TSTP Solution File: PUZ132+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ132+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Sun Sep 18 14:11:32 EDT 2022
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 36
% Syntax : Number of formulae : 69 ( 15 unt; 8 typ; 0 def)
% Number of atoms : 191 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 223 ( 99 ~; 78 |; 10 &)
% ( 27 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(city_type,type,
city: $i > $o ).
tff(capital_city_type,type,
capital_city: $i > $i ).
tff(usa_type,type,
usa: $i ).
tff(capital_type,type,
capital: $i > $o ).
tff(washington_type,type,
washington: $i ).
tff(has_crime_type,type,
has_crime: $i > $o ).
tff(beautiful_type,type,
beautiful: $i > $o ).
tff(country_type,type,
country: $i > $o ).
tff(1,plain,
( capital(washington)
<=> capital(capital_city(usa)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( capital(washington)
<=> capital(washington) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
capital(washington),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',washington_type) ).
tff(4,plain,
capital(washington),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
capital(capital_city(usa)),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [A: $i] :
refl(
( ( city(A)
| ~ capital(A) )
<=> ( city(A)
| ~ capital(A) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [A: $i] :
( city(A)
| ~ capital(A) )
<=> ! [A: $i] :
( city(A)
| ~ capital(A) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [A: $i] :
( city(A)
| ~ capital(A) )
<=> ! [A: $i] :
( city(A)
| ~ capital(A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
^ [A: $i] :
rewrite(
( ( capital(A)
=> city(A) )
<=> ( city(A)
| ~ capital(A) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [A: $i] :
( capital(A)
=> city(A) )
<=> ! [A: $i] :
( city(A)
| ~ capital(A) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [A: $i] :
( capital(A)
=> city(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',capital_city_type) ).
tff(12,plain,
! [A: $i] :
( city(A)
| ~ capital(A) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [A: $i] :
( city(A)
| ~ capital(A) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [A: $i] :
( city(A)
| ~ capital(A) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [A: $i] :
( city(A)
| ~ capital(A) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
( ( ~ ! [A: $i] :
( city(A)
| ~ capital(A) )
| city(capital_city(usa))
| ~ capital(capital_city(usa)) )
<=> ( ~ ! [A: $i] :
( city(A)
| ~ capital(A) )
| city(capital_city(usa))
| ~ capital(capital_city(usa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ~ ! [A: $i] :
( city(A)
| ~ capital(A) )
| city(capital_city(usa))
| ~ capital(capital_city(usa)) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
( ~ ! [A: $i] :
( city(A)
| ~ capital(A) )
| city(capital_city(usa))
| ~ capital(capital_city(usa)) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
city(capital_city(usa)),
inference(unit_resolution,[status(thm)],[18,15,5]) ).
tff(20,plain,
^ [X: $i] :
refl(
( ( beautiful(capital_city(X))
| ~ country(X) )
<=> ( beautiful(capital_city(X))
| ~ country(X) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) )
<=> ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) )
<=> ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
^ [X: $i] :
rewrite(
( ( country(X)
=> beautiful(capital_city(X)) )
<=> ( beautiful(capital_city(X))
| ~ country(X) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [X: $i] :
( country(X)
=> beautiful(capital_city(X)) )
<=> ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [X: $i] :
( country(X)
=> beautiful(capital_city(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beautiful_capital_axiom) ).
tff(26,plain,
! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
( country(usa)
<=> country(usa) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
country(usa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',usa_type) ).
tff(32,plain,
country(usa),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ( ~ ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) )
| beautiful(capital_city(usa))
| ~ country(usa) )
<=> ( ~ ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) )
| beautiful(capital_city(usa))
| ~ country(usa) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) )
| beautiful(capital_city(usa))
| ~ country(usa) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) )
| beautiful(capital_city(usa))
| ~ country(usa) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
beautiful(capital_city(usa)),
inference(unit_resolution,[status(thm)],[35,32,29]) ).
tff(37,plain,
( ~ ~ ( ~ beautiful(capital_city(usa))
| ~ has_crime(capital_city(usa)) )
<=> ( ~ beautiful(capital_city(usa))
| ~ has_crime(capital_city(usa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( beautiful(capital_city(usa))
& has_crime(capital_city(usa)) )
<=> ~ ( ~ beautiful(capital_city(usa))
| ~ has_crime(capital_city(usa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ( beautiful(capital_city(usa))
& has_crime(capital_city(usa)) )
<=> ~ ~ ( ~ beautiful(capital_city(usa))
| ~ has_crime(capital_city(usa)) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ~ ( beautiful(capital_city(usa))
& has_crime(capital_city(usa)) )
<=> ( ~ beautiful(capital_city(usa))
| ~ has_crime(capital_city(usa)) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ( beautiful(washington)
& has_crime(washington) )
<=> ~ ( beautiful(capital_city(usa))
& has_crime(capital_city(usa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ~ ( beautiful(washington)
& has_crime(washington) )
<=> ~ ( beautiful(washington)
& has_crime(washington) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
~ ( beautiful(washington)
& has_crime(washington) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',washington_conjecture) ).
tff(44,plain,
~ ( beautiful(washington)
& has_crime(washington) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ ( beautiful(capital_city(usa))
& has_crime(capital_city(usa)) ),
inference(modus_ponens,[status(thm)],[44,41]) ).
tff(46,plain,
( ~ beautiful(capital_city(usa))
| ~ has_crime(capital_city(usa)) ),
inference(modus_ponens,[status(thm)],[45,40]) ).
tff(47,plain,
~ has_crime(capital_city(usa)),
inference(unit_resolution,[status(thm)],[46,36]) ).
tff(48,plain,
^ [X: $i] :
refl(
( ( has_crime(X)
| ~ city(X) )
<=> ( has_crime(X)
| ~ city(X) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X: $i] :
( has_crime(X)
| ~ city(X) )
<=> ! [X: $i] :
( has_crime(X)
| ~ city(X) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X: $i] :
( has_crime(X)
| ~ city(X) )
<=> ! [X: $i] :
( has_crime(X)
| ~ city(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
^ [X: $i] :
rewrite(
( ( city(X)
=> has_crime(X) )
<=> ( has_crime(X)
| ~ city(X) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X: $i] :
( city(X)
=> has_crime(X) )
<=> ! [X: $i] :
( has_crime(X)
| ~ city(X) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [X: $i] :
( city(X)
=> has_crime(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crime_axiom) ).
tff(54,plain,
! [X: $i] :
( has_crime(X)
| ~ city(X) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [X: $i] :
( has_crime(X)
| ~ city(X) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [X: $i] :
( has_crime(X)
| ~ city(X) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [X: $i] :
( has_crime(X)
| ~ city(X) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( ( ~ ! [X: $i] :
( has_crime(X)
| ~ city(X) )
| has_crime(capital_city(usa))
| ~ city(capital_city(usa)) )
<=> ( ~ ! [X: $i] :
( has_crime(X)
| ~ city(X) )
| has_crime(capital_city(usa))
| ~ city(capital_city(usa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ~ ! [X: $i] :
( has_crime(X)
| ~ city(X) )
| has_crime(capital_city(usa))
| ~ city(capital_city(usa)) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [X: $i] :
( has_crime(X)
| ~ city(X) )
| has_crime(capital_city(usa))
| ~ city(capital_city(usa)) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
$false,
inference(unit_resolution,[status(thm)],[60,57,47,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : PUZ132+1 : TPTP v8.1.0. Released v4.1.0.
% 0.05/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Sep 2 19:18:23 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.35 Usage: tptp [options] [-file:]file
% 0.15/0.35 -h, -? prints this message.
% 0.15/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.35 -m, -model generate model.
% 0.15/0.35 -p, -proof generate proof.
% 0.15/0.35 -c, -core generate unsat core of named formulas.
% 0.15/0.35 -st, -statistics display statistics.
% 0.15/0.35 -t:timeout set timeout (in second).
% 0.15/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.35 -<param>:<value> configuration parameter and value.
% 0.15/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------