TSTP Solution File: SEU129+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU129+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 : n026.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 17:51:06 EDT 2023
% Result : Theorem 0.21s 0.49s
% 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 : SEU129+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 : n026.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 : Wed Aug 23 18:48:46 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.49 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.49
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49
% 0.21/0.50 % SZS output start Proof
% 0.21/0.50 Take the following subset of the input axioms:
% 0.21/0.50 fof(commutativity_k3_xboole_0, axiom, ![A, B]: set_intersection2(A, B)=set_intersection2(B, A)).
% 0.21/0.50 fof(t17_xboole_1, lemma, ![A3, B2]: subset(set_intersection2(A3, B2), A3)).
% 0.21/0.50 fof(t19_xboole_1, lemma, ![C, A2, B2]: ((subset(A2, B2) & subset(A2, C)) => subset(A2, set_intersection2(B2, C)))).
% 0.21/0.50 fof(t1_xboole_1, lemma, ![B2, C2, A2_2]: ((subset(A2_2, B2) & subset(B2, C2)) => subset(A2_2, C2))).
% 0.21/0.50 fof(t26_xboole_1, conjecture, ![A3, B2, C2]: (subset(A3, B2) => subset(set_intersection2(A3, C2), set_intersection2(B2, C2)))).
% 0.21/0.50
% 0.21/0.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.50 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.50 fresh(y, y, x1...xn) = u
% 0.21/0.50 C => fresh(s, t, x1...xn) = v
% 0.21/0.50 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.50 variables of u and v.
% 0.21/0.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.50 input problem has no model of domain size 1).
% 0.21/0.50
% 0.21/0.50 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.50
% 0.21/0.50 Axiom 1 (commutativity_k3_xboole_0): set_intersection2(X, Y) = set_intersection2(Y, X).
% 0.21/0.50 Axiom 2 (t26_xboole_1): subset(a, b) = true2.
% 0.21/0.50 Axiom 3 (t1_xboole_1): fresh12(X, X, Y, Z) = true2.
% 0.21/0.50 Axiom 4 (t17_xboole_1): subset(set_intersection2(X, Y), X) = true2.
% 0.21/0.50 Axiom 5 (t19_xboole_1): fresh15(X, X, Y, Z, W) = subset(Y, set_intersection2(Z, W)).
% 0.21/0.50 Axiom 6 (t19_xboole_1): fresh14(X, X, Y, Z, W) = true2.
% 0.21/0.50 Axiom 7 (t1_xboole_1): fresh13(X, X, Y, Z, W) = subset(Y, W).
% 0.21/0.50 Axiom 8 (t19_xboole_1): fresh15(subset(X, Y), true2, X, Z, Y) = fresh14(subset(X, Z), true2, X, Z, Y).
% 0.21/0.50 Axiom 9 (t1_xboole_1): fresh13(subset(X, Y), true2, Z, X, Y) = fresh12(subset(Z, X), true2, Z, Y).
% 0.21/0.50
% 0.21/0.50 Goal 1 (t26_xboole_1_1): subset(set_intersection2(a, c3), set_intersection2(b, c3)) = true2.
% 0.21/0.50 Proof:
% 0.21/0.50 subset(set_intersection2(a, c3), set_intersection2(b, c3))
% 0.21/0.50 = { by axiom 1 (commutativity_k3_xboole_0) R->L }
% 0.21/0.50 subset(set_intersection2(a, c3), set_intersection2(c3, b))
% 0.21/0.50 = { by axiom 1 (commutativity_k3_xboole_0) R->L }
% 0.21/0.50 subset(set_intersection2(c3, a), set_intersection2(c3, b))
% 0.21/0.50 = { by axiom 5 (t19_xboole_1) R->L }
% 0.21/0.50 fresh15(true2, true2, set_intersection2(c3, a), c3, b)
% 0.21/0.50 = { by axiom 3 (t1_xboole_1) R->L }
% 0.21/0.50 fresh15(fresh12(true2, true2, set_intersection2(a, c3), b), true2, set_intersection2(c3, a), c3, b)
% 0.21/0.50 = { by axiom 4 (t17_xboole_1) R->L }
% 0.21/0.50 fresh15(fresh12(subset(set_intersection2(a, c3), a), true2, set_intersection2(a, c3), b), true2, set_intersection2(c3, a), c3, b)
% 0.21/0.50 = { by axiom 9 (t1_xboole_1) R->L }
% 0.21/0.50 fresh15(fresh13(subset(a, b), true2, set_intersection2(a, c3), a, b), true2, set_intersection2(c3, a), c3, b)
% 0.21/0.50 = { by axiom 2 (t26_xboole_1) }
% 0.21/0.50 fresh15(fresh13(true2, true2, set_intersection2(a, c3), a, b), true2, set_intersection2(c3, a), c3, b)
% 0.21/0.50 = { by axiom 7 (t1_xboole_1) }
% 0.21/0.50 fresh15(subset(set_intersection2(a, c3), b), true2, set_intersection2(c3, a), c3, b)
% 0.21/0.50 = { by axiom 1 (commutativity_k3_xboole_0) }
% 0.21/0.50 fresh15(subset(set_intersection2(c3, a), b), true2, set_intersection2(c3, a), c3, b)
% 0.21/0.50 = { by axiom 8 (t19_xboole_1) }
% 0.21/0.50 fresh14(subset(set_intersection2(c3, a), c3), true2, set_intersection2(c3, a), c3, b)
% 0.21/0.50 = { by axiom 4 (t17_xboole_1) }
% 0.21/0.50 fresh14(true2, true2, set_intersection2(c3, a), c3, b)
% 0.21/0.50 = { by axiom 6 (t19_xboole_1) }
% 0.21/0.50 true2
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50
% 0.21/0.50 RESULT: Theorem (the conjecture is true).
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