TSTP Solution File: LAT037-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT037-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 Sep 17 18:31:49 EDT 2022
% Result : Unsatisfiable 0.16s 0.44s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 54
% Syntax : Number of formulae : 136 ( 84 unt; 7 typ; 0 def)
% Number of atoms : 210 ( 199 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 113 ( 42 ~; 34 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 205 ( 185 !; 0 ?; 205 :)
% 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/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,
^ [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/sandbox2/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) = join(xx,yy) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( join(xx,zz) = n1 )
<=> ( join(xx,zz) = n1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
join(xx,zz) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs2) ).
tff(23,plain,
join(xx,zz) = n1,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
join(xx,zz) = join(xx,yy),
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
join(xx,yy) = join(xx,zz),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
join(xx,yy) = join(zz,xx),
inference(transitivity,[status(thm)],[25,19]) ).
tff(27,plain,
meet(zz,join(xx,yy)) = meet(zz,join(zz,xx)),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(yy,xx) = join(xx,yy) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
join(yy,xx) = join(xx,yy),
inference(unit_resolution,[status(thm)],[28,16]) ).
tff(30,plain,
meet(zz,join(yy,xx)) = meet(zz,join(xx,yy)),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,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(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(quant_intro,[status(thm)],[31]) ).
tff(33,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(34,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(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)],[34,33]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,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(39,plain,
meet(zz,join(yy,xx)) = join(meet(zz,yy),meet(zz,xx)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
join(meet(zz,yy),meet(zz,xx)) = meet(zz,join(yy,xx)),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(42,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)],[41]) ).
tff(43,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(44,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(45,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(zz,xx) = meet(xx,zz) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
meet(zz,xx) = meet(xx,zz),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
meet(xx,zz) = meet(zz,xx),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
^ [X: $i] :
refl(
( ( meet(X,meet(xx,zz)) = meet(xx,zz) )
<=> ( meet(X,meet(xx,zz)) = meet(xx,zz) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X: $i] : ( meet(X,meet(xx,zz)) = meet(xx,zz) )
<=> ! [X: $i] : ( meet(X,meet(xx,zz)) = meet(xx,zz) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
^ [X: $i] :
rewrite(
( ( meet(X,meet(xx,yy)) = meet(xx,yy) )
<=> ( meet(X,meet(xx,zz)) = meet(xx,zz) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [X: $i] : ( meet(X,meet(xx,yy)) = meet(xx,yy) )
<=> ! [X: $i] : ( meet(X,meet(xx,zz)) = meet(xx,zz) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
^ [X: $i] :
rewrite(
( ( meet(X,n0) = n0 )
<=> ( meet(X,meet(xx,yy)) = meet(xx,yy) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [X: $i] : ( meet(X,n0) = n0 )
<=> ! [X: $i] : ( meet(X,meet(xx,yy)) = meet(xx,yy) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [X: $i] : ( meet(X,n0) = n0 )
<=> ! [X: $i] : ( meet(X,n0) = n0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
! [X: $i] : ( meet(X,n0) = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_meet_0) ).
tff(59,plain,
! [X: $i] : ( meet(X,n0) = n0 ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [X: $i] : ( meet(X,meet(xx,yy)) = meet(xx,yy) ),
inference(modus_ponens,[status(thm)],[59,56]) ).
tff(61,plain,
! [X: $i] : ( meet(X,meet(xx,zz)) = meet(xx,zz) ),
inference(modus_ponens,[status(thm)],[60,54]) ).
tff(62,plain,
! [X: $i] : ( meet(X,meet(xx,zz)) = meet(xx,zz) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [X: $i] : ( meet(X,meet(xx,zz)) = meet(xx,zz) ),
inference(modus_ponens,[status(thm)],[62,52]) ).
tff(64,plain,
( ~ ! [X: $i] : ( meet(X,meet(xx,zz)) = meet(xx,zz) )
| ( meet(zz,meet(xx,zz)) = meet(xx,zz) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
meet(zz,meet(xx,zz)) = meet(xx,zz),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( ( meet(xx,zz) = n0 )
<=> ( meet(xx,zz) = meet(xx,yy) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( meet(xx,zz) = n0 )
<=> ( meet(xx,zz) = n0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
meet(xx,zz) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs4) ).
tff(69,plain,
meet(xx,zz) = n0,
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
meet(xx,zz) = meet(xx,yy),
inference(modus_ponens,[status(thm)],[69,66]) ).
tff(71,plain,
meet(xx,yy) = meet(xx,zz),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
meet(zz,meet(xx,yy)) = meet(zz,meet(xx,zz)),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(yy,xx) = meet(xx,yy) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
meet(yy,xx) = meet(xx,yy),
inference(unit_resolution,[status(thm)],[73,47]) ).
tff(75,plain,
meet(zz,meet(yy,xx)) = meet(zz,meet(xx,yy)),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,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(77,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)],[76]) ).
tff(78,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(79,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(80,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,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(84,plain,
meet(meet(zz,yy),xx) = meet(zz,meet(yy,xx)),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
meet(meet(zz,yy),xx) = meet(zz,xx),
inference(transitivity,[status(thm)],[84,75,72,65,50]) ).
tff(86,plain,
join(meet(zz,yy),meet(meet(zz,yy),xx)) = join(meet(zz,yy),meet(zz,xx)),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(88,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)],[87]) ).
tff(89,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(90,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(91,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,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(95,plain,
join(meet(zz,yy),meet(meet(zz,yy),xx)) = meet(zz,yy),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
meet(zz,yy) = join(meet(zz,yy),meet(meet(zz,yy),xx)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
meet(zz,yy) = zz,
inference(transitivity,[status(thm)],[96,86,40,30,27,9]) ).
tff(98,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(zz,meet(zz,xx)) = zz ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
join(zz,meet(zz,xx)) = zz,
inference(unit_resolution,[status(thm)],[98,93]) ).
tff(100,plain,
meet(xx,yy) = meet(zz,xx),
inference(transitivity,[status(thm)],[71,50]) ).
tff(101,plain,
join(zz,meet(xx,yy)) = join(zz,meet(zz,xx)),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
join(zz,meet(xx,yy)) = zz,
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(yy,join(yy,xx)) = yy ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
meet(yy,join(yy,xx)) = yy,
inference(unit_resolution,[status(thm)],[103,7]) ).
tff(105,plain,
join(xx,yy) = join(yy,xx),
inference(symmetry,[status(thm)],[29]) ).
tff(106,plain,
meet(yy,join(xx,yy)) = meet(yy,join(yy,xx)),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
join(zz,xx) = join(xx,yy),
inference(transitivity,[status(thm)],[18,24]) ).
tff(108,plain,
meet(yy,join(zz,xx)) = meet(yy,join(xx,yy)),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
meet(yy,join(zz,xx)) = yy,
inference(transitivity,[status(thm)],[108,106,104]) ).
tff(110,plain,
( ( meet(yy,join(zz,xx)) = join(zz,meet(xx,yy)) )
<=> ( yy = zz ) ),
inference(monotonicity,[status(thm)],[109,102]) ).
tff(111,plain,
( ( yy = zz )
<=> ( meet(yy,join(zz,xx)) = join(zz,meet(xx,yy)) ) ),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ( yy != zz )
<=> ( meet(yy,join(zz,xx)) != join(zz,meet(xx,yy)) ) ),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( ( yy != zz )
<=> ( yy != zz ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,axiom,
yy != zz,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rhs) ).
tff(115,plain,
yy != zz,
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
meet(yy,join(zz,xx)) != join(zz,meet(xx,yy)),
inference(modus_ponens,[status(thm)],[115,112]) ).
tff(117,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(118,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)],[117]) ).
tff(119,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(120,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular) ).
tff(121,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)],[120,119]) ).
tff(122,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)],[121]) ).
tff(123,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)],[122,118]) ).
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)) ) )
<=> ( ~ ! [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(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(quant_inst,[status(thm)],]) ).
tff(126,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)],[125,124]) ).
tff(127,plain,
( ( meet(zz,yy) != zz )
| ( meet(yy,join(zz,xx)) = join(zz,meet(xx,yy)) ) ),
inference(unit_resolution,[status(thm)],[126,123]) ).
tff(128,plain,
meet(zz,yy) != zz,
inference(unit_resolution,[status(thm)],[127,116]) ).
tff(129,plain,
$false,
inference(unit_resolution,[status(thm)],[128,97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : LAT037-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n011.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Sep 1 10:48:27 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.31 Usage: tptp [options] [-file:]file
% 0.16/0.31 -h, -? prints this message.
% 0.16/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.31 -m, -model generate model.
% 0.16/0.31 -p, -proof generate proof.
% 0.16/0.31 -c, -core generate unsat core of named formulas.
% 0.16/0.31 -st, -statistics display statistics.
% 0.16/0.31 -t:timeout set timeout (in second).
% 0.16/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.31 -<param>:<value> configuration parameter and value.
% 0.16/0.31 -o:<output-file> file to place output in.
% 0.16/0.44 % SZS status Unsatisfiable
% 0.16/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------