109,90,88,83]) ).
tff(114,plain,
meet2(join(meet2(a,b),meet(a,b)),b) = meet2(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),b)),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
meet2(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),b)) = meet2(join(meet2(a,b),meet(a,b)),b),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [Y: $i,X: $i] : ( meet2(X,join(X,Y)) = X )
| ( meet2(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),b)) = join(meet2(a,b),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
meet2(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),b)) = join(meet2(a,b),meet(a,b)),
inference(unit_resolution,[status(thm)],[116,7]) ).
tff(118,plain,
join(meet2(a,b),meet(a,b)) = meet2(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),b)),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(123,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),b)) = join(meet2(a,b),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
meet(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),b)) = join(meet2(a,b),meet(a,b)),
inference(unit_resolution,[status(thm)],[126,125]) ).
tff(128,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),a)) = join(meet2(a,b),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
meet(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),a)) = join(meet2(a,b),meet(a,b)),
inference(unit_resolution,[status(thm)],[128,125]) ).
tff(130,plain,
meet(join(meet2(a,b),meet(a,b)),a) = meet(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),a)),
inference(monotonicity,[status(thm)],[74]) ).
tff(131,plain,
meet(join(meet2(a,b),meet(a,b)),a) = join(meet2(a,b),meet(a,b)),
inference(transitivity,[status(thm)],[130,129]) ).
tff(132,plain,
meet(meet(join(meet2(a,b),meet(a,b)),a),b) = meet(join(meet2(a,b),meet(a,b)),join(join(meet2(a,b),meet(a,b)),b)),
inference(monotonicity,[status(thm)],[131,113]) ).
tff(133,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(134,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)],[133]) ).
tff(135,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(136,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
tff(137,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[137]) ).
tff(139,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[138,134]) ).
tff(140,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(meet2(a,b),meet(a,b)),a),b) = meet(join(meet2(a,b),meet(a,b)),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
meet(meet(join(meet2(a,b),meet(a,b)),a),b) = meet(join(meet2(a,b),meet(a,b)),meet(a,b)),
inference(unit_resolution,[status(thm)],[140,139]) ).
tff(142,plain,
meet(join(meet2(a,b),meet(a,b)),meet(a,b)) = meet(meet(join(meet2(a,b),meet(a,b)),a),b),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet2(a,b),meet(a,b)),meet(a,b)) = meet(meet(a,b),join(meet2(a,b),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,plain,
meet(join(meet2(a,b),meet(a,b)),meet(a,b)) = meet(meet(a,b),join(meet2(a,b),meet(a,b))),
inference(unit_resolution,[status(thm)],[143,102]) ).
tff(145,plain,
meet(meet(a,b),join(meet2(a,b),meet(a,b))) = meet(join(meet2(a,b),meet(a,b)),meet(a,b)),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
meet(meet(a,b),join(meet(a,b),meet2(a,b))) = meet(meet(a,b),join(meet2(a,b),meet(a,b))),
inference(monotonicity,[status(thm)],[85]) ).
tff(147,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(a,b),join(meet(a,b),meet2(a,b))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
meet(meet(a,b),join(meet(a,b),meet2(a,b))) = meet(a,b),
inference(unit_resolution,[status(thm)],[147,125]) ).
tff(149,plain,
meet(a,b) = meet(meet(a,b),join(meet(a,b),meet2(a,b))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
meet(a,b) = meet2(a,b),
inference(transitivity,[status(thm)],[149,146,145,142,132,127,118,115,80,78,31,28,19,9]) ).
tff(151,plain,
( ( meet(a,b) != meet2(a,b) )
<=> ( meet(a,b) != meet2(a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,axiom,
meet(a,b) != meet2(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_meets_are_same) ).
tff(153,plain,
meet(a,b) != meet2(a,b),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
$false,
inference(unit_resolution,[status(thm)],[153,150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LAT011-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n020.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 10:44:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------