TSTP Solution File: LAT014-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT014-1 : TPTP v8.1.0. Released v2.2.0.
% 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 18:31:44 EDT 2022
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 53 ( 37 unt; 4 typ; 0 def)
% Number of atoms : 67 ( 63 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 9 ~; 5 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 96 ( 87 !; 0 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(X,join(Y,join(X,Z))) = X )
<=> ( meet(X,join(Y,join(X,Z))) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mckenzie2) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(a,join(join(a,b),join(a,b))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
meet(a,join(join(a,b),join(a,b))) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,join(X,Z))) = X )
| ( meet(join(a,b),join(b,join(join(a,b),meet(b,meet(join(a,b),a))))) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(11,plain,
meet(join(a,b),join(b,join(join(a,b),meet(b,meet(join(a,b),a))))) = join(a,b),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(X,meet(Y,meet(X,Z))) = X )
<=> ( join(X,meet(Y,meet(X,Z))) = X ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mckenzie1) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(join(a,b),meet(b,meet(join(a,b),a))) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
join(join(a,b),meet(b,meet(join(a,b),a))) = join(a,b),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
join(b,join(join(a,b),meet(b,meet(join(a,b),a)))) = join(b,join(a,b)),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
join(b,join(a,b)) = join(b,join(join(a,b),meet(b,meet(join(a,b),a)))),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
meet(join(a,b),join(b,join(a,b))) = meet(join(a,b),join(b,join(join(a,b),meet(b,meet(join(a,b),a))))),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
meet(join(a,b),join(b,join(a,b))) = join(a,b),
inference(transitivity,[status(thm)],[23,11]) ).
tff(25,plain,
meet(meet(join(a,join(a,b)),join(join(a,b),a)),meet(join(a,b),join(b,join(a,b)))) = meet(meet(join(a,join(a,b)),join(join(a,b),a)),join(a,b)),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
meet(meet(join(a,join(a,b)),join(join(a,b),a)),join(a,b)) = meet(meet(join(a,join(a,b)),join(join(a,b),a)),meet(join(a,b),join(b,join(a,b)))),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
<=> ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mckenzie4) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(join(X,Y),join(Y,Z)),Y) = Y )
| ( meet(meet(join(a,join(a,b)),join(join(a,b),a)),join(a,b)) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
meet(meet(join(a,join(a,b)),join(join(a,b),a)),join(a,b)) = join(a,b),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
join(a,b) = meet(meet(join(a,join(a,b)),join(join(a,b),a)),join(a,b)),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
join(a,b) = meet(meet(join(a,join(a,b)),join(join(a,b),a)),meet(join(a,b),join(b,join(a,b)))),
inference(transitivity,[status(thm)],[36,26]) ).
tff(38,plain,
join(join(a,b),join(a,b)) = join(join(a,b),meet(meet(join(a,join(a,b)),join(join(a,b),a)),meet(join(a,b),join(b,join(a,b))))),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
join(join(a,b),meet(meet(join(a,join(a,b)),join(join(a,b),a)),meet(join(a,b),join(b,join(a,b))))) = join(join(a,b),join(a,b)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,meet(X,Z))) = X )
| ( join(join(a,b),meet(meet(join(a,join(a,b)),join(join(a,b),a)),meet(join(a,b),join(b,join(a,b))))) = join(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
join(join(a,b),meet(meet(join(a,join(a,b)),join(join(a,b),a)),meet(join(a,b),join(b,join(a,b))))) = join(a,b),
inference(unit_resolution,[status(thm)],[40,18]) ).
tff(42,plain,
join(a,b) = join(join(a,b),meet(meet(join(a,join(a,b)),join(join(a,b),a)),meet(join(a,b),join(b,join(a,b))))),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
join(a,b) = join(join(a,b),join(a,b)),
inference(transitivity,[status(thm)],[42,39]) ).
tff(44,plain,
meet(a,join(a,b)) = meet(a,join(join(a,b),join(a,b))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
meet(a,join(a,b)) = a,
inference(transitivity,[status(thm)],[44,9]) ).
tff(46,plain,
( ( meet(a,join(a,b)) != a )
<=> ( meet(a,join(a,b)) != a ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
meet(a,join(a,b)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_absorbtion) ).
tff(48,plain,
meet(a,join(a,b)) != a,
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT014-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n011.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 Sep 1 10:40:42 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------