%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ132+1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 Jun 21 05:23:28 AM UTC 2025
% Result : Theorem 0.20s 0.36s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 28
% Syntax : Number of formulae : 62 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 189 ( 4 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 216 ( 95 ~; 78 |; 7 &)
% ( 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(beautiful_type,type,
beautiful: $i > $o ).
tff(washington_type,type,
washington: $i ).
tff(capital_city_type,type,
capital_city: $i > $i ).
tff(usa_type,type,
usa: $i ).
tff(country_type,type,
country: $i > $o ).
tff(has_crime_type,type,
has_crime: $i > $o ).
tff(city_type,type,
city: $i > $o ).
tff(capital_type,type,
capital: $i > $o ).
tff(1,plain,
( ( capital_city(usa) = washington )
<=> ( capital_city(usa) = washington ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
capital_city(usa) = washington,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',usa_capital_axiom) ).
tff(3,plain,
capital_city(usa) = washington,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( beautiful(capital_city(usa))
<=> beautiful(washington) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
refl(( ( beautiful(capital_city(X))
| ~ country(X) )
<=> ( beautiful(capital_city(X))
| ~ country(X) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) )
<=> ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) )
<=> ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
^ [X: $i] :
rewrite(( ( country(X)
=> beautiful(capital_city(X)) )
<=> ( beautiful(capital_city(X))
| ~ country(X) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( country(X)
=> beautiful(capital_city(X)) )
<=> ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,axiom,
! [X: $i] :
( country(X)
=> beautiful(capital_city(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beautiful_capital_axiom) ).
tff(11,plain,
! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) ),
inference(modus_ponens,[status(thm)],[13,6]) ).
tff(15,plain,
( country(usa)
<=> country(usa) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
country(usa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',usa_type) ).
tff(17,plain,
country(usa),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,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(19,plain,
( ~ ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) )
| beautiful(capital_city(usa))
| ~ country(usa) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [X: $i] :
( beautiful(capital_city(X))
| ~ country(X) )
| beautiful(capital_city(usa))
| ~ country(usa) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
beautiful(capital_city(usa)),
inference(unit_resolution,[status(thm)],[20,17,14]) ).
tff(22,plain,
beautiful(washington),
inference(modus_ponens,[status(thm)],[21,4]) ).
tff(23,plain,
( capital(washington)
<=> capital(washington) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
capital(washington),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',washington_type) ).
tff(25,plain,
capital(washington),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
^ [A: $i] :
refl(( ( city(A)
| ~ capital(A) )
<=> ( city(A)
| ~ capital(A) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [A: $i] :
( city(A)
| ~ capital(A) )
<=> ! [A: $i] :
( city(A)
| ~ capital(A) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [A: $i] :
( city(A)
| ~ capital(A) )
<=> ! [A: $i] :
( city(A)
| ~ capital(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
^ [A: $i] :
rewrite(( ( capital(A)
=> city(A) )
<=> ( city(A)
| ~ capital(A) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [A: $i] :
( capital(A)
=> city(A) )
<=> ! [A: $i] :
( city(A)
| ~ capital(A) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [A: $i] :
( capital(A)
=> city(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',capital_city_type) ).
tff(32,plain,
! [A: $i] :
( city(A)
| ~ capital(A) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [A: $i] :
( city(A)
| ~ capital(A) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [A: $i] :
( city(A)
| ~ capital(A) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [A: $i] :
( city(A)
| ~ capital(A) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
( ( ~ ! [A: $i] :
( city(A)
| ~ capital(A) )
| city(washington)
| ~ capital(washington) )
<=> ( ~ ! [A: $i] :
( city(A)
| ~ capital(A) )
| city(washington)
| ~ capital(washington) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [A: $i] :
( city(A)
| ~ capital(A) )
| city(washington)
| ~ capital(washington) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [A: $i] :
( city(A)
| ~ capital(A) )
| city(washington)
| ~ capital(washington) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
city(washington),
inference(unit_resolution,[status(thm)],[38,35,25]) ).
tff(40,plain,
^ [X: $i] :
refl(( ( has_crime(X)
| ~ city(X) )
<=> ( has_crime(X)
| ~ city(X) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [X: $i] :
( has_crime(X)
| ~ city(X) )
<=> ! [X: $i] :
( has_crime(X)
| ~ city(X) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [X: $i] :
( has_crime(X)
| ~ city(X) )
<=> ! [X: $i] :
( has_crime(X)
| ~ city(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
^ [X: $i] :
rewrite(( ( city(X)
=> has_crime(X) )
<=> ( has_crime(X)
| ~ city(X) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [X: $i] :
( city(X)
=> has_crime(X) )
<=> ! [X: $i] :
( has_crime(X)
| ~ city(X) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [X: $i] :
( city(X)
=> has_crime(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crime_axiom) ).
tff(46,plain,
! [X: $i] :
( has_crime(X)
| ~ city(X) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [X: $i] :
( has_crime(X)
| ~ city(X) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [X: $i] :
( has_crime(X)
| ~ city(X) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X: $i] :
( has_crime(X)
| ~ city(X) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [X: $i] :
( has_crime(X)
| ~ city(X) )
| has_crime(washington)
| ~ city(washington) )
<=> ( ~ ! [X: $i] :
( has_crime(X)
| ~ city(X) )
| has_crime(washington)
| ~ city(washington) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [X: $i] :
( has_crime(X)
| ~ city(X) )
| has_crime(washington)
| ~ city(washington) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [X: $i] :
( has_crime(X)
| ~ city(X) )
| has_crime(washington)
| ~ city(washington) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
has_crime(washington),
inference(unit_resolution,[status(thm)],[52,49,39]) ).
tff(54,plain,
( ~ ~ ( ~ beautiful(washington)
| ~ has_crime(washington) )
<=> ( ~ beautiful(washington)
| ~ has_crime(washington) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( beautiful(washington)
& has_crime(washington) )
<=> ~ ( ~ beautiful(washington)
| ~ has_crime(washington) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ~ ( beautiful(washington)
& has_crime(washington) )
<=> ~ ~ ( ~ beautiful(washington)
| ~ has_crime(washington) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ~ ( beautiful(washington)
& has_crime(washington) )
<=> ( ~ beautiful(washington)
| ~ has_crime(washington) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ( beautiful(washington)
& has_crime(washington) )
<=> ~ ( beautiful(washington)
& has_crime(washington) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
~ ( beautiful(washington)
& has_crime(washington) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',washington_conjecture) ).
tff(60,plain,
~ ( beautiful(washington)
& has_crime(washington) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ beautiful(washington)
| ~ has_crime(washington) ),
inference(modus_ponens,[status(thm)],[60,57]) ).
tff(62,plain,
$false,
inference(unit_resolution,[status(thm)],[61,53,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ132+1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:46:40 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.36 % SZS status Theorem
% 0.20/0.36 % SZS output start Proof
% See solution above
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------