%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PUZ132+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:32:08 PM UTC 2026
% Result : Theorem 3.08s 0.87s
% Output : Proof 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 35 unt; 0 def)
% Number of atoms : 69 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 39 ( 22 ~; 12 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 23 ( 2 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,conjecture,
( has_crime(washington)
& beautiful(washington) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',washington_conjecture) ).
fof(f10_neg,negated_conjecture,
~ ( has_crime(washington)
& beautiful(washington) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
( ~ has_crime(washington)
| ~ beautiful(washington) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ~ has_crime(washington)
| ~ beautiful(washington) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ has_crime(washington)
| ~ beautiful(washington) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t24,plain,
ifeq(beautiful(washington),true,ifeq(has_crime(washington),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
fof(f2,axiom,
! [A] :
( capital(A)
=> city(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',capital_city_type) ).
fof(f2_nnf,plain,
! [A] :
( city(A)
| ~ capital(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] :
( city(A)
| ~ capital(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( city(X0)
| ~ capital(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(capital(X0),true,city(X0),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
fof(f4,axiom,
capital(washington),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',washington_type) ).
fof(f4_nnf,plain,
capital(washington),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
capital(washington),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,axiom,
capital(washington) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h4,plain,
city(washington) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi4]) ).
fof(f7,axiom,
! [X] :
( city(X)
=> has_crime(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crime_axiom) ).
fof(f7_nnf,plain,
! [X] :
( has_crime(X)
| ~ city(X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X] :
( has_crime(X)
| ~ city(X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( has_crime(X0)
| ~ city(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(city(X0),true,has_crime(X0),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t10,plain,
has_crime(washington) = true,
inference(hyper_resolution,[status(thm)],[hi7,h4]) ).
cnf(t33,plain,
has_crime(washington) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t61,plain,
ifeq(beautiful(washington),true,ifeq(true,true,false,true),true) = true,
inference(step,[status(thm)],[t24,t33]) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t25,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t19]) ).
cnf(t62,plain,
ifeq(beautiful(washington),true,false,true) = true,
inference(step,[status(thm)],[t61,t25]) ).
cnf(t45,plain,
ifeq(beautiful(washington),true,false,true) = true,
inference(orient,[status(thm)],[t62]) ).
fof(f9,axiom,
! [X] :
( country(X)
=> beautiful(capital_city(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beautiful_capital_axiom) ).
fof(f9_nnf,plain,
! [X] :
( beautiful(capital_city(X))
| ~ country(X) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] :
( beautiful(capital_city(X))
| ~ country(X) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( beautiful(capital_city(X0))
| ~ country(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
ifeq(country(X0),true,beautiful(capital_city(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f3,axiom,
? [A] : country(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',country_type) ).
fof(f3_nnf,plain,
? [A] : country(A),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
country(sk2),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f3_nnf]) ).
cnf(c3,plain,
country(sk2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
country(sk2) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t11,plain,
beautiful(capital_city(sk2)) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi3]) ).
cnf(t57,plain,
beautiful(capital_city(sk2)) = true,
inference(orient,[status(thm)],[t11]) ).
fof(f8,axiom,
capital_city(usa) = washington,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',usa_capital_axiom) ).
fof(f8_nnf,plain,
capital_city(usa) = washington,
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
capital_city(usa) = washington,
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(t2,plain,
capital_city(usa) = washington,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t58,plain,
capital_city(usa) = washington,
inference(orient,[status(thm)],[t2]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(g0_0,plain,
true != ifeq(beautiful(washington),true,false,true),
inference(rw,[status(thm)],[goal_0,t45]) ).
cnf(g0_1,plain,
true != ifeq(beautiful(washington),beautiful(capital_city(usa)),false,true),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
true != ifeq(beautiful(washington),beautiful(capital_city(usa)),false,beautiful(capital_city(sk2))),
inference(rw,[status(thm)],[g0_1,t57]) ).
cnf(g0_3,plain,
true != ifeq(beautiful(washington),beautiful(washington),false,beautiful(capital_city(sk2))),
inference(rw,[status(thm)],[g0_2,t58]) ).
cnf(g0_4,plain,
true != false,
inference(rw,[status(thm)],[g0_3,t25]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ132+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 07:02:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.08/0.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.08/0.87 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------