TSTP Solution File: SEU126+2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU126+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 : n015.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 17:51:05 EDT 2023
% Result : Theorem 0.21s 0.45s
% 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
% 0.12/0.13 % Problem : SEU126+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % 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 : n015.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 00:31:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.45 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.45
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45
% 0.21/0.46 % SZS output start Proof
% 0.21/0.46 Take the following subset of the input axioms:
% 0.21/0.46 fof(commutativity_k2_xboole_0, axiom, ![A, B]: set_union2(A, B)=set_union2(B, A)).
% 0.21/0.46 fof(d10_xboole_0, axiom, ![A2, B2]: (A2=B2 <=> (subset(A2, B2) & subset(B2, A2)))).
% 0.21/0.46 fof(t12_xboole_1, conjecture, ![B2, A3]: (subset(A3, B2) => set_union2(A3, B2)=B2)).
% 0.21/0.46 fof(t7_xboole_1, lemma, ![B2, A3]: subset(A3, set_union2(A3, B2))).
% 0.21/0.46 fof(t8_xboole_1, lemma, ![C, B2, A2_2]: ((subset(A2_2, B2) & subset(C, B2)) => subset(set_union2(A2_2, C), B2))).
% 0.21/0.46
% 0.21/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.46 fresh(y, y, x1...xn) = u
% 0.21/0.46 C => fresh(s, t, x1...xn) = v
% 0.21/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.46 variables of u and v.
% 0.21/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.46 input problem has no model of domain size 1).
% 0.21/0.46
% 0.21/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.46
% 0.21/0.46 Axiom 1 (d10_xboole_0): subset(X, X) = true2.
% 0.21/0.46 Axiom 2 (t12_xboole_1): subset(a, b) = true2.
% 0.21/0.46 Axiom 3 (commutativity_k2_xboole_0): set_union2(X, Y) = set_union2(Y, X).
% 0.21/0.46 Axiom 4 (t7_xboole_1): subset(X, set_union2(X, Y)) = true2.
% 0.21/0.46 Axiom 5 (d10_xboole_0_1): fresh6(X, X, Y, Z) = Y.
% 0.21/0.46 Axiom 6 (d10_xboole_0_1): fresh5(X, X, Y, Z) = Z.
% 0.21/0.46 Axiom 7 (t8_xboole_1): fresh8(X, X, Y, Z, W) = subset(set_union2(Y, W), Z).
% 0.21/0.46 Axiom 8 (t8_xboole_1): fresh7(X, X, Y, Z, W) = true2.
% 0.21/0.46 Axiom 9 (d10_xboole_0_1): fresh6(subset(X, Y), true2, Y, X) = fresh5(subset(Y, X), true2, Y, X).
% 0.21/0.46 Axiom 10 (t8_xboole_1): fresh8(subset(X, Y), true2, Z, Y, X) = fresh7(subset(Z, Y), true2, Z, Y, X).
% 0.21/0.46
% 0.21/0.46 Goal 1 (t12_xboole_1_1): set_union2(a, b) = b.
% 0.21/0.46 Proof:
% 0.21/0.46 set_union2(a, b)
% 0.21/0.46 = { by axiom 5 (d10_xboole_0_1) R->L }
% 0.21/0.46 fresh6(true2, true2, set_union2(a, b), b)
% 0.21/0.46 = { by axiom 4 (t7_xboole_1) R->L }
% 0.21/0.46 fresh6(subset(b, set_union2(b, a)), true2, set_union2(a, b), b)
% 0.21/0.46 = { by axiom 3 (commutativity_k2_xboole_0) R->L }
% 0.21/0.46 fresh6(subset(b, set_union2(a, b)), true2, set_union2(a, b), b)
% 0.21/0.46 = { by axiom 9 (d10_xboole_0_1) }
% 0.21/0.46 fresh5(subset(set_union2(a, b), b), true2, set_union2(a, b), b)
% 0.21/0.46 = { by axiom 3 (commutativity_k2_xboole_0) }
% 0.21/0.46 fresh5(subset(set_union2(b, a), b), true2, set_union2(a, b), b)
% 0.21/0.46 = { by axiom 7 (t8_xboole_1) R->L }
% 0.21/0.46 fresh5(fresh8(true2, true2, b, b, a), true2, set_union2(a, b), b)
% 0.21/0.46 = { by axiom 2 (t12_xboole_1) R->L }
% 0.21/0.46 fresh5(fresh8(subset(a, b), true2, b, b, a), true2, set_union2(a, b), b)
% 0.21/0.46 = { by axiom 10 (t8_xboole_1) }
% 0.21/0.46 fresh5(fresh7(subset(b, b), true2, b, b, a), true2, set_union2(a, b), b)
% 0.21/0.46 = { by axiom 1 (d10_xboole_0) }
% 0.21/0.46 fresh5(fresh7(true2, true2, b, b, a), true2, set_union2(a, b), b)
% 0.21/0.46 = { by axiom 8 (t8_xboole_1) }
% 0.21/0.46 fresh5(true2, true2, set_union2(a, b), b)
% 0.21/0.46 = { by axiom 6 (d10_xboole_0_1) }
% 0.21/0.46 b
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46
% 0.21/0.46 RESULT: Theorem (the conjecture is true).
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