%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ132+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 : Sun Sep 27 08:23:22 AM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 39 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 9 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 10 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(capital_city_type,axiom,
! [A] :
( capital(A)
=> city(A) ),
file('theBenchmark.p',capital_city_type) ).
fof(country_capital_type,axiom,
! [A] :
( country(A)
=> capital(capital_city(A)) ),
file('theBenchmark.p',country_capital_type) ).
fof(crime_axiom,axiom,
! [X] :
( city(X)
=> has_crime(X) ),
file('theBenchmark.p',crime_axiom) ).
fof(beautiful_capital_axiom,axiom,
! [X] :
( country(X)
=> beautiful(capital_city(X)) ),
file('theBenchmark.p',beautiful_capital_axiom) ).
fof(washington_conjecture,conjecture,
( has_crime(washington)
& beautiful(washington) ),
file('theBenchmark.p',washington_conjecture) ).
fof(washington_conjecture_neg,negated_conjecture,
~ ( has_crime(washington)
& beautiful(washington) ),
inference(assume_negation,[status(cth)],[washington_conjecture]) ).
cnf(c_9,plain,
( city(A)
| ~ capital(A) ),
inference(clausify,[status(thm)],[capital_city_type]) ).
cnf(c_12,plain,
( capital(capital_city(A))
| ~ country(A) ),
inference(clausify,[status(thm)],[country_capital_type]) ).
cnf(c_13,plain,
( has_crime(A)
| ~ city(A) ),
inference(clausify,[status(thm)],[crime_axiom]) ).
cnf(c_16,plain,
( city(capital_city(A))
| ~ country(A) ),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_19,plain,
( ~ country(A)
| has_crime(capital_city(A)) ),
inference(resolve,[status(thm)],[c_13,c_16]) ).
fof(usa_type,axiom,
country(usa),
file('theBenchmark.p',usa_type) ).
cnf(c_20,plain,
country(usa),
inference(clausify,[status(thm)],[usa_type]) ).
cnf(c_21,plain,
( beautiful(capital_city(A))
| ~ country(A) ),
inference(clausify,[status(thm)],[beautiful_capital_axiom]) ).
cnf(c_23,plain,
beautiful(capital_city(usa)),
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_24,plain,
has_crime(capital_city(usa)),
inference(resolve,[status(thm)],[c_20,c_19]) ).
cnf(c_26,negated_conjecture,
( ~ has_crime(washington)
| ~ beautiful(washington) ),
inference(clausify,[status(thm)],[washington_conjecture_neg]) ).
fof(usa_capital_axiom,axiom,
capital_city(usa) = washington,
file('theBenchmark.p',usa_capital_axiom) ).
cnf(c_27,plain,
capital_city(usa) = washington,
inference(clausify,[status(thm)],[usa_capital_axiom]) ).
cnf(c_28,plain,
washington = capital_city(usa),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_33,negated_conjecture,
( ~ has_crime(washington)
| ~ beautiful(capital_city(usa)) ),
inference(paramod,[status(thm)],[c_28,c_26]) ).
cnf(c_34,negated_conjecture,
( ~ has_crime(capital_city(usa))
| ~ beautiful(capital_city(usa)) ),
inference(paramod,[status(thm)],[c_28,c_33]) ).
cnf(c_35,negated_conjecture,
~ has_crime(capital_city(usa)),
inference(resolve,[status(thm)],[c_23,c_34]) ).
cnf(c_32,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_24,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ132+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 05:22:15 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3210461 was started by sandbox2 on n015,
% 0.08/0.37 % Sat Sep 26 05:22:15 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.39
% 0.08/0.39 % SZS status Theorem for theBenchmark
% 0.08/0.39
% 0.08/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.39 % Length of proof is 18.
% 0.08/0.39 % Level of proof is 5.
% 0.08/0.39 % Maximum clause weight is 4.000.
% 0.08/0.39 % Given clauses 0.
% 0.08/0.39
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------