TSTP Solution File: LAT023-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT023-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 18:31:46 EDT 2022
% Result : Unsatisfiable 3.34s 2.40s
% Output : Proof 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 56
% Syntax : Number of formulae : 156 ( 110 unt; 5 typ; 0 def)
% Number of atoms : 210 ( 200 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 76 ( 26 ~; 22 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 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 : 242 ( 221 !; 0 ?; 242 :)
% Comments :
%------------------------------------------------------------------------------
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',commutativity_of_join) ).
tff(5,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,c),meet(a,b)) = join(meet(a,b),meet(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
join(meet(a,c),meet(a,b)) = join(meet(a,b),meet(a,c)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,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)],[13,12]) ).
tff(15,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)],[14]) ).
tff(16,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)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )
| ( meet(join(meet(a,c),meet(a,b)),join(meet(a,c),a)) = join(meet(a,c),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
meet(join(meet(a,c),meet(a,b)),join(meet(a,c),a)) = join(meet(a,c),meet(a,b)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
join(meet(a,b),meet(a,c)) = join(meet(a,c),meet(a,b)),
inference(symmetry,[status(thm)],[9]) ).
tff(20,plain,
meet(join(meet(a,b),meet(a,c)),join(meet(a,c),a)) = meet(join(meet(a,c),meet(a,b)),join(meet(a,c),a)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(22,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)],[21]) ).
tff(23,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(24,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',commutativity_of_meet) ).
tff(25,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,c),a),join(meet(a,b),meet(a,c))) = meet(join(meet(a,b),meet(a,c)),join(meet(a,c),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
meet(join(meet(a,c),a),join(meet(a,b),meet(a,c))) = meet(join(meet(a,b),meet(a,c)),join(meet(a,c),a)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,c),a) = join(a,meet(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
join(meet(a,c),a) = join(a,meet(a,c)),
inference(unit_resolution,[status(thm)],[30,7]) ).
tff(32,plain,
join(a,meet(a,c)) = join(meet(a,c),a),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
meet(join(a,meet(a,c)),join(meet(a,b),meet(a,c))) = meet(join(meet(a,c),a),join(meet(a,b),meet(a,c))),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,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(35,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)],[34]) ).
tff(36,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(37,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(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)],[37,36]) ).
tff(39,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)],[38]) ).
tff(40,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)],[39,35]) ).
tff(41,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(a,c)),join(meet(a,b),meet(a,c))),meet(join(a,meet(a,c)),meet(a,b))) = meet(join(a,meet(a,c)),join(meet(a,b),meet(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
join(meet(join(a,meet(a,c)),join(meet(a,b),meet(a,c))),meet(join(a,meet(a,c)),meet(a,b))) = meet(join(a,meet(a,c)),join(meet(a,b),meet(a,c))),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
meet(join(meet(a,c),a),meet(a,b)) = meet(join(a,meet(a,c)),meet(a,b)),
inference(monotonicity,[status(thm)],[31]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,a) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
meet(b,a) = meet(a,b),
inference(unit_resolution,[status(thm)],[44,27]) ).
tff(46,plain,
meet(join(a,meet(a,c)),meet(b,a)) = meet(join(meet(a,c),a),meet(a,b)),
inference(monotonicity,[status(thm)],[32,45]) ).
tff(47,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(48,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)],[47]) ).
tff(49,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(50,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(51,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,meet(a,c)),b),a) = meet(join(a,meet(a,c)),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
meet(meet(join(a,meet(a,c)),b),a) = meet(join(a,meet(a,c)),meet(b,a)),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
^ [X: $i] :
refl(
( ( join(X,X) = X )
<=> ( join(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X: $i] : ( join(X,X) = X )
<=> ! [X: $i] : ( join(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
! [X: $i] : ( join(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_of_join) ).
tff(60,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [X: $i] : ( join(X,X) = X ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [X: $i] : ( join(X,X) = X ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( ~ ! [X: $i] : ( join(X,X) = X )
| ( join(a,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
join(a,a) = a,
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,join(a,meet(a,c))) = meet(join(a,meet(a,c)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
meet(b,join(a,meet(a,c))) = meet(join(a,meet(a,c)),b),
inference(unit_resolution,[status(thm)],[65,27]) ).
tff(67,plain,
meet(meet(b,join(a,meet(a,c))),join(a,a)) = meet(meet(join(a,meet(a,c)),b),a),
inference(monotonicity,[status(thm)],[66,64]) ).
tff(68,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(b,join(a,meet(a,c))),join(a,a)) = meet(b,meet(join(a,meet(a,c)),join(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
meet(meet(b,join(a,meet(a,c))),join(a,a)) = meet(b,meet(join(a,meet(a,c)),join(a,a))),
inference(unit_resolution,[status(thm)],[68,53]) ).
tff(70,plain,
meet(b,meet(join(a,meet(a,c)),join(a,a))) = meet(meet(b,join(a,meet(a,c))),join(a,a)),
inference(symmetry,[status(thm)],[69]) ).
tff(71,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(a,c)),join(a,a)) = join(a,meet(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
meet(join(a,meet(a,c)),join(a,a)) = join(a,meet(a,c)),
inference(unit_resolution,[status(thm)],[71,16]) ).
tff(73,plain,
join(a,meet(a,c)) = meet(join(a,meet(a,c)),join(a,a)),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
meet(b,join(a,meet(a,c))) = meet(b,meet(join(a,meet(a,c)),join(a,a))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
meet(join(a,meet(a,c)),b) = meet(b,join(a,meet(a,c))),
inference(symmetry,[status(thm)],[66]) ).
tff(76,plain,
meet(join(a,meet(a,c)),b) = meet(join(a,meet(a,c)),meet(a,b)),
inference(transitivity,[status(thm)],[75,74,70,67,55,46,43]) ).
tff(77,plain,
meet(join(meet(a,c),a),join(meet(a,b),meet(a,c))) = meet(join(a,meet(a,c)),join(meet(a,b),meet(a,c))),
inference(symmetry,[status(thm)],[33]) ).
tff(78,plain,
meet(join(meet(a,b),meet(a,c)),join(meet(a,c),a)) = meet(join(meet(a,c),a),join(meet(a,b),meet(a,c))),
inference(symmetry,[status(thm)],[29]) ).
tff(79,plain,
meet(join(meet(a,c),meet(a,b)),join(meet(a,c),a)) = meet(join(meet(a,b),meet(a,c)),join(meet(a,c),a)),
inference(symmetry,[status(thm)],[20]) ).
tff(80,plain,
join(meet(a,c),meet(a,b)) = meet(join(meet(a,c),meet(a,b)),join(meet(a,c),a)),
inference(symmetry,[status(thm)],[18]) ).
tff(81,plain,
join(meet(a,b),meet(a,c)) = meet(join(a,meet(a,c)),join(meet(a,b),meet(a,c))),
inference(transitivity,[status(thm)],[19,80,79,78,77]) ).
tff(82,plain,
join(join(meet(a,b),meet(a,c)),meet(join(a,meet(a,c)),b)) = join(meet(join(a,meet(a,c)),join(meet(a,b),meet(a,c))),meet(join(a,meet(a,c)),meet(a,b))),
inference(monotonicity,[status(thm)],[81,76]) ).
tff(83,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(84,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)],[83]) ).
tff(85,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(86,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(87,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(a,b),meet(a,c)),meet(join(a,meet(a,c)),b)) = join(meet(a,b),join(meet(a,c),meet(join(a,meet(a,c)),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
join(join(meet(a,b),meet(a,c)),meet(join(a,meet(a,c)),b)) = join(meet(a,b),join(meet(a,c),meet(join(a,meet(a,c)),b))),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
join(meet(a,b),join(meet(a,c),meet(join(a,meet(a,c)),b))) = join(join(meet(a,b),meet(a,c)),meet(join(a,meet(a,c)),b)),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,c),meet(join(a,meet(a,c)),b)) = join(meet(join(a,meet(a,c)),b),meet(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
join(meet(a,c),meet(join(a,meet(a,c)),b)) = join(meet(join(a,meet(a,c)),b),meet(a,c)),
inference(unit_resolution,[status(thm)],[93,7]) ).
tff(95,plain,
join(meet(join(a,meet(a,c)),b),meet(a,c)) = join(meet(a,c),meet(join(a,meet(a,c)),b)),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y) )
<=> ( join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modularity_axiom) ).
tff(100,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y) ),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y) )
| ( join(meet(join(b,meet(a,c)),a),meet(a,c)) = join(meet(join(a,meet(a,c)),b),meet(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
join(meet(join(b,meet(a,c)),a),meet(a,c)) = join(meet(join(a,meet(a,c)),b),meet(a,c)),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,meet(a,c)),a) = meet(a,join(b,meet(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
meet(join(b,meet(a,c)),a) = meet(a,join(b,meet(a,c))),
inference(unit_resolution,[status(thm)],[105,27]) ).
tff(107,plain,
meet(a,join(b,meet(a,c))) = meet(join(b,meet(a,c)),a),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
join(meet(a,join(b,meet(a,c))),meet(a,c)) = join(meet(join(b,meet(a,c)),a),meet(a,c)),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
join(meet(a,join(b,meet(a,c))),meet(a,c)) = join(meet(a,c),meet(join(a,meet(a,c)),b)),
inference(transitivity,[status(thm)],[108,104,95]) ).
tff(110,plain,
join(meet(a,b),join(meet(a,join(b,meet(a,c))),meet(a,c))) = join(meet(a,b),join(meet(a,c),meet(join(a,meet(a,c)),b))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(a,b),meet(a,join(b,meet(a,c)))),meet(a,c)) = join(meet(a,b),join(meet(a,join(b,meet(a,c))),meet(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
join(join(meet(a,b),meet(a,join(b,meet(a,c)))),meet(a,c)) = join(meet(a,b),join(meet(a,join(b,meet(a,c))),meet(a,c))),
inference(unit_resolution,[status(thm)],[111,89]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),meet(a,join(b,meet(a,c)))) = join(meet(a,join(b,meet(a,c))),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
join(meet(a,b),meet(a,join(b,meet(a,c)))) = join(meet(a,join(b,meet(a,c))),meet(a,b)),
inference(unit_resolution,[status(thm)],[113,7]) ).
tff(115,plain,
join(meet(a,join(b,meet(a,c))),meet(a,b)) = join(meet(a,b),meet(a,join(b,meet(a,c)))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,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(b,meet(a,c))),meet(a,b)) = meet(a,join(b,meet(a,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
join(meet(a,join(b,meet(a,c))),meet(a,b)) = meet(a,join(b,meet(a,c))),
inference(unit_resolution,[status(thm)],[116,40]) ).
tff(118,plain,
meet(a,join(b,meet(a,c))) = join(meet(a,join(b,meet(a,c))),meet(a,b)),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
meet(join(b,meet(a,c)),a) = join(meet(a,b),meet(a,join(b,meet(a,c)))),
inference(transitivity,[status(thm)],[106,118,115]) ).
tff(120,plain,
join(meet(join(b,meet(a,c)),a),meet(a,c)) = join(join(meet(a,b),meet(a,join(b,meet(a,c)))),meet(a,c)),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
^ [X: $i] :
refl(
( ( meet(X,X) = X )
<=> ( meet(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,axiom,
! [X: $i] : ( meet(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_of_meet) ).
tff(125,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(a,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
meet(a,a) = a,
inference(unit_resolution,[status(thm)],[128,127]) ).
tff(130,plain,
a = meet(a,a),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
meet(a,c) = meet(meet(a,a),c),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
meet(meet(a,a),c) = meet(a,c),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,a),c) = meet(a,meet(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
meet(meet(a,a),c) = meet(a,meet(a,c)),
inference(unit_resolution,[status(thm)],[133,53]) ).
tff(135,plain,
meet(a,meet(a,c)) = meet(meet(a,a),c),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
meet(a,meet(a,c)) = meet(a,c),
inference(transitivity,[status(thm)],[135,132]) ).
tff(137,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,c),b) = join(b,meet(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
join(meet(a,c),b) = join(b,meet(a,c)),
inference(unit_resolution,[status(thm)],[137,7]) ).
tff(139,plain,
join(b,meet(a,c)) = join(meet(a,c),b),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
meet(a,join(b,meet(a,c))) = meet(a,join(meet(a,c),b)),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
meet(a,join(meet(a,c),b)) = meet(a,join(b,meet(a,c))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
meet(a,join(meet(a,c),b)) = meet(join(b,meet(a,c)),a),
inference(transitivity,[status(thm)],[141,107]) ).
tff(143,plain,
join(meet(a,join(meet(a,c),b)),meet(a,meet(a,c))) = join(meet(join(b,meet(a,c)),a),meet(a,c)),
inference(monotonicity,[status(thm)],[142,136]) ).
tff(144,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(meet(a,c),b)),meet(a,meet(a,c))) = meet(a,join(meet(a,c),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
join(meet(a,join(meet(a,c),b)),meet(a,meet(a,c))) = meet(a,join(meet(a,c),b)),
inference(unit_resolution,[status(thm)],[144,40]) ).
tff(146,plain,
meet(a,join(meet(a,c),b)) = join(meet(a,join(meet(a,c),b)),meet(a,meet(a,c))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
meet(a,join(b,meet(a,c))) = join(meet(a,b),meet(a,c)),
inference(transitivity,[status(thm)],[140,146,143,120,112,110,92,82,42,33,29,20,18,9]) ).
tff(148,plain,
( ( meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)) )
<=> ( meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,axiom,
meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_modularity) ).
tff(150,plain,
meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
$false,
inference(unit_resolution,[status(thm)],[150,147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : LAT023-1 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Sep 1 10:10:37 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 3.34/2.40 % SZS status Unsatisfiable
% 3.34/2.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------