TSTP Solution File: SEU264+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU264+2 : 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 : n028.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 17:51:54 EDT 2023
% Result : Theorem 126.43s 16.54s
% Output : Proof 126.43s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU264+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % 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 : n028.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 : Thu Aug 24 01:49:34 EDT 2023
% 0.13/0.35 % CPUTime :
% 126.43/16.54 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 126.43/16.54
% 126.43/16.54 % SZS status Theorem
% 126.43/16.54
% 126.43/16.55 % SZS output start Proof
% 126.43/16.55 Take the following subset of the input axioms:
% 126.43/16.55 fof(t12_relset_1, lemma, ![B, C, A2]: (relation_of2_as_subset(C, A2, B) => (subset(relation_dom(C), A2) & subset(relation_rng(C), B)))).
% 126.43/16.55 fof(t14_relset_1, lemma, ![A, D, B2, C2]: (relation_of2_as_subset(D, C2, A) => (subset(relation_rng(D), B2) => relation_of2_as_subset(D, C2, B2)))).
% 126.43/16.55 fof(t16_relset_1, conjecture, ![B2, C2, A3, D2]: (relation_of2_as_subset(D2, C2, A3) => (subset(A3, B2) => relation_of2_as_subset(D2, C2, B2)))).
% 126.43/16.55 fof(t1_xboole_1, lemma, ![B2, C2, A2_2]: ((subset(A2_2, B2) & subset(B2, C2)) => subset(A2_2, C2))).
% 126.43/16.55
% 126.43/16.55 Now clausify the problem and encode Horn clauses using encoding 3 of
% 126.43/16.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 126.43/16.55 We repeatedly replace C & s=t => u=v by the two clauses:
% 126.43/16.55 fresh(y, y, x1...xn) = u
% 126.43/16.55 C => fresh(s, t, x1...xn) = v
% 126.43/16.55 where fresh is a fresh function symbol and x1..xn are the free
% 126.43/16.55 variables of u and v.
% 126.43/16.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 126.43/16.55 input problem has no model of domain size 1).
% 126.43/16.55
% 126.43/16.55 The encoding turns the above axioms into the following unit equations and goals:
% 126.43/16.55
% 126.43/16.55 Axiom 1 (t16_relset_1): subset(a, b5) = true2.
% 126.43/16.55 Axiom 2 (t16_relset_1_1): relation_of2_as_subset(d5, c8, a) = true2.
% 126.43/16.55 Axiom 3 (t12_relset_1_1): fresh228(X, X, Y, Z) = true2.
% 126.43/16.55 Axiom 4 (t1_xboole_1): fresh185(X, X, Y, Z) = true2.
% 126.43/16.55 Axiom 5 (t14_relset_1): fresh213(X, X, Y, Z, W) = relation_of2_as_subset(W, Z, Y).
% 126.43/16.55 Axiom 6 (t14_relset_1): fresh212(X, X, Y, Z, W) = true2.
% 126.43/16.55 Axiom 7 (t1_xboole_1): fresh186(X, X, Y, Z, W) = subset(Y, W).
% 126.43/16.55 Axiom 8 (t12_relset_1_1): fresh228(relation_of2_as_subset(X, Y, Z), true2, Z, X) = subset(relation_rng(X), Z).
% 126.43/16.55 Axiom 9 (t1_xboole_1): fresh186(subset(X, Y), true2, Z, X, Y) = fresh185(subset(Z, X), true2, Z, Y).
% 126.43/16.55 Axiom 10 (t14_relset_1): fresh213(relation_of2_as_subset(X, Y, Z), true2, W, Y, X) = fresh212(subset(relation_rng(X), W), true2, W, Y, X).
% 126.43/16.55
% 126.43/16.55 Goal 1 (t16_relset_1_2): relation_of2_as_subset(d5, c8, b5) = true2.
% 126.43/16.55 Proof:
% 126.43/16.55 relation_of2_as_subset(d5, c8, b5)
% 126.43/16.55 = { by axiom 5 (t14_relset_1) R->L }
% 126.43/16.55 fresh213(true2, true2, b5, c8, d5)
% 126.43/16.55 = { by axiom 2 (t16_relset_1_1) R->L }
% 126.43/16.55 fresh213(relation_of2_as_subset(d5, c8, a), true2, b5, c8, d5)
% 126.43/16.55 = { by axiom 10 (t14_relset_1) }
% 126.43/16.55 fresh212(subset(relation_rng(d5), b5), true2, b5, c8, d5)
% 126.43/16.55 = { by axiom 7 (t1_xboole_1) R->L }
% 126.43/16.55 fresh212(fresh186(true2, true2, relation_rng(d5), a, b5), true2, b5, c8, d5)
% 126.43/16.55 = { by axiom 1 (t16_relset_1) R->L }
% 126.43/16.55 fresh212(fresh186(subset(a, b5), true2, relation_rng(d5), a, b5), true2, b5, c8, d5)
% 126.43/16.55 = { by axiom 9 (t1_xboole_1) }
% 126.43/16.55 fresh212(fresh185(subset(relation_rng(d5), a), true2, relation_rng(d5), b5), true2, b5, c8, d5)
% 126.43/16.55 = { by axiom 8 (t12_relset_1_1) R->L }
% 126.43/16.55 fresh212(fresh185(fresh228(relation_of2_as_subset(d5, c8, a), true2, a, d5), true2, relation_rng(d5), b5), true2, b5, c8, d5)
% 126.43/16.55 = { by axiom 2 (t16_relset_1_1) }
% 126.43/16.55 fresh212(fresh185(fresh228(true2, true2, a, d5), true2, relation_rng(d5), b5), true2, b5, c8, d5)
% 126.43/16.55 = { by axiom 3 (t12_relset_1_1) }
% 126.43/16.55 fresh212(fresh185(true2, true2, relation_rng(d5), b5), true2, b5, c8, d5)
% 126.43/16.55 = { by axiom 4 (t1_xboole_1) }
% 126.43/16.55 fresh212(true2, true2, b5, c8, d5)
% 126.43/16.55 = { by axiom 6 (t14_relset_1) }
% 126.43/16.55 true2
% 126.43/16.55 % SZS output end Proof
% 126.43/16.55
% 126.43/16.55 RESULT: Theorem (the conjecture is true).
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