%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT037-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:13:46 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 46
% Syntax : Number of formulae : 128 ( 84 unt; 0 typ; 0 def)
% Number of atoms : 212 ( 204 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 131 ( 54 ~; 46 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 7 ( 7 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 181 ( 166 !; 0 ?; 181 :)
% Comments :
%------------------------------------------------------------------------------
tff(zz_type,type,
zz: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(yy_type,type,
yy: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(xx_type,type,
xx: $i ).
tff(n1_type,type,
n1: $i ).
tff(n0_type,type,
n0: $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(zz,xx) = join(xx,zz) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
join(zz,xx) = join(xx,zz),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
join(xx,zz) = join(zz,xx),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ( join(xx,zz) = n1 )
<=> ( join(xx,zz) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
join(xx,zz) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs2) ).
tff(22,plain,
join(xx,zz) = n1,
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
n1 = join(xx,zz),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
n1 = join(zz,xx),
inference(transitivity,[status(thm)],[23,19]) ).
tff(25,plain,
meet(zz,n1) = meet(zz,join(zz,xx)),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( join(xx,yy) = n1 )
<=> ( join(xx,yy) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
join(xx,yy) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs1) ).
tff(28,plain,
join(xx,yy) = n1,
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
meet(zz,join(xx,yy)) = meet(zz,n1),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,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(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(quant_intro,[status(thm)],[30]) ).
tff(32,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(33,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(34,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,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(38,plain,
meet(zz,join(xx,yy)) = join(meet(zz,xx),meet(zz,yy)),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
join(meet(zz,xx),meet(zz,yy)) = meet(zz,join(xx,yy)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(41,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)],[40]) ).
tff(42,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(43,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(44,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(zz,xx) = meet(xx,zz) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
meet(zz,xx) = meet(xx,zz),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
meet(xx,zz) = meet(zz,xx),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
( ( meet(xx,zz) = n0 )
<=> ( meet(xx,zz) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
meet(xx,zz) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs4) ).
tff(52,plain,
meet(xx,zz) = n0,
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
n0 = meet(xx,zz),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
n0 = meet(zz,xx),
inference(transitivity,[status(thm)],[53,49]) ).
tff(55,plain,
join(n0,meet(zz,yy)) = join(meet(zz,xx),meet(zz,yy)),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
^ [X: $i] :
refl(( ( meet(X,n0) = n0 )
<=> ( meet(X,n0) = n0 ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [X: $i] : ( meet(X,n0) = n0 )
<=> ! [X: $i] : ( meet(X,n0) = n0 ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X: $i] : ( meet(X,n0) = n0 )
<=> ! [X: $i] : ( meet(X,n0) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
! [X: $i] : ( meet(X,n0) = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_0) ).
tff(60,plain,
! [X: $i] : ( meet(X,n0) = n0 ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [X: $i] : ( meet(X,n0) = n0 ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [X: $i] : ( meet(X,n0) = n0 ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( ~ ! [X: $i] : ( meet(X,n0) = n0 )
| ( meet(yy,n0) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
meet(yy,n0) = n0,
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(n0,yy) = meet(yy,n0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
meet(n0,yy) = meet(yy,n0),
inference(unit_resolution,[status(thm)],[65,46]) ).
tff(67,plain,
meet(n0,yy) = n0,
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
<=> ( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular) ).
tff(72,plain,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(n0,yy) != n0 )
| ( meet(yy,join(n0,zz)) = join(n0,meet(zz,yy)) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(n0,yy) != n0 )
| ( meet(yy,join(n0,zz)) = join(n0,meet(zz,yy)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(n0,yy) != n0 )
| ( meet(yy,join(n0,zz)) = join(n0,meet(zz,yy)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(n0,yy) != n0 )
| ( meet(yy,join(n0,zz)) = join(n0,meet(zz,yy)) ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
meet(yy,join(n0,zz)) = join(n0,meet(zz,yy)),
inference(unit_resolution,[status(thm)],[77,74,67]) ).
tff(79,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(n0,zz) = join(zz,n0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
join(n0,zz) = join(zz,n0),
inference(unit_resolution,[status(thm)],[79,16]) ).
tff(81,plain,
join(zz,n0) = join(n0,zz),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
join(zz,n0) = join(zz,meet(zz,xx)),
inference(monotonicity,[status(thm)],[54]) ).
tff(83,plain,
join(zz,meet(zz,xx)) = join(zz,n0),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(85,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)],[84]) ).
tff(86,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(87,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(88,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(zz,meet(zz,xx)) = zz ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
join(zz,meet(zz,xx)) = zz,
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
zz = join(zz,meet(zz,xx)),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
zz = join(n0,zz),
inference(transitivity,[status(thm)],[93,83,81]) ).
tff(95,plain,
meet(yy,zz) = meet(yy,join(n0,zz)),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(zz,yy) = meet(yy,zz) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
meet(zz,yy) = meet(yy,zz),
inference(unit_resolution,[status(thm)],[96,46]) ).
tff(98,plain,
meet(zz,yy) = zz,
inference(transitivity,[status(thm)],[97,95,78,55,39,29,25,9]) ).
tff(99,plain,
( ( meet(xx,yy) = n0 )
<=> ( meet(xx,yy) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
meet(xx,yy) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs3) ).
tff(101,plain,
meet(xx,yy) = n0,
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
meet(xx,yy) = meet(zz,xx),
inference(transitivity,[status(thm)],[101,53,49]) ).
tff(103,plain,
join(zz,meet(xx,yy)) = join(zz,meet(zz,xx)),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
join(zz,meet(xx,yy)) = zz,
inference(transitivity,[status(thm)],[103,92]) ).
tff(105,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(yy,join(yy,xx)) = yy ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
meet(yy,join(yy,xx)) = yy,
inference(unit_resolution,[status(thm)],[105,7]) ).
tff(107,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(yy,xx) = join(xx,yy) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
join(yy,xx) = join(xx,yy),
inference(unit_resolution,[status(thm)],[107,16]) ).
tff(109,plain,
join(xx,yy) = join(yy,xx),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
n1 = join(xx,yy),
inference(symmetry,[status(thm)],[28]) ).
tff(111,plain,
n1 = join(yy,xx),
inference(transitivity,[status(thm)],[110,109]) ).
tff(112,plain,
meet(yy,n1) = meet(yy,join(yy,xx)),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
join(zz,xx) = n1,
inference(transitivity,[status(thm)],[18,22]) ).
tff(114,plain,
meet(yy,join(zz,xx)) = meet(yy,n1),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
meet(yy,join(zz,xx)) = yy,
inference(transitivity,[status(thm)],[114,112,106]) ).
tff(116,plain,
( ( meet(yy,join(zz,xx)) = join(zz,meet(xx,yy)) )
<=> ( yy = zz ) ),
inference(monotonicity,[status(thm)],[115,104]) ).
tff(117,plain,
( ( yy = zz )
<=> ( meet(yy,join(zz,xx)) = join(zz,meet(xx,yy)) ) ),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
( ( yy != zz )
<=> ( meet(yy,join(zz,xx)) != join(zz,meet(xx,yy)) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( yy != zz )
<=> ( yy != zz ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,axiom,
yy != zz,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rhs) ).
tff(121,plain,
yy != zz,
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
meet(yy,join(zz,xx)) != join(zz,meet(xx,yy)),
inference(modus_ponens,[status(thm)],[121,118]) ).
tff(123,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(zz,yy) != zz )
| ( meet(yy,join(zz,xx)) = join(zz,meet(xx,yy)) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(zz,yy) != zz )
| ( meet(yy,join(zz,xx)) = join(zz,meet(xx,yy)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(zz,yy) != zz )
| ( meet(yy,join(zz,xx)) = join(zz,meet(xx,yy)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(zz,yy) != zz )
| ( meet(yy,join(zz,xx)) = join(zz,meet(xx,yy)) ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( ( meet(zz,yy) != zz )
| ( meet(yy,join(zz,xx)) = join(zz,meet(xx,yy)) ) ),
inference(unit_resolution,[status(thm)],[125,74]) ).
tff(127,plain,
meet(zz,yy) != zz,
inference(unit_resolution,[status(thm)],[126,122]) ).
tff(128,plain,
$false,
inference(unit_resolution,[status(thm)],[127,98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT037-1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.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 Jun 19 19:28:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------