TSTP Solution File: PUZ060+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ060+1 : TPTP v8.1.2. Released v3.1.0.
% 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 13:24:08 EDT 2023
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : PUZ060+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % 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 22:29:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.38 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.14/0.38
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38
% 0.14/0.38 % SZS output start Proof
% 0.14/0.38 Take the following subset of the input axioms:
% 0.14/0.38 fof(prove_this, conjecture, ![Peanuts, John, Bill, Sue, Apples, Chicken]: ((![X]: (food(X) => likes(John, X)) & (food(Apples) & (food(Chicken) & (![X2]: (?[Y]: (eats(Y, X2) & not_killed_by(Y, X2)) => food(X2)) & (eats(Bill, Peanuts) & (alive(Bill) & (![X2]: (eats(Bill, X2) => eats(Sue, X2)) & ![Y2]: (alive(Y2) => ![X2]: not_killed_by(Y2, X2))))))))) => likes(John, Peanuts))).
% 0.14/0.38
% 0.14/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.38 fresh(y, y, x1...xn) = u
% 0.19/0.38 C => fresh(s, t, x1...xn) = v
% 0.19/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.38 variables of u and v.
% 0.19/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.38 input problem has no model of domain size 1).
% 0.19/0.38
% 0.19/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.38
% 0.19/0.38 Axiom 1 (prove_this_3): alive(bill) = true.
% 0.19/0.38 Axiom 2 (prove_this_2): eats(bill, peanuts) = true.
% 0.19/0.38 Axiom 3 (prove_this_4): fresh4(X, X, Y) = true.
% 0.19/0.38 Axiom 4 (prove_this_6): fresh3(X, X, Y) = true.
% 0.19/0.38 Axiom 5 (prove_this_8): fresh(X, X, Y, Z) = true.
% 0.19/0.38 Axiom 6 (prove_this_6): fresh5(X, X, Y, Z) = food(Y).
% 0.19/0.38 Axiom 7 (prove_this_4): fresh4(food(X), true, X) = likes(john, X).
% 0.19/0.38 Axiom 8 (prove_this_8): fresh(alive(X), true, X, Y) = not_killed_by(X, Y).
% 0.19/0.38 Axiom 9 (prove_this_6): fresh5(not_killed_by(X, Y), true, Y, X) = fresh3(eats(X, Y), true, Y).
% 0.19/0.38
% 0.19/0.38 Goal 1 (prove_this_5): likes(john, peanuts) = true.
% 0.19/0.38 Proof:
% 0.19/0.38 likes(john, peanuts)
% 0.19/0.38 = { by axiom 7 (prove_this_4) R->L }
% 0.19/0.38 fresh4(food(peanuts), true, peanuts)
% 0.19/0.38 = { by axiom 6 (prove_this_6) R->L }
% 0.19/0.38 fresh4(fresh5(true, true, peanuts, bill), true, peanuts)
% 0.19/0.38 = { by axiom 5 (prove_this_8) R->L }
% 0.19/0.38 fresh4(fresh5(fresh(true, true, bill, peanuts), true, peanuts, bill), true, peanuts)
% 0.19/0.38 = { by axiom 1 (prove_this_3) R->L }
% 0.19/0.38 fresh4(fresh5(fresh(alive(bill), true, bill, peanuts), true, peanuts, bill), true, peanuts)
% 0.19/0.38 = { by axiom 8 (prove_this_8) }
% 0.19/0.38 fresh4(fresh5(not_killed_by(bill, peanuts), true, peanuts, bill), true, peanuts)
% 0.19/0.38 = { by axiom 9 (prove_this_6) }
% 0.19/0.38 fresh4(fresh3(eats(bill, peanuts), true, peanuts), true, peanuts)
% 0.19/0.38 = { by axiom 2 (prove_this_2) }
% 0.19/0.38 fresh4(fresh3(true, true, peanuts), true, peanuts)
% 0.19/0.38 = { by axiom 4 (prove_this_6) }
% 0.19/0.38 fresh4(true, true, peanuts)
% 0.19/0.38 = { by axiom 3 (prove_this_4) }
% 0.19/0.38 true
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38
% 0.19/0.38 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------