TSTP Solution File: LAT005-3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT005-3 : TPTP v8.1.0. Released v1.0.0.
% 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 18:31:40 EDT 2022
% Result : Unsatisfiable 1.68s 1.34s
% Output : Proof 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 62
% Syntax : Number of formulae : 163 ( 99 unt; 8 typ; 0 def)
% Number of atoms : 277 ( 235 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 206 ( 91 ~; 87 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 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 : 228 ( 212 !; 0 ?; 228 :)
% Comments :
%------------------------------------------------------------------------------
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(r2_type,type,
r2: $i ).
tff(r1_type,type,
r1: $i ).
tff(b_type,type,
b: $i ).
tff(n0_type,type,
n0: $i ).
tff(complement_type,type,
complement: ( $i * $i ) > $o ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(5,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))) = meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))) = meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(14,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(r1,join(r1,meet(r2,a))) = r1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
meet(r1,join(r1,meet(r2,a))) = r1,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,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/Axioms/LAT001-1.ax',modular) ).
tff(23,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)],[22,21]) ).
tff(24,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)],[23]) ).
tff(25,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)],[24,20]) ).
tff(26,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,join(r1,meet(r2,a))) != r1 )
| ( meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))) = join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,join(r1,meet(r2,a))) != r1 )
| ( meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))) = join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,join(r1,meet(r2,a))) != r1 )
| ( meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))) = join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(r1,join(r1,meet(r2,a))) != r1 )
| ( meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))) = join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))) = join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))),
inference(unit_resolution,[status(thm)],[28,25,18]) ).
tff(30,plain,
join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))) = meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,b),join(a,b)) = meet(r2,meet(b,join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
meet(meet(r2,b),join(a,b)) = meet(r2,meet(b,join(a,b))),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
meet(r2,meet(b,join(a,b))) = meet(meet(r2,b),join(a,b)),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(b,join(b,a)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
meet(b,join(b,a)) = b,
inference(unit_resolution,[status(thm)],[41,16]) ).
tff(43,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(44,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)],[43]) ).
tff(45,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(46,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(47,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,a) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
join(b,a) = join(a,b),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
join(a,b) = join(b,a),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
meet(b,join(a,b)) = meet(b,join(b,a)),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
meet(b,join(a,b)) = b,
inference(transitivity,[status(thm)],[53,42]) ).
tff(55,plain,
meet(r2,meet(b,join(a,b))) = meet(r2,b),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
meet(r2,b) = meet(r2,meet(b,join(a,b))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
meet(r2,b) = meet(meet(r2,b),join(a,b)),
inference(transitivity,[status(thm)],[56,40]) ).
tff(58,plain,
meet(meet(r2,b),join(r1,meet(r2,a))) = meet(meet(meet(r2,b),join(a,b)),join(r1,meet(r2,a))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
meet(meet(meet(r2,b),join(a,b)),join(r1,meet(r2,a))) = meet(meet(r2,b),join(r1,meet(r2,a))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(r2,b),join(a,b)),join(r1,meet(r2,a))) = meet(meet(r2,b),meet(join(a,b),join(r1,meet(r2,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
meet(meet(meet(r2,b),join(a,b)),join(r1,meet(r2,a))) = meet(meet(r2,b),meet(join(a,b),join(r1,meet(r2,a)))),
inference(unit_resolution,[status(thm)],[60,37]) ).
tff(62,plain,
meet(meet(r2,b),meet(join(a,b),join(r1,meet(r2,a)))) = meet(meet(meet(r2,b),join(a,b)),join(r1,meet(r2,a))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),join(r1,meet(r2,a))) = meet(join(r1,meet(r2,a)),join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
meet(join(a,b),join(r1,meet(r2,a))) = meet(join(r1,meet(r2,a)),join(a,b)),
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
meet(meet(r2,b),meet(join(a,b),join(r1,meet(r2,a)))) = meet(meet(r2,b),meet(join(r1,meet(r2,a)),join(a,b))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
meet(meet(r2,b),meet(join(r1,meet(r2,a)),join(a,b))) = meet(meet(r2,b),meet(join(a,b),join(r1,meet(r2,a)))),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(68,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)],[67]) ).
tff(69,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(70,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(71,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(r2,a),meet(meet(r2,a),b)) = meet(r2,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
join(meet(r2,a),meet(meet(r2,a),b)) = meet(r2,a),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,a),b) = meet(r2,meet(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
meet(meet(r2,a),b) = meet(r2,meet(a,b)),
inference(unit_resolution,[status(thm)],[76,37]) ).
tff(78,plain,
meet(r2,meet(a,b)) = meet(meet(r2,a),b),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
( complement(r2,meet(a,b))
<=> complement(r2,meet(a,b)) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
complement(r2,meet(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_meet_b) ).
tff(81,plain,
complement(r2,meet(a,b)),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
<=> ( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
<=> ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
<=> ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-2.ax',complement_meet) ).
tff(86,plain,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r2,meet(a,b))
| ( meet(r2,meet(a,b)) = n0 ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r2,meet(a,b))
| ( meet(r2,meet(a,b)) = n0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r2,meet(a,b))
| ( meet(r2,meet(a,b)) = n0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r2,meet(a,b))
| ( meet(r2,meet(a,b)) = n0 ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
meet(r2,meet(a,b)) = n0,
inference(unit_resolution,[status(thm)],[91,88,81]) ).
tff(93,plain,
n0 = meet(r2,meet(a,b)),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( complement(r1,join(a,b))
<=> complement(r1,join(a,b)) ),
inference(rewrite,[status(thm)],]) ).
tff(95,axiom,
complement(r1,join(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_join_b) ).
tff(96,plain,
complement(r1,join(a,b)),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r1,join(a,b))
| ( meet(r1,join(a,b)) = n0 ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r1,join(a,b))
| ( meet(r1,join(a,b)) = n0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r1,join(a,b))
| ( meet(r1,join(a,b)) = n0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] :
( ~ complement(X,Y)
| ( meet(X,Y) = n0 ) )
| ~ complement(r1,join(a,b))
| ( meet(r1,join(a,b)) = n0 ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
meet(r1,join(a,b)) = n0,
inference(unit_resolution,[status(thm)],[99,88,96]) ).
tff(101,plain,
meet(r1,join(a,b)) = meet(meet(r2,a),b),
inference(transitivity,[status(thm)],[100,93,78]) ).
tff(102,plain,
join(meet(r2,a),meet(r1,join(a,b))) = join(meet(r2,a),meet(meet(r2,a),b)),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,b)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
meet(a,join(a,b)) = a,
inference(unit_resolution,[status(thm)],[103,16]) ).
tff(105,plain,
meet(r2,meet(a,join(a,b))) = meet(r2,a),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,a),join(a,b)) = meet(r2,meet(a,join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
meet(meet(r2,a),join(a,b)) = meet(r2,meet(a,join(a,b))),
inference(unit_resolution,[status(thm)],[106,37]) ).
tff(108,plain,
meet(meet(r2,a),join(a,b)) = meet(r2,a),
inference(transitivity,[status(thm)],[107,105]) ).
tff(109,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,a),join(a,b)) != meet(r2,a) )
| ( meet(join(a,b),join(meet(r2,a),r1)) = join(meet(r2,a),meet(r1,join(a,b))) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,a),join(a,b)) != meet(r2,a) )
| ( meet(join(a,b),join(meet(r2,a),r1)) = join(meet(r2,a),meet(r1,join(a,b))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,a),join(a,b)) != meet(r2,a) )
| ( meet(join(a,b),join(meet(r2,a),r1)) = join(meet(r2,a),meet(r1,join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( meet(X,Z) != X )
| ( meet(Z,join(X,Y)) = join(X,meet(Y,Z)) ) )
| ( meet(meet(r2,a),join(a,b)) != meet(r2,a) )
| ( meet(join(a,b),join(meet(r2,a),r1)) = join(meet(r2,a),meet(r1,join(a,b))) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
meet(join(a,b),join(meet(r2,a),r1)) = join(meet(r2,a),meet(r1,join(a,b))),
inference(unit_resolution,[status(thm)],[111,25,108]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(r2,a),r1) = join(r1,meet(r2,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
join(meet(r2,a),r1) = join(r1,meet(r2,a)),
inference(unit_resolution,[status(thm)],[113,49]) ).
tff(115,plain,
join(r1,meet(r2,a)) = join(meet(r2,a),r1),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
meet(join(a,b),join(r1,meet(r2,a))) = meet(join(a,b),join(meet(r2,a),r1)),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
meet(join(r1,meet(r2,a)),join(a,b)) = meet(join(a,b),join(r1,meet(r2,a))),
inference(symmetry,[status(thm)],[64]) ).
tff(118,plain,
meet(join(r1,meet(r2,a)),join(a,b)) = meet(r2,a),
inference(transitivity,[status(thm)],[117,116,112,102,75]) ).
tff(119,plain,
meet(meet(r2,b),meet(join(r1,meet(r2,a)),join(a,b))) = meet(meet(r2,b),meet(r2,a)),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
meet(meet(r2,b),meet(r2,a)) = meet(meet(r2,b),meet(join(r1,meet(r2,a)),join(a,b))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,r2) = meet(r2,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
meet(b,r2) = meet(r2,b),
inference(unit_resolution,[status(thm)],[121,7]) ).
tff(123,plain,
meet(r2,b) = meet(b,r2),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
meet(meet(r2,b),meet(r2,a)) = meet(meet(b,r2),meet(r2,a)),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
meet(meet(b,r2),meet(r2,a)) = meet(meet(r2,b),meet(r2,a)),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(b,r2),meet(r2,a)) = meet(b,meet(r2,meet(r2,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
meet(meet(b,r2),meet(r2,a)) = meet(b,meet(r2,meet(r2,a))),
inference(unit_resolution,[status(thm)],[126,37]) ).
tff(128,plain,
meet(b,meet(r2,meet(r2,a))) = meet(meet(b,r2),meet(r2,a)),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(r2,join(r2,meet(r2,b))) = r2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
meet(r2,join(r2,meet(r2,b))) = r2,
inference(unit_resolution,[status(thm)],[129,16]) ).
tff(131,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(r2,meet(r2,b)) = r2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
join(r2,meet(r2,b)) = r2,
inference(unit_resolution,[status(thm)],[131,73]) ).
tff(133,plain,
r2 = join(r2,meet(r2,b)),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
meet(r2,r2) = meet(r2,join(r2,meet(r2,b))),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
meet(r2,r2) = r2,
inference(transitivity,[status(thm)],[134,130]) ).
tff(136,plain,
meet(meet(r2,r2),a) = meet(r2,a),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,r2),a) = meet(r2,meet(r2,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
meet(meet(r2,r2),a) = meet(r2,meet(r2,a)),
inference(unit_resolution,[status(thm)],[137,37]) ).
tff(139,plain,
meet(r2,meet(r2,a)) = meet(meet(r2,r2),a),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
meet(r2,meet(r2,a)) = meet(r2,a),
inference(transitivity,[status(thm)],[139,136]) ).
tff(141,plain,
meet(b,meet(r2,meet(r2,a))) = meet(b,meet(r2,a)),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
meet(b,meet(r2,a)) = meet(b,meet(r2,meet(r2,a))),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,meet(r2,a)) = meet(meet(r2,a),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,plain,
meet(b,meet(r2,a)) = meet(meet(r2,a),b),
inference(unit_resolution,[status(thm)],[143,7]) ).
tff(145,plain,
meet(meet(r2,a),b) = meet(b,meet(r2,a)),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
meet(r1,join(a,b)) = meet(meet(r2,b),join(r1,meet(r2,a))),
inference(transitivity,[status(thm)],[100,93,78,145,142,128,125,120,66,62,59]) ).
tff(147,plain,
join(r1,meet(r1,join(a,b))) = join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(r1,meet(r1,join(a,b))) = r1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
join(r1,meet(r1,join(a,b))) = r1,
inference(unit_resolution,[status(thm)],[148,73]) ).
tff(150,plain,
r1 = join(r1,meet(r1,join(a,b))),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
r1 = meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
inference(transitivity,[status(thm)],[150,147,30,9]) ).
tff(152,plain,
( ( r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) )
<=> ( r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,axiom,
r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lemma) ).
tff(154,plain,
r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
$false,
inference(unit_resolution,[status(thm)],[154,151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT005-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.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 Sep 1 10:03:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.68/1.34 % SZS status Unsatisfiable
% 1.68/1.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------