TSTP Solution File: SEU180+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : SEU180+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 : n002.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 17:51:25 EDT 2023
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% 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 : SEU180+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
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Wed Aug 23 14:58:16 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.48 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.48
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 Take the following subset of the input axioms:
% 0.19/0.49 fof(commutativity_k2_xboole_0, axiom, ![A, B]: set_union2(A, B)=set_union2(B, A)).
% 0.19/0.49 fof(d2_xboole_0, axiom, ![C, A2, B2]: (C=set_union2(A2, B2) <=> ![D]: (in(D, C) <=> (in(D, A2) | in(D, B2))))).
% 0.19/0.49 fof(d4_relat_1, axiom, ![A2_2]: (relation(A2_2) => ![B2]: (B2=relation_dom(A2_2) <=> ![C2]: (in(C2, B2) <=> ?[D2]: in(ordered_pair(C2, D2), A2_2))))).
% 0.19/0.49 fof(d5_relat_1, axiom, ![A2_2]: (relation(A2_2) => ![B2]: (B2=relation_rng(A2_2) <=> ![C2]: (in(C2, B2) <=> ?[D2]: in(ordered_pair(D2, C2), A2_2))))).
% 0.19/0.49 fof(d6_relat_1, axiom, ![A2_2]: (relation(A2_2) => relation_field(A2_2)=set_union2(relation_dom(A2_2), relation_rng(A2_2)))).
% 0.19/0.49 fof(t30_relat_1, conjecture, ![A3, B2, C2]: (relation(C2) => (in(ordered_pair(A3, B2), C2) => (in(A3, relation_field(C2)) & in(B2, relation_field(C2)))))).
% 0.19/0.49
% 0.19/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.49 fresh(y, y, x1...xn) = u
% 0.19/0.49 C => fresh(s, t, x1...xn) = v
% 0.19/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.49 variables of u and v.
% 0.19/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.49 input problem has no model of domain size 1).
% 0.19/0.49
% 0.19/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.49
% 0.19/0.49 Axiom 1 (t30_relat_1_1): relation(c) = true2.
% 0.19/0.49 Axiom 2 (commutativity_k2_xboole_0): set_union2(X, Y) = set_union2(Y, X).
% 0.19/0.49 Axiom 3 (d6_relat_1): fresh12(X, X, Y) = relation_field(Y).
% 0.19/0.49 Axiom 4 (d4_relat_1_1): fresh33(X, X, Y, Z) = true2.
% 0.19/0.49 Axiom 5 (d5_relat_1_1): fresh27(X, X, Y, Z) = true2.
% 0.19/0.49 Axiom 6 (d2_xboole_0_2): fresh20(X, X, Y, Z) = true2.
% 0.19/0.49 Axiom 7 (d6_relat_1): fresh12(relation(X), true2, X) = set_union2(relation_dom(X), relation_rng(X)).
% 0.19/0.49 Axiom 8 (t30_relat_1): in(ordered_pair(a, b), c) = true2.
% 0.19/0.49 Axiom 9 (d2_xboole_0_3): fresh19(X, X, Y, Z, W) = true2.
% 0.19/0.49 Axiom 10 (d4_relat_1_1): fresh15(X, X, Y, Z, W) = in(W, Z).
% 0.19/0.49 Axiom 11 (d5_relat_1_1): fresh13(X, X, Y, Z, W) = in(W, Z).
% 0.19/0.49 Axiom 12 (d4_relat_1_1): fresh32(X, X, Y, Z, W, V) = fresh33(Z, relation_dom(Y), Z, W).
% 0.19/0.49 Axiom 13 (d5_relat_1_1): fresh26(X, X, Y, Z, W, V) = fresh27(Z, relation_rng(Y), Z, W).
% 0.19/0.49 Axiom 14 (d2_xboole_0_2): fresh21(X, X, Y, Z, W, V) = in(V, W).
% 0.19/0.49 Axiom 15 (d2_xboole_0_3): fresh19(in(X, Y), true2, Y, Z, X) = equiv(Y, Z, X).
% 0.19/0.49 Axiom 16 (d2_xboole_0_2): fresh21(equiv(X, Y, Z), true2, X, Y, W, Z) = fresh20(W, set_union2(X, Y), W, Z).
% 0.19/0.49 Axiom 17 (d4_relat_1_1): fresh32(relation(X), true2, X, Y, Z, W) = fresh15(in(ordered_pair(Z, W), X), true2, X, Y, Z).
% 0.19/0.49 Axiom 18 (d5_relat_1_1): fresh26(relation(X), true2, X, Y, Z, W) = fresh13(in(ordered_pair(W, Z), X), true2, X, Y, Z).
% 0.19/0.49
% 0.19/0.49 Goal 1 (t30_relat_1_2): tuple(in(a, relation_field(c)), in(b, relation_field(c))) = tuple(true2, true2).
% 0.19/0.49 Proof:
% 0.19/0.49 tuple(in(a, relation_field(c)), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 14 (d2_xboole_0_2) R->L }
% 0.19/0.49 tuple(fresh21(true2, true2, relation_dom(c), relation_rng(c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 9 (d2_xboole_0_3) R->L }
% 0.19/0.49 tuple(fresh21(fresh19(true2, true2, relation_dom(c), relation_rng(c), a), true2, relation_dom(c), relation_rng(c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 4 (d4_relat_1_1) R->L }
% 0.19/0.49 tuple(fresh21(fresh19(fresh33(relation_dom(c), relation_dom(c), relation_dom(c), a), true2, relation_dom(c), relation_rng(c), a), true2, relation_dom(c), relation_rng(c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 12 (d4_relat_1_1) R->L }
% 0.19/0.49 tuple(fresh21(fresh19(fresh32(true2, true2, c, relation_dom(c), a, b), true2, relation_dom(c), relation_rng(c), a), true2, relation_dom(c), relation_rng(c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 1 (t30_relat_1_1) R->L }
% 0.19/0.49 tuple(fresh21(fresh19(fresh32(relation(c), true2, c, relation_dom(c), a, b), true2, relation_dom(c), relation_rng(c), a), true2, relation_dom(c), relation_rng(c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 17 (d4_relat_1_1) }
% 0.19/0.49 tuple(fresh21(fresh19(fresh15(in(ordered_pair(a, b), c), true2, c, relation_dom(c), a), true2, relation_dom(c), relation_rng(c), a), true2, relation_dom(c), relation_rng(c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 8 (t30_relat_1) }
% 0.19/0.49 tuple(fresh21(fresh19(fresh15(true2, true2, c, relation_dom(c), a), true2, relation_dom(c), relation_rng(c), a), true2, relation_dom(c), relation_rng(c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 10 (d4_relat_1_1) }
% 0.19/0.49 tuple(fresh21(fresh19(in(a, relation_dom(c)), true2, relation_dom(c), relation_rng(c), a), true2, relation_dom(c), relation_rng(c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 15 (d2_xboole_0_3) }
% 0.19/0.49 tuple(fresh21(equiv(relation_dom(c), relation_rng(c), a), true2, relation_dom(c), relation_rng(c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 16 (d2_xboole_0_2) }
% 0.19/0.49 tuple(fresh20(relation_field(c), set_union2(relation_dom(c), relation_rng(c)), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 7 (d6_relat_1) R->L }
% 0.19/0.49 tuple(fresh20(relation_field(c), fresh12(relation(c), true2, c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 1 (t30_relat_1_1) }
% 0.19/0.49 tuple(fresh20(relation_field(c), fresh12(true2, true2, c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 3 (d6_relat_1) }
% 0.19/0.49 tuple(fresh20(relation_field(c), relation_field(c), relation_field(c), a), in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 6 (d2_xboole_0_2) }
% 0.19/0.49 tuple(true2, in(b, relation_field(c)))
% 0.19/0.49 = { by axiom 3 (d6_relat_1) R->L }
% 0.19/0.49 tuple(true2, in(b, fresh12(true2, true2, c)))
% 0.19/0.49 = { by axiom 1 (t30_relat_1_1) R->L }
% 0.19/0.49 tuple(true2, in(b, fresh12(relation(c), true2, c)))
% 0.19/0.49 = { by axiom 7 (d6_relat_1) }
% 0.19/0.49 tuple(true2, in(b, set_union2(relation_dom(c), relation_rng(c))))
% 0.19/0.49 = { by axiom 2 (commutativity_k2_xboole_0) R->L }
% 0.19/0.49 tuple(true2, in(b, set_union2(relation_rng(c), relation_dom(c))))
% 0.19/0.49 = { by axiom 14 (d2_xboole_0_2) R->L }
% 0.19/0.49 tuple(true2, fresh21(true2, true2, relation_rng(c), relation_dom(c), set_union2(relation_rng(c), relation_dom(c)), b))
% 0.19/0.49 = { by axiom 9 (d2_xboole_0_3) R->L }
% 0.19/0.49 tuple(true2, fresh21(fresh19(true2, true2, relation_rng(c), relation_dom(c), b), true2, relation_rng(c), relation_dom(c), set_union2(relation_rng(c), relation_dom(c)), b))
% 0.19/0.49 = { by axiom 5 (d5_relat_1_1) R->L }
% 0.19/0.49 tuple(true2, fresh21(fresh19(fresh27(relation_rng(c), relation_rng(c), relation_rng(c), b), true2, relation_rng(c), relation_dom(c), b), true2, relation_rng(c), relation_dom(c), set_union2(relation_rng(c), relation_dom(c)), b))
% 0.19/0.49 = { by axiom 13 (d5_relat_1_1) R->L }
% 0.19/0.49 tuple(true2, fresh21(fresh19(fresh26(true2, true2, c, relation_rng(c), b, a), true2, relation_rng(c), relation_dom(c), b), true2, relation_rng(c), relation_dom(c), set_union2(relation_rng(c), relation_dom(c)), b))
% 0.19/0.49 = { by axiom 1 (t30_relat_1_1) R->L }
% 0.19/0.49 tuple(true2, fresh21(fresh19(fresh26(relation(c), true2, c, relation_rng(c), b, a), true2, relation_rng(c), relation_dom(c), b), true2, relation_rng(c), relation_dom(c), set_union2(relation_rng(c), relation_dom(c)), b))
% 0.19/0.49 = { by axiom 18 (d5_relat_1_1) }
% 0.19/0.49 tuple(true2, fresh21(fresh19(fresh13(in(ordered_pair(a, b), c), true2, c, relation_rng(c), b), true2, relation_rng(c), relation_dom(c), b), true2, relation_rng(c), relation_dom(c), set_union2(relation_rng(c), relation_dom(c)), b))
% 0.19/0.49 = { by axiom 8 (t30_relat_1) }
% 0.19/0.49 tuple(true2, fresh21(fresh19(fresh13(true2, true2, c, relation_rng(c), b), true2, relation_rng(c), relation_dom(c), b), true2, relation_rng(c), relation_dom(c), set_union2(relation_rng(c), relation_dom(c)), b))
% 0.19/0.49 = { by axiom 11 (d5_relat_1_1) }
% 0.19/0.50 tuple(true2, fresh21(fresh19(in(b, relation_rng(c)), true2, relation_rng(c), relation_dom(c), b), true2, relation_rng(c), relation_dom(c), set_union2(relation_rng(c), relation_dom(c)), b))
% 0.19/0.50 = { by axiom 15 (d2_xboole_0_3) }
% 0.19/0.50 tuple(true2, fresh21(equiv(relation_rng(c), relation_dom(c), b), true2, relation_rng(c), relation_dom(c), set_union2(relation_rng(c), relation_dom(c)), b))
% 0.19/0.50 = { by axiom 16 (d2_xboole_0_2) }
% 0.19/0.50 tuple(true2, fresh20(set_union2(relation_rng(c), relation_dom(c)), set_union2(relation_rng(c), relation_dom(c)), set_union2(relation_rng(c), relation_dom(c)), b))
% 0.19/0.50 = { by axiom 6 (d2_xboole_0_2) }
% 0.19/0.50 tuple(true2, true2)
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50
% 0.19/0.50 RESULT: Theorem (the conjecture is true).
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