TSTP Solution File: PUZ132+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : PUZ132+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n014.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 : Thu Aug 31 13:24:22 EDT 2023
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : PUZ132+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 22:42:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.39 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 Take the following subset of the input axioms:
% 0.14/0.39 fof(beautiful_capital_axiom, axiom, ![X]: (country(X) => beautiful(capital_city(X)))).
% 0.14/0.39 fof(capital_city_type, axiom, ![A2]: (capital(A2) => city(A2))).
% 0.14/0.39 fof(crime_axiom, axiom, ![X2]: (city(X2) => has_crime(X2))).
% 0.14/0.39 fof(usa_capital_axiom, axiom, capital_city(usa)=washington).
% 0.14/0.39 fof(usa_type, axiom, country(usa)).
% 0.14/0.39 fof(washington_conjecture, conjecture, beautiful(washington) & has_crime(washington)).
% 0.14/0.39 fof(washington_type, axiom, capital(washington)).
% 0.20/0.39
% 0.20/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.39 fresh(y, y, x1...xn) = u
% 0.20/0.39 C => fresh(s, t, x1...xn) = v
% 0.20/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.39 variables of u and v.
% 0.20/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.39 input problem has no model of domain size 1).
% 0.20/0.39
% 0.20/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.39
% 0.20/0.39 Axiom 1 (washington_type): capital(washington) = true.
% 0.20/0.39 Axiom 2 (usa_type): country(usa) = true.
% 0.20/0.39 Axiom 3 (usa_capital_axiom): capital_city(usa) = washington.
% 0.20/0.39 Axiom 4 (crime_axiom): fresh(X, X, Y) = true.
% 0.20/0.39 Axiom 5 (capital_city_type): fresh4(X, X, Y) = true.
% 0.20/0.39 Axiom 6 (beautiful_capital_axiom): fresh3(X, X, Y) = true.
% 0.20/0.39 Axiom 7 (crime_axiom): fresh(city(X), true, X) = has_crime(X).
% 0.20/0.39 Axiom 8 (capital_city_type): fresh4(capital(X), true, X) = city(X).
% 0.20/0.39 Axiom 9 (beautiful_capital_axiom): fresh3(country(X), true, X) = beautiful(capital_city(X)).
% 0.20/0.39
% 0.20/0.39 Goal 1 (washington_conjecture): tuple(has_crime(washington), beautiful(washington)) = tuple(true, true).
% 0.20/0.39 Proof:
% 0.20/0.39 tuple(has_crime(washington), beautiful(washington))
% 0.20/0.39 = { by axiom 7 (crime_axiom) R->L }
% 0.20/0.39 tuple(fresh(city(washington), true, washington), beautiful(washington))
% 0.20/0.39 = { by axiom 8 (capital_city_type) R->L }
% 0.20/0.39 tuple(fresh(fresh4(capital(washington), true, washington), true, washington), beautiful(washington))
% 0.20/0.39 = { by axiom 1 (washington_type) }
% 0.20/0.39 tuple(fresh(fresh4(true, true, washington), true, washington), beautiful(washington))
% 0.20/0.39 = { by axiom 5 (capital_city_type) }
% 0.20/0.39 tuple(fresh(true, true, washington), beautiful(washington))
% 0.20/0.39 = { by axiom 4 (crime_axiom) }
% 0.20/0.39 tuple(true, beautiful(washington))
% 0.20/0.39 = { by axiom 3 (usa_capital_axiom) R->L }
% 0.20/0.39 tuple(true, beautiful(capital_city(usa)))
% 0.20/0.39 = { by axiom 9 (beautiful_capital_axiom) R->L }
% 0.20/0.39 tuple(true, fresh3(country(usa), true, usa))
% 0.20/0.39 = { by axiom 2 (usa_type) }
% 0.20/0.39 tuple(true, fresh3(true, true, usa))
% 0.20/0.39 = { by axiom 6 (beautiful_capital_axiom) }
% 0.20/0.39 tuple(true, true)
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39
% 0.20/0.39 RESULT: Theorem (the conjecture is true).
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