TSTP Solution File: SEU264+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU264+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 : n001.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 17:51:53 EDT 2023
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% 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+1 : 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
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 18:10:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.40 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.40
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Take the following subset of the input axioms:
% 0.21/0.41 fof(t12_relset_1, axiom, ![B, C, A2]: (relation_of2_as_subset(C, A2, B) => (subset(relation_dom(C), A2) & subset(relation_rng(C), B)))).
% 0.21/0.41 fof(t14_relset_1, axiom, ![D, B2, C2, A2_2]: (relation_of2_as_subset(D, C2, A2_2) => (subset(relation_rng(D), B2) => relation_of2_as_subset(D, C2, B2)))).
% 0.21/0.41 fof(t16_relset_1, conjecture, ![A, B2, C2, D2]: (relation_of2_as_subset(D2, C2, A) => (subset(A, B2) => relation_of2_as_subset(D2, C2, B2)))).
% 0.21/0.41 fof(t1_xboole_1, axiom, ![B2, C2, A2_2]: ((subset(A2_2, B2) & subset(B2, C2)) => subset(A2_2, C2))).
% 0.21/0.41
% 0.21/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.41 fresh(y, y, x1...xn) = u
% 0.21/0.41 C => fresh(s, t, x1...xn) = v
% 0.21/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.41 variables of u and v.
% 0.21/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.41 input problem has no model of domain size 1).
% 0.21/0.41
% 0.21/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.41
% 0.21/0.41 Axiom 1 (t16_relset_1_1): subset(a, b) = true.
% 0.21/0.41 Axiom 2 (t16_relset_1): relation_of2_as_subset(d, c, a) = true.
% 0.21/0.41 Axiom 3 (t12_relset_1_1): fresh7(X, X, Y, Z) = true.
% 0.21/0.41 Axiom 4 (t1_xboole_1): fresh3(X, X, Y, Z) = true.
% 0.21/0.41 Axiom 5 (t14_relset_1): fresh5(X, X, Y, Z, W) = true.
% 0.21/0.41 Axiom 6 (t1_xboole_1): fresh4(X, X, Y, Z, W) = subset(Y, W).
% 0.21/0.41 Axiom 7 (t14_relset_1): fresh6(X, X, Y, Z, W, V) = relation_of2_as_subset(V, W, Z).
% 0.21/0.41 Axiom 8 (t12_relset_1_1): fresh7(relation_of2_as_subset(X, Y, Z), true, Z, X) = subset(relation_rng(X), Z).
% 0.21/0.41 Axiom 9 (t1_xboole_1): fresh4(subset(X, Y), true, Z, X, Y) = fresh3(subset(Z, X), true, Z, Y).
% 0.21/0.41 Axiom 10 (t14_relset_1): fresh6(subset(relation_rng(X), Y), true, Z, Y, W, X) = fresh5(relation_of2_as_subset(X, W, Z), true, Y, W, X).
% 0.21/0.41
% 0.21/0.41 Goal 1 (t16_relset_1_2): relation_of2_as_subset(d, c, b) = true.
% 0.21/0.41 Proof:
% 0.21/0.41 relation_of2_as_subset(d, c, b)
% 0.21/0.41 = { by axiom 7 (t14_relset_1) R->L }
% 0.21/0.41 fresh6(true, true, a, b, c, d)
% 0.21/0.41 = { by axiom 4 (t1_xboole_1) R->L }
% 0.21/0.41 fresh6(fresh3(true, true, relation_rng(d), b), true, a, b, c, d)
% 0.21/0.41 = { by axiom 3 (t12_relset_1_1) R->L }
% 0.21/0.41 fresh6(fresh3(fresh7(true, true, a, d), true, relation_rng(d), b), true, a, b, c, d)
% 0.21/0.41 = { by axiom 2 (t16_relset_1) R->L }
% 0.21/0.41 fresh6(fresh3(fresh7(relation_of2_as_subset(d, c, a), true, a, d), true, relation_rng(d), b), true, a, b, c, d)
% 0.21/0.41 = { by axiom 8 (t12_relset_1_1) }
% 0.21/0.41 fresh6(fresh3(subset(relation_rng(d), a), true, relation_rng(d), b), true, a, b, c, d)
% 0.21/0.41 = { by axiom 9 (t1_xboole_1) R->L }
% 0.21/0.41 fresh6(fresh4(subset(a, b), true, relation_rng(d), a, b), true, a, b, c, d)
% 0.21/0.41 = { by axiom 1 (t16_relset_1_1) }
% 0.21/0.41 fresh6(fresh4(true, true, relation_rng(d), a, b), true, a, b, c, d)
% 0.21/0.41 = { by axiom 6 (t1_xboole_1) }
% 0.21/0.41 fresh6(subset(relation_rng(d), b), true, a, b, c, d)
% 0.21/0.41 = { by axiom 10 (t14_relset_1) }
% 0.21/0.41 fresh5(relation_of2_as_subset(d, c, a), true, b, c, d)
% 0.21/0.41 = { by axiom 2 (t16_relset_1) }
% 0.21/0.41 fresh5(true, true, b, c, d)
% 0.21/0.41 = { by axiom 5 (t14_relset_1) }
% 0.21/0.41 true
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41
% 0.21/0.41 RESULT: Theorem (the conjecture is true).
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