TSTP Solution File: LAT040-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT040-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 18:31:50 EDT 2022
% Result : Unsatisfiable 0.18s 0.44s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 50
% Syntax : Number of formulae : 138 ( 98 unt; 5 typ; 0 def)
% Number of atoms : 182 ( 174 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 64 ( 22 ~; 18 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 7 ( 7 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 : 193 ( 176 !; 0 ?; 193 :)
% Comments :
%------------------------------------------------------------------------------
tff(zz_type,type,
zz: $i ).
tff(yy_type,type,
yy: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(xx_type,type,
xx: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(5,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(zz,join(zz,xx)) = zz ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
meet(zz,join(zz,xx)) = zz,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( join(xx,yy) = join(xx,zz) )
<=> ( join(xx,yy) = join(xx,zz) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
join(xx,yy) = join(xx,zz),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs1) ).
tff(12,plain,
join(xx,yy) = join(xx,zz),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
join(xx,zz) = join(xx,yy),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(15,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)],[14]) ).
tff(16,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(17,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(18,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(zz,xx) = join(xx,zz) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
join(zz,xx) = join(xx,zz),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
join(zz,xx) = join(xx,yy),
inference(transitivity,[status(thm)],[22,13]) ).
tff(24,plain,
meet(zz,join(zz,xx)) = meet(zz,join(xx,yy)),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
meet(zz,join(xx,yy)) = meet(zz,join(zz,xx)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,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(27,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)],[26]) ).
tff(28,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(29,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_meet) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(zz,join(xx,yy)) = join(meet(zz,xx),meet(zz,yy)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
meet(zz,join(xx,yy)) = join(meet(zz,xx),meet(zz,yy)),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
join(meet(zz,xx),meet(zz,yy)) = meet(zz,join(xx,yy)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(37,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)],[36]) ).
tff(38,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(39,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(40,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(zz,xx) = meet(xx,zz) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
meet(zz,xx) = meet(xx,zz),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
join(meet(zz,xx),meet(zz,yy)) = join(meet(xx,zz),meet(zz,yy)),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
join(meet(xx,zz),meet(zz,yy)) = join(meet(zz,xx),meet(zz,yy)),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
<=> ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_join) ).
tff(51,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
| ( join(meet(xx,zz),meet(zz,yy)) = meet(join(meet(xx,zz),zz),join(meet(xx,zz),yy)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
join(meet(xx,zz),meet(zz,yy)) = meet(join(meet(xx,zz),zz),join(meet(xx,zz),yy)),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
meet(join(meet(xx,zz),zz),join(meet(xx,zz),yy)) = join(meet(xx,zz),meet(zz,yy)),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(58,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)],[57]) ).
tff(59,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(60,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(61,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(yy,meet(yy,xx)) = yy ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
join(yy,meet(yy,xx)) = yy,
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(yy,xx) = meet(xx,yy) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
meet(yy,xx) = meet(xx,yy),
inference(unit_resolution,[status(thm)],[66,42]) ).
tff(68,plain,
meet(xx,yy) = meet(yy,xx),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ( meet(xx,yy) = meet(xx,zz) )
<=> ( meet(xx,yy) = meet(xx,zz) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,axiom,
meet(xx,yy) = meet(xx,zz),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs2) ).
tff(71,plain,
meet(xx,yy) = meet(xx,zz),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
meet(xx,zz) = meet(xx,yy),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
meet(xx,zz) = meet(yy,xx),
inference(transitivity,[status(thm)],[72,68]) ).
tff(74,plain,
join(yy,meet(xx,zz)) = join(yy,meet(yy,xx)),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(xx,zz),yy) = join(yy,meet(xx,zz)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
join(meet(xx,zz),yy) = join(yy,meet(xx,zz)),
inference(unit_resolution,[status(thm)],[75,20]) ).
tff(77,plain,
join(meet(xx,zz),yy) = yy,
inference(transitivity,[status(thm)],[76,74,65]) ).
tff(78,plain,
meet(join(meet(xx,zz),zz),join(meet(xx,zz),yy)) = meet(join(meet(xx,zz),zz),yy),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
meet(join(meet(xx,zz),zz),yy) = meet(join(meet(xx,zz),zz),join(meet(xx,zz),yy)),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(zz,meet(zz,xx)) = zz ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
join(zz,meet(zz,xx)) = zz,
inference(unit_resolution,[status(thm)],[80,63]) ).
tff(82,plain,
meet(xx,zz) = meet(zz,xx),
inference(symmetry,[status(thm)],[44]) ).
tff(83,plain,
join(zz,meet(xx,zz)) = join(zz,meet(zz,xx)),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(xx,zz),zz) = join(zz,meet(xx,zz)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
join(meet(xx,zz),zz) = join(zz,meet(xx,zz)),
inference(unit_resolution,[status(thm)],[84,20]) ).
tff(86,plain,
join(meet(xx,zz),zz) = zz,
inference(transitivity,[status(thm)],[85,83,81]) ).
tff(87,plain,
meet(join(meet(xx,zz),zz),yy) = meet(zz,yy),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
meet(zz,yy) = meet(join(meet(xx,zz),zz),yy),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(zz,yy) = meet(yy,zz) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
meet(zz,yy) = meet(yy,zz),
inference(unit_resolution,[status(thm)],[89,42]) ).
tff(91,plain,
meet(yy,zz) = meet(zz,yy),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(yy,zz),meet(meet(yy,zz),xx)) = meet(yy,zz) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
join(meet(yy,zz),meet(meet(yy,zz),xx)) = meet(yy,zz),
inference(unit_resolution,[status(thm)],[92,63]) ).
tff(94,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(xx,zz),join(meet(xx,zz),yy)) = meet(xx,zz) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
meet(meet(xx,zz),join(meet(xx,zz),yy)) = meet(xx,zz),
inference(unit_resolution,[status(thm)],[94,7]) ).
tff(96,plain,
join(yy,meet(xx,zz)) = join(meet(xx,zz),yy),
inference(symmetry,[status(thm)],[76]) ).
tff(97,plain,
meet(meet(xx,zz),join(yy,meet(xx,zz))) = meet(meet(xx,zz),join(meet(xx,zz),yy)),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
join(yy,meet(yy,xx)) = join(yy,meet(xx,zz)),
inference(symmetry,[status(thm)],[74]) ).
tff(99,plain,
yy = join(yy,meet(yy,xx)),
inference(symmetry,[status(thm)],[65]) ).
tff(100,plain,
yy = join(yy,meet(xx,zz)),
inference(transitivity,[status(thm)],[99,98]) ).
tff(101,plain,
meet(meet(xx,zz),yy) = meet(meet(xx,zz),join(yy,meet(xx,zz))),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(xx,zz),yy) = meet(yy,meet(xx,zz)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
meet(meet(xx,zz),yy) = meet(yy,meet(xx,zz)),
inference(unit_resolution,[status(thm)],[102,42]) ).
tff(104,plain,
meet(yy,meet(xx,zz)) = meet(meet(xx,zz),yy),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
meet(yy,meet(zz,xx)) = meet(yy,meet(xx,zz)),
inference(monotonicity,[status(thm)],[44]) ).
tff(106,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(107,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)],[106]) ).
tff(108,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(109,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(110,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(yy,zz),xx) = meet(yy,meet(zz,xx)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
meet(meet(yy,zz),xx) = meet(yy,meet(zz,xx)),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
meet(meet(yy,zz),xx) = meet(yy,xx),
inference(transitivity,[status(thm)],[114,105,104,101,97,95,72,68]) ).
tff(116,plain,
join(meet(yy,zz),meet(meet(yy,zz),xx)) = join(meet(yy,zz),meet(yy,xx)),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
join(meet(yy,zz),meet(yy,xx)) = join(meet(yy,zz),meet(meet(yy,zz),xx)),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(yy,join(zz,xx)) = join(meet(yy,zz),meet(yy,xx)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
meet(yy,join(zz,xx)) = join(meet(yy,zz),meet(yy,xx)),
inference(unit_resolution,[status(thm)],[118,32]) ).
tff(120,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(yy,xx) = join(xx,yy) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
join(yy,xx) = join(xx,yy),
inference(unit_resolution,[status(thm)],[120,20]) ).
tff(122,plain,
join(xx,yy) = join(yy,xx),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
join(zz,xx) = join(yy,xx),
inference(transitivity,[status(thm)],[22,13,122]) ).
tff(124,plain,
meet(yy,join(zz,xx)) = meet(yy,join(yy,xx)),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
meet(yy,join(yy,xx)) = meet(yy,join(zz,xx)),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(yy,join(yy,xx)) = yy ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
meet(yy,join(yy,xx)) = yy,
inference(unit_resolution,[status(thm)],[126,7]) ).
tff(128,plain,
yy = meet(yy,join(yy,xx)),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
yy = zz,
inference(transitivity,[status(thm)],[128,125,119,117,93,91,88,79,56,46,35,25,9]) ).
tff(130,plain,
( ( yy != zz )
<=> ( yy != zz ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,axiom,
yy != zz,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rhs) ).
tff(132,plain,
yy != zz,
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
$false,
inference(unit_resolution,[status(thm)],[132,129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT040-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Sep 1 10:44:43 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.
% 0.18/0.44 % SZS status Unsatisfiable
% 0.18/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------