%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT040-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 Jun 21 05:13:47 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 43
% Syntax : Number of formulae : 128 ( 94 unt; 0 typ; 0 def)
% Number of atoms : 174 ( 167 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 63 ( 23 ~; 19 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 169 ( 155 !; 0 ?; 169 :)
% 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/sandbox/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,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(14,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(yy,xx) = join(xx,yy) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
join(yy,xx) = join(xx,yy),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
join(xx,yy) = join(yy,xx),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ( join(xx,yy) = join(xx,zz) )
<=> ( join(xx,yy) = join(xx,zz) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
join(xx,yy) = join(xx,zz),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs1) ).
tff(22,plain,
join(xx,yy) = join(xx,zz),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
join(xx,zz) = join(xx,yy),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(zz,xx) = join(xx,zz) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
join(zz,xx) = join(xx,zz),
inference(unit_resolution,[status(thm)],[24,16]) ).
tff(26,plain,
join(zz,xx) = join(yy,xx),
inference(transitivity,[status(thm)],[25,23,19]) ).
tff(27,plain,
meet(zz,join(zz,xx)) = meet(zz,join(yy,xx)),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
meet(zz,join(yy,xx)) = meet(zz,join(zz,xx)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,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(30,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)],[29]) ).
tff(31,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(32,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',dist_meet) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) )
| ( meet(zz,join(yy,xx)) = join(meet(zz,yy),meet(zz,xx)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
meet(zz,join(yy,xx)) = join(meet(zz,yy),meet(zz,xx)),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
join(meet(zz,yy),meet(zz,xx)) = meet(zz,join(yy,xx)),
inference(symmetry,[status(thm)],[37]) ).
tff(39,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(40,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)],[39]) ).
tff(41,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(42,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
tff(43,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(zz,yy),xx) = meet(zz,meet(yy,xx)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
meet(meet(zz,yy),xx) = meet(zz,meet(yy,xx)),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
meet(zz,meet(yy,xx)) = meet(meet(zz,yy),xx),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ( meet(xx,yy) = meet(xx,zz) )
<=> ( meet(xx,yy) = meet(xx,zz) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
meet(xx,yy) = meet(xx,zz),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs2) ).
tff(51,plain,
meet(xx,yy) = meet(xx,zz),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(53,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)],[52]) ).
tff(54,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(55,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(56,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(yy,xx) = meet(xx,yy) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
meet(yy,xx) = meet(xx,yy),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
meet(yy,xx) = meet(xx,zz),
inference(transitivity,[status(thm)],[60,51]) ).
tff(62,plain,
meet(zz,meet(yy,xx)) = meet(zz,meet(xx,zz)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
meet(zz,meet(xx,zz)) = meet(zz,meet(yy,xx)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(xx,zz),zz) = meet(zz,meet(xx,zz)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
meet(meet(xx,zz),zz) = meet(zz,meet(xx,zz)),
inference(unit_resolution,[status(thm)],[64,58]) ).
tff(66,plain,
meet(xx,yy) = meet(yy,xx),
inference(symmetry,[status(thm)],[60]) ).
tff(67,plain,
meet(xx,zz) = meet(xx,yy),
inference(symmetry,[status(thm)],[51]) ).
tff(68,plain,
meet(xx,zz) = meet(yy,xx),
inference(transitivity,[status(thm)],[67,66]) ).
tff(69,plain,
meet(meet(xx,zz),zz) = meet(meet(yy,xx),zz),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
meet(meet(yy,xx),zz) = meet(meet(xx,zz),zz),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(yy,xx),zz) = meet(yy,meet(xx,zz)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
meet(meet(yy,xx),zz) = meet(yy,meet(xx,zz)),
inference(unit_resolution,[status(thm)],[71,45]) ).
tff(73,plain,
meet(yy,meet(xx,zz)) = meet(meet(yy,xx),zz),
inference(symmetry,[status(thm)],[72]) ).
tff(74,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(75,plain,
meet(meet(xx,zz),yy) = meet(yy,meet(xx,zz)),
inference(unit_resolution,[status(thm)],[74,58]) ).
tff(76,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(77,plain,
join(meet(xx,zz),yy) = join(yy,meet(xx,zz)),
inference(unit_resolution,[status(thm)],[76,16]) ).
tff(78,plain,
join(yy,meet(xx,zz)) = join(meet(xx,zz),yy),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
join(yy,meet(xx,zz)) = join(yy,meet(yy,xx)),
inference(monotonicity,[status(thm)],[68]) ).
tff(80,plain,
join(yy,meet(yy,xx)) = join(yy,meet(xx,zz)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(82,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)],[81]) ).
tff(83,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(84,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(85,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(yy,meet(yy,xx)) = yy ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
join(yy,meet(yy,xx)) = yy,
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
yy = join(yy,meet(yy,xx)),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
yy = join(meet(xx,zz),yy),
inference(transitivity,[status(thm)],[90,80,78]) ).
tff(92,plain,
meet(meet(xx,zz),yy) = meet(meet(xx,zz),join(meet(xx,zz),yy)),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
meet(meet(xx,zz),join(meet(xx,zz),yy)) = meet(meet(xx,zz),yy),
inference(symmetry,[status(thm)],[92]) ).
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,
meet(xx,zz) = meet(meet(xx,zz),join(meet(xx,zz),yy)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(zz,xx) = meet(xx,zz) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
meet(zz,xx) = meet(xx,zz),
inference(unit_resolution,[status(thm)],[97,58]) ).
tff(99,plain,
meet(zz,xx) = meet(meet(zz,yy),xx),
inference(transitivity,[status(thm)],[98,96,93,75,73,70,65,63,48]) ).
tff(100,plain,
join(meet(zz,yy),meet(zz,xx)) = join(meet(zz,yy),meet(meet(zz,yy),xx)),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
join(meet(zz,yy),meet(meet(zz,yy),xx)) = join(meet(zz,yy),meet(zz,xx)),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(zz,yy),meet(meet(zz,yy),xx)) = meet(zz,yy) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
join(meet(zz,yy),meet(meet(zz,yy),xx)) = meet(zz,yy),
inference(unit_resolution,[status(thm)],[102,87]) ).
tff(104,plain,
meet(zz,yy) = join(meet(zz,yy),meet(meet(zz,yy),xx)),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(zz,yy) = meet(yy,zz) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
meet(zz,yy) = meet(yy,zz),
inference(unit_resolution,[status(thm)],[105,58]) ).
tff(107,plain,
meet(yy,zz) = meet(zz,yy),
inference(symmetry,[status(thm)],[106]) ).
tff(108,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(109,plain,
join(meet(yy,zz),meet(meet(yy,zz),xx)) = meet(yy,zz),
inference(unit_resolution,[status(thm)],[108,87]) ).
tff(110,plain,
meet(yy,meet(xx,zz)) = meet(meet(xx,zz),yy),
inference(symmetry,[status(thm)],[75]) ).
tff(111,plain,
meet(yy,meet(zz,xx)) = meet(yy,meet(xx,zz)),
inference(monotonicity,[status(thm)],[98]) ).
tff(112,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(113,plain,
meet(meet(yy,zz),xx) = meet(yy,meet(zz,xx)),
inference(unit_resolution,[status(thm)],[112,45]) ).
tff(114,plain,
meet(meet(yy,zz),xx) = meet(yy,xx),
inference(transitivity,[status(thm)],[113,111,110,92,95,67,66]) ).
tff(115,plain,
join(meet(yy,zz),meet(meet(yy,zz),xx)) = join(meet(yy,zz),meet(yy,xx)),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
join(meet(yy,zz),meet(yy,xx)) = join(meet(yy,zz),meet(meet(yy,zz),xx)),
inference(symmetry,[status(thm)],[115]) ).
tff(117,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(118,plain,
meet(yy,join(zz,xx)) = join(meet(yy,zz),meet(yy,xx)),
inference(unit_resolution,[status(thm)],[117,35]) ).
tff(119,plain,
meet(yy,join(zz,xx)) = meet(yy,join(yy,xx)),
inference(monotonicity,[status(thm)],[26]) ).
tff(120,plain,
meet(yy,join(yy,xx)) = meet(yy,join(zz,xx)),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(yy,join(yy,xx)) = yy ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
meet(yy,join(yy,xx)) = yy,
inference(unit_resolution,[status(thm)],[121,7]) ).
tff(123,plain,
yy = meet(yy,join(yy,xx)),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
yy = zz,
inference(transitivity,[status(thm)],[123,120,118,116,109,107,104,101,38,28,9]) ).
tff(125,plain,
( ( yy != zz )
<=> ( yy != zz ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,axiom,
yy != zz,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rhs) ).
tff(127,plain,
yy != zz,
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
$false,
inference(unit_resolution,[status(thm)],[127,124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : LAT040-1 : TPTP v9.0.0. Released v2.4.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 Jun 19 19:28:42 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------