TSTP Solution File: LAT044-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT044-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 18:31:51 EDT 2022
% Result : Unsatisfiable 0.96s 0.84s
% Output : Proof 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 59
% Syntax : Number of formulae : 164 ( 115 unt; 7 typ; 0 def)
% Number of atoms : 217 ( 207 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 78 ( 27 ~; 23 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 201 ( 184 !; 0 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
tff(n1_type,type,
n1: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(n0_type,type,
n0: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( join(complement(X),X) = n1 )
<=> ( join(complement(X),X) = n1 ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( join(complement(X),X) = n1 )
<=> ! [X: $i] : ( join(complement(X),X) = n1 ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( join(complement(X),X) = n1 )
<=> ! [X: $i] : ( join(complement(X),X) = n1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( join(complement(X),X) = n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',invertability1) ).
tff(5,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( join(complement(X),X) = n1 ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( join(complement(X),X) = n1 )
| ( join(complement(meet(a,b)),meet(a,b)) = n1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
join(complement(meet(a,b)),meet(a,b)) = n1,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(
( ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
<=> ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
<=> ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
<=> ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility2) ).
tff(14,plain,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
| ( complement(meet(a,b)) = join(complement(a),complement(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
complement(meet(a,b)) = join(complement(a),complement(b)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
join(complement(a),complement(b)) = complement(meet(a,b)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(21,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)],[20]) ).
tff(22,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(23,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(24,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(a),meet(complement(a),join(a,b))) = complement(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
join(complement(a),meet(complement(a),join(a,b))) = complement(a),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(30,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)],[29]) ).
tff(31,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(32,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(33,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(complement(a),join(a,b)),complement(a)) = join(complement(a),meet(complement(a),join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
join(meet(complement(a),join(a,b)),complement(a)) = join(complement(a),meet(complement(a),join(a,b))),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
<=> ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
<=> ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
<=> ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',orthomodular_law) ).
tff(42,plain,
! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
| ( join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a)))) = join(meet(complement(a),join(a,b)),complement(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a)))) = join(meet(complement(a),join(a,b)),complement(a)),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
join(meet(complement(a),join(a,b)),complement(a)) = complement(a),
inference(transitivity,[status(thm)],[37,28]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
| ( complement(meet(complement(a),join(a,b))) = join(complement(complement(a)),complement(join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
complement(meet(complement(a),join(a,b))) = join(complement(complement(a)),complement(join(a,b))),
inference(unit_resolution,[status(thm)],[48,16]) ).
tff(50,plain,
meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a))) = meet(join(complement(complement(a)),complement(join(a,b))),complement(a)),
inference(monotonicity,[status(thm)],[49,47]) ).
tff(51,plain,
meet(join(complement(complement(a)),complement(join(a,b))),complement(a)) = meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a))),
inference(symmetry,[status(thm)],[50]) ).
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/sandbox2/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(join(complement(complement(a)),complement(join(a,b))),complement(a)) = meet(complement(a),join(complement(complement(a)),complement(join(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
meet(join(complement(complement(a)),complement(join(a,b))),complement(a)) = meet(complement(a),join(complement(complement(a)),complement(join(a,b)))),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
meet(complement(a),join(complement(complement(a)),complement(join(a,b)))) = meet(join(complement(complement(a)),complement(join(a,b))),complement(a)),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
join(complement(complement(a)),complement(join(a,b))) = complement(meet(complement(a),join(a,b))),
inference(symmetry,[status(thm)],[49]) ).
tff(63,plain,
meet(complement(a),join(complement(complement(a)),complement(join(a,b)))) = meet(complement(a),complement(meet(complement(a),join(a,b)))),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
meet(complement(a),complement(meet(complement(a),join(a,b)))) = meet(complement(a),join(complement(complement(a)),complement(join(a,b)))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
^ [Y: $i,X: $i] :
refl(
( ( complement(join(X,Y)) = meet(complement(X),complement(Y)) )
<=> ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) )
<=> ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) )
<=> ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility1) ).
tff(69,plain,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ~ ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) )
| ( complement(join(a,meet(complement(a),join(a,b)))) = meet(complement(a),complement(meet(complement(a),join(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
complement(join(a,meet(complement(a),join(a,b)))) = meet(complement(a),complement(meet(complement(a),join(a,b)))),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(complement(X),join(X,Y))) = join(X,Y) )
| ( join(a,meet(complement(a),join(a,b))) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
join(a,meet(complement(a),join(a,b))) = join(a,b),
inference(unit_resolution,[status(thm)],[74,44]) ).
tff(76,plain,
complement(join(a,meet(complement(a),join(a,b)))) = complement(join(a,b)),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
complement(join(a,b)) = complement(join(a,meet(complement(a),join(a,b)))),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
( ~ ! [Y: $i,X: $i] : ( complement(join(X,Y)) = meet(complement(X),complement(Y)) )
| ( complement(join(a,b)) = meet(complement(a),complement(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
complement(join(a,b)) = meet(complement(a),complement(b)),
inference(unit_resolution,[status(thm)],[78,71]) ).
tff(80,plain,
meet(complement(a),complement(b)) = complement(join(a,b)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
meet(complement(a),complement(b)) = meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a))),
inference(transitivity,[status(thm)],[80,77,73,64,61,51]) ).
tff(82,plain,
join(meet(complement(a),join(a,b)),meet(complement(a),complement(b))) = join(meet(complement(a),join(a,b)),meet(complement(meet(complement(a),join(a,b))),join(meet(complement(a),join(a,b)),complement(a)))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(complement(a),join(a,b)),meet(complement(a),complement(b))) = join(meet(complement(a),complement(b)),meet(complement(a),join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
join(meet(complement(a),join(a,b)),meet(complement(a),complement(b))) = join(meet(complement(a),complement(b)),meet(complement(a),join(a,b))),
inference(unit_resolution,[status(thm)],[83,35]) ).
tff(85,plain,
join(meet(complement(a),complement(b)),meet(complement(a),join(a,b))) = join(meet(complement(a),join(a,b)),meet(complement(a),complement(b))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
join(meet(complement(a),complement(b)),meet(complement(a),join(a,b))) = complement(a),
inference(transitivity,[status(thm)],[85,82,46,37,28]) ).
tff(87,plain,
join(join(meet(complement(a),complement(b)),meet(complement(a),join(a,b))),complement(b)) = join(complement(a),complement(b)),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
tff(92,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(complement(a),complement(b)),meet(complement(a),join(a,b))),complement(b)) = join(meet(complement(a),complement(b)),join(meet(complement(a),join(a,b)),complement(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
join(join(meet(complement(a),complement(b)),meet(complement(a),join(a,b))),complement(b)) = join(meet(complement(a),complement(b)),join(meet(complement(a),join(a,b)),complement(b))),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
join(meet(complement(a),complement(b)),join(meet(complement(a),join(a,b)),complement(b))) = join(join(meet(complement(a),complement(b)),meet(complement(a),join(a,b))),complement(b)),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(complement(b),meet(complement(a),join(a,b))) = join(meet(complement(a),join(a,b)),complement(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
join(complement(b),meet(complement(a),join(a,b))) = join(meet(complement(a),join(a,b)),complement(b)),
inference(unit_resolution,[status(thm)],[98,35]) ).
tff(100,plain,
^ [X: $i] :
refl(
( ( meet(complement(X),X) = n0 )
<=> ( meet(complement(X),X) = n0 ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [X: $i] : ( meet(complement(X),X) = n0 )
<=> ! [X: $i] : ( meet(complement(X),X) = n0 ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [X: $i] : ( meet(complement(X),X) = n0 )
<=> ! [X: $i] : ( meet(complement(X),X) = n0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,axiom,
! [X: $i] : ( meet(complement(X),X) = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',invertability2) ).
tff(104,plain,
! [X: $i] : ( meet(complement(X),X) = n0 ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [X: $i] : ( meet(complement(X),X) = n0 ),
inference(skolemize,[status(sab)],[104]) ).
tff(106,plain,
! [X: $i] : ( meet(complement(X),X) = n0 ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
( ~ ! [X: $i] : ( meet(complement(X),X) = n0 )
| ( meet(complement(b),b) = n0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
meet(complement(b),b) = n0,
inference(unit_resolution,[status(thm)],[107,106]) ).
tff(109,plain,
n0 = meet(complement(b),b),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
join(complement(b),n0) = join(complement(b),meet(complement(b),b)),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
join(complement(b),meet(complement(b),b)) = join(complement(b),n0),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(b),meet(complement(b),b)) = complement(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
join(complement(b),meet(complement(b),b)) = complement(b),
inference(unit_resolution,[status(thm)],[112,26]) ).
tff(114,plain,
complement(b) = join(complement(b),meet(complement(b),b)),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
complement(b) = join(complement(b),n0),
inference(transitivity,[status(thm)],[114,111]) ).
tff(116,plain,
join(complement(b),meet(complement(a),join(a,b))) = join(join(complement(b),n0),meet(complement(a),join(a,b))),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
join(join(complement(b),n0),meet(complement(a),join(a,b))) = join(complement(b),meet(complement(a),join(a,b))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(b),n0),meet(complement(a),join(a,b))) = join(complement(b),join(n0,meet(complement(a),join(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
join(join(complement(b),n0),meet(complement(a),join(a,b))) = join(complement(b),join(n0,meet(complement(a),join(a,b)))),
inference(unit_resolution,[status(thm)],[118,94]) ).
tff(120,plain,
join(complement(b),join(n0,meet(complement(a),join(a,b)))) = join(join(complement(b),n0),meet(complement(a),join(a,b))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
join(complement(b),join(n0,meet(complement(a),join(a,b)))) = join(meet(complement(a),join(a,b)),complement(b)),
inference(transitivity,[status(thm)],[120,117,99]) ).
tff(122,plain,
join(meet(complement(a),complement(b)),join(complement(b),join(n0,meet(complement(a),join(a,b))))) = join(meet(complement(a),complement(b)),join(meet(complement(a),join(a,b)),complement(b))),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(complement(a),complement(b)),complement(b)),join(n0,meet(complement(a),join(a,b)))) = join(meet(complement(a),complement(b)),join(complement(b),join(n0,meet(complement(a),join(a,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
join(join(meet(complement(a),complement(b)),complement(b)),join(n0,meet(complement(a),join(a,b)))) = join(meet(complement(a),complement(b)),join(complement(b),join(n0,meet(complement(a),join(a,b))))),
inference(unit_resolution,[status(thm)],[123,94]) ).
tff(125,plain,
join(meet(complement(a),complement(b)),complement(b)) = join(complement(join(a,b)),complement(b)),
inference(monotonicity,[status(thm)],[80]) ).
tff(126,plain,
join(complement(join(a,b)),complement(b)) = join(meet(complement(a),complement(b)),complement(b)),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
| ( complement(meet(join(a,b),b)) = join(complement(join(a,b)),complement(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
complement(meet(join(a,b),b)) = join(complement(join(a,b)),complement(b)),
inference(unit_resolution,[status(thm)],[127,16]) ).
tff(129,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),b) = meet(b,join(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
meet(join(a,b),b) = meet(b,join(a,b)),
inference(unit_resolution,[status(thm)],[129,58]) ).
tff(131,plain,
complement(meet(join(a,b),b)) = complement(meet(b,join(a,b))),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
complement(meet(b,join(a,b))) = complement(meet(join(a,b),b)),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [Y: $i,X: $i] : ( complement(meet(X,Y)) = join(complement(X),complement(Y)) )
| ( complement(meet(b,join(a,b))) = join(complement(b),complement(join(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
complement(meet(b,join(a,b))) = join(complement(b),complement(join(a,b))),
inference(unit_resolution,[status(thm)],[133,16]) ).
tff(135,plain,
join(complement(b),complement(join(a,b))) = complement(meet(b,join(a,b))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(complement(b),complement(a)) = meet(complement(a),complement(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
meet(complement(b),complement(a)) = meet(complement(a),complement(b)),
inference(unit_resolution,[status(thm)],[136,58]) ).
tff(138,plain,
meet(complement(a),complement(b)) = meet(complement(b),complement(a)),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
complement(join(a,b)) = meet(complement(b),complement(a)),
inference(transitivity,[status(thm)],[79,138]) ).
tff(140,plain,
join(complement(b),complement(join(a,b))) = join(complement(b),meet(complement(b),complement(a))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
join(complement(b),meet(complement(b),complement(a))) = join(complement(b),complement(join(a,b))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(b),meet(complement(b),complement(a))) = complement(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
join(complement(b),meet(complement(b),complement(a))) = complement(b),
inference(unit_resolution,[status(thm)],[142,26]) ).
tff(144,plain,
complement(b) = join(complement(b),meet(complement(b),complement(a))),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
complement(b) = join(meet(complement(a),complement(b)),complement(b)),
inference(transitivity,[status(thm)],[144,141,135,132,128,126]) ).
tff(146,plain,
join(complement(b),join(n0,meet(complement(a),join(a,b)))) = join(join(meet(complement(a),complement(b)),complement(b)),join(n0,meet(complement(a),join(a,b)))),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
join(meet(complement(a),join(a,b)),complement(b)) = join(complement(b),meet(complement(a),join(a,b))),
inference(symmetry,[status(thm)],[99]) ).
tff(148,plain,
join(meet(complement(a),join(a,b)),complement(b)) = complement(meet(a,b)),
inference(transitivity,[status(thm)],[147,116,119,146,124,122,97,87,19]) ).
tff(149,plain,
join(join(meet(complement(a),join(a,b)),complement(b)),meet(a,b)) = join(complement(meet(a,b)),meet(a,b)),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(complement(a),join(a,b)),complement(b)),meet(a,b)) = join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
join(join(meet(complement(a),join(a,b)),complement(b)),meet(a,b)) = join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))),
inference(unit_resolution,[status(thm)],[150,94]) ).
tff(152,plain,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) = join(join(meet(complement(a),join(a,b)),complement(b)),meet(a,b)),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) = n1,
inference(transitivity,[status(thm)],[152,149,9]) ).
tff(154,plain,
( ( join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1 )
<=> ( join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(155,axiom,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_orthomodular_law) ).
tff(156,plain,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1,
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
$false,
inference(unit_resolution,[status(thm)],[156,153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT044-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n016.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 11:16:04 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 0.96/0.84 % SZS status Unsatisfiable
% 0.96/0.84 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------