TSTP Solution File: SET920+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET920+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n025.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 15:33:44 EDT 2023
% Result : Theorem 0.20s 0.44s
% 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
% 0.00/0.12 % Problem : SET920+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n025.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
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 12:53:52 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.44 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.20/0.44
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 Take the following subset of the input axioms:
% 0.20/0.45 fof(commutativity_k3_xboole_0, axiom, ![A, B]: set_intersection2(A, B)=set_intersection2(B, A)).
% 0.20/0.45 fof(d2_tarski, axiom, ![C, A2, B2]: (C=unordered_pair(A2, B2) <=> ![D]: (in(D, C) <=> (D=A2 | D=B2)))).
% 0.20/0.45 fof(d3_xboole_0, axiom, ![B2, C2, A2_2]: (C2=set_intersection2(A2_2, B2) <=> ![D2]: (in(D2, C2) <=> (in(D2, A2_2) & in(D2, B2))))).
% 0.20/0.45 fof(t63_zfmisc_1, conjecture, ![A3, B2, C2]: (set_intersection2(unordered_pair(A3, B2), C2)=unordered_pair(A3, B2) => in(A3, C2))).
% 0.20/0.45
% 0.20/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.45 fresh(y, y, x1...xn) = u
% 0.20/0.45 C => fresh(s, t, x1...xn) = v
% 0.20/0.45 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.45 variables of u and v.
% 0.20/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.45 input problem has no model of domain size 1).
% 0.20/0.45
% 0.20/0.45 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.45
% 0.20/0.45 Axiom 1 (commutativity_k3_xboole_0): set_intersection2(X, Y) = set_intersection2(Y, X).
% 0.20/0.45 Axiom 2 (d2_tarski_1): equiv2(X, Y, X) = true2.
% 0.20/0.45 Axiom 3 (t63_zfmisc_1): set_intersection2(unordered_pair(a, b), c) = unordered_pair(a, b).
% 0.20/0.45 Axiom 4 (d2_tarski_4): fresh13(X, X, Y, Z) = true2.
% 0.20/0.45 Axiom 5 (d3_xboole_0_5): fresh4(X, X, Y, Z) = true2.
% 0.20/0.45 Axiom 6 (d3_xboole_0_1): fresh10(X, X, Y, Z, W) = true2.
% 0.20/0.45 Axiom 7 (d2_tarski_4): fresh14(X, X, Y, Z, W, V) = in(V, W).
% 0.20/0.45 Axiom 8 (d3_xboole_0_1): fresh11(X, X, Y, Z, W, V) = equiv(Y, Z, V).
% 0.20/0.45 Axiom 9 (d3_xboole_0_5): fresh4(equiv(X, Y, Z), true2, X, Z) = in(Z, X).
% 0.20/0.45 Axiom 10 (d3_xboole_0_1): fresh11(in(X, Y), true2, Z, W, Y, X) = fresh10(Y, set_intersection2(Z, W), Z, W, X).
% 0.20/0.45 Axiom 11 (d2_tarski_4): fresh14(equiv2(X, Y, Z), true2, X, Y, W, Z) = fresh13(W, unordered_pair(X, Y), W, Z).
% 0.20/0.45
% 0.20/0.45 Goal 1 (t63_zfmisc_1_1): in(a, c) = true2.
% 0.20/0.45 Proof:
% 0.20/0.45 in(a, c)
% 0.20/0.45 = { by axiom 9 (d3_xboole_0_5) R->L }
% 0.20/0.45 fresh4(equiv(c, unordered_pair(a, b), a), true2, c, a)
% 0.20/0.45 = { by axiom 8 (d3_xboole_0_1) R->L }
% 0.20/0.45 fresh4(fresh11(true2, true2, c, unordered_pair(a, b), unordered_pair(a, b), a), true2, c, a)
% 0.20/0.45 = { by axiom 4 (d2_tarski_4) R->L }
% 0.20/0.45 fresh4(fresh11(fresh13(unordered_pair(a, b), unordered_pair(a, b), unordered_pair(a, b), a), true2, c, unordered_pair(a, b), unordered_pair(a, b), a), true2, c, a)
% 0.20/0.45 = { by axiom 11 (d2_tarski_4) R->L }
% 0.20/0.45 fresh4(fresh11(fresh14(equiv2(a, b, a), true2, a, b, unordered_pair(a, b), a), true2, c, unordered_pair(a, b), unordered_pair(a, b), a), true2, c, a)
% 0.20/0.45 = { by axiom 2 (d2_tarski_1) }
% 0.20/0.45 fresh4(fresh11(fresh14(true2, true2, a, b, unordered_pair(a, b), a), true2, c, unordered_pair(a, b), unordered_pair(a, b), a), true2, c, a)
% 0.20/0.45 = { by axiom 7 (d2_tarski_4) }
% 0.20/0.45 fresh4(fresh11(in(a, unordered_pair(a, b)), true2, c, unordered_pair(a, b), unordered_pair(a, b), a), true2, c, a)
% 0.20/0.45 = { by axiom 10 (d3_xboole_0_1) }
% 0.20/0.45 fresh4(fresh10(unordered_pair(a, b), set_intersection2(c, unordered_pair(a, b)), c, unordered_pair(a, b), a), true2, c, a)
% 0.20/0.45 = { by axiom 1 (commutativity_k3_xboole_0) R->L }
% 0.20/0.45 fresh4(fresh10(unordered_pair(a, b), set_intersection2(unordered_pair(a, b), c), c, unordered_pair(a, b), a), true2, c, a)
% 0.20/0.45 = { by axiom 3 (t63_zfmisc_1) }
% 0.20/0.45 fresh4(fresh10(unordered_pair(a, b), unordered_pair(a, b), c, unordered_pair(a, b), a), true2, c, a)
% 0.20/0.45 = { by axiom 6 (d3_xboole_0_1) }
% 0.20/0.45 fresh4(true2, true2, c, a)
% 0.20/0.45 = { by axiom 5 (d3_xboole_0_5) }
% 0.20/0.45 true2
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45
% 0.20/0.45 RESULT: Theorem (the conjecture is true).
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