TSTP Solution File: SWV383+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV383+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n011.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 23:04:02 EDT 2023
% Result : Theorem 0.20s 0.47s
% 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
% 0.11/0.12 % Problem : SWV383+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 09:24:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.47
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 Take the following subset of the input axioms:
% 0.20/0.48 fof(l19_co, conjecture, ![U, V, W]: (~check_cpq(triple(U, V, W)) => ![X, Y, Z]: (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => (~ok(triple(X, Y, Z)) | ~check_cpq(triple(X, Y, Z)))))).
% 0.20/0.48 fof(l19_l20, lemma, ![U2, V2, W2]: ((~check_cpq(triple(U2, V2, W2)) | ~ok(triple(U2, V2, W2))) => ![X2, Y2, Z2]: (succ_cpq(triple(U2, V2, W2), triple(X2, Y2, Z2)) => (~ok(triple(X2, Y2, Z2)) | ~check_cpq(triple(X2, Y2, Z2)))))).
% 0.20/0.48
% 0.20/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.48 fresh(y, y, x1...xn) = u
% 0.20/0.48 C => fresh(s, t, x1...xn) = v
% 0.20/0.48 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.48 variables of u and v.
% 0.20/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.48 input problem has no model of domain size 1).
% 0.20/0.48
% 0.20/0.48 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.48
% 0.20/0.48 Axiom 1 (l19_co_2): ok(triple(x, y, z)) = true2.
% 0.20/0.48 Axiom 2 (l19_co_1): check_cpq(triple(x, y, z)) = true2.
% 0.20/0.48 Axiom 3 (l19_l20): fresh5(X, X, Y, Z, W) = true2.
% 0.20/0.48 Axiom 4 (l19_l20): fresh25(X, X, Y, Z, W, V, U, T) = check_cpq(triple(Y, Z, W)).
% 0.20/0.48 Axiom 5 (l19_co): succ_cpq(triple(u, v, w), triple(x, y, z)) = true2.
% 0.20/0.48 Axiom 6 (l19_l20): fresh24(X, X, Y, Z, W, V, U, T) = fresh25(check_cpq(triple(V, U, T)), true2, Y, Z, W, V, U, T).
% 0.20/0.48 Axiom 7 (l19_l20): fresh24(ok(triple(X, Y, Z)), true2, W, V, U, X, Y, Z) = fresh5(succ_cpq(triple(W, V, U), triple(X, Y, Z)), true2, W, V, U).
% 0.20/0.48
% 0.20/0.48 Goal 1 (l19_co_3): check_cpq(triple(u, v, w)) = true2.
% 0.20/0.48 Proof:
% 0.20/0.48 check_cpq(triple(u, v, w))
% 0.20/0.48 = { by axiom 4 (l19_l20) R->L }
% 0.20/0.48 fresh25(true2, true2, u, v, w, x, y, z)
% 0.20/0.48 = { by axiom 2 (l19_co_1) R->L }
% 0.20/0.48 fresh25(check_cpq(triple(x, y, z)), true2, u, v, w, x, y, z)
% 0.20/0.48 = { by axiom 6 (l19_l20) R->L }
% 0.20/0.48 fresh24(true2, true2, u, v, w, x, y, z)
% 0.20/0.48 = { by axiom 1 (l19_co_2) R->L }
% 0.20/0.48 fresh24(ok(triple(x, y, z)), true2, u, v, w, x, y, z)
% 0.20/0.48 = { by axiom 7 (l19_l20) }
% 0.20/0.48 fresh5(succ_cpq(triple(u, v, w), triple(x, y, z)), true2, u, v, w)
% 0.20/0.48 = { by axiom 5 (l19_co) }
% 0.20/0.48 fresh5(true2, true2, u, v, w)
% 0.20/0.48 = { by axiom 3 (l19_l20) }
% 0.20/0.48 true2
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48
% 0.20/0.48 RESULT: Theorem (the conjecture is true).
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