TSTP Solution File: SEU230+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU230+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 : n018.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 17:51:42 EDT 2023
% Result : Theorem 19.77s 2.91s
% Output : Proof 19.77s
% 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 : SEU230+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 01:16:57 EDT 2023
% 0.12/0.34 % CPUTime :
% 19.77/2.91 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 19.77/2.91
% 19.77/2.91 % SZS status Theorem
% 19.77/2.91
% 19.77/2.91 % SZS output start Proof
% 19.77/2.91 Take the following subset of the input axioms:
% 19.77/2.91 fof(commutativity_k2_xboole_0, axiom, ![A, B]: set_union2(A, B)=set_union2(B, A)).
% 19.77/2.91 fof(d1_ordinal1, axiom, ![A3]: succ(A3)=set_union2(A3, singleton(A3))).
% 19.77/2.91 fof(l2_zfmisc_1, lemma, ![A2, B2]: (subset(singleton(A2), B2) <=> in(A2, B2))).
% 19.77/2.91 fof(t10_ordinal1, conjecture, ![A3]: in(A3, succ(A3))).
% 19.77/2.91 fof(t7_xboole_1, lemma, ![A3, B2]: subset(A3, set_union2(A3, B2))).
% 19.77/2.91
% 19.77/2.91 Now clausify the problem and encode Horn clauses using encoding 3 of
% 19.77/2.91 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 19.77/2.91 We repeatedly replace C & s=t => u=v by the two clauses:
% 19.77/2.91 fresh(y, y, x1...xn) = u
% 19.77/2.91 C => fresh(s, t, x1...xn) = v
% 19.77/2.91 where fresh is a fresh function symbol and x1..xn are the free
% 19.77/2.91 variables of u and v.
% 19.77/2.91 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 19.77/2.91 input problem has no model of domain size 1).
% 19.77/2.91
% 19.77/2.91 The encoding turns the above axioms into the following unit equations and goals:
% 19.77/2.91
% 19.77/2.91 Axiom 1 (commutativity_k2_xboole_0): set_union2(X, Y) = set_union2(Y, X).
% 19.77/2.91 Axiom 2 (t7_xboole_1): subset(X, set_union2(X, Y)) = true2.
% 19.77/2.91 Axiom 3 (d1_ordinal1): succ(X) = set_union2(X, singleton(X)).
% 19.77/2.91 Axiom 4 (l2_zfmisc_1_1): fresh216(X, X, Y, Z) = true2.
% 19.77/2.91 Axiom 5 (l2_zfmisc_1_1): fresh216(subset(singleton(X), Y), true2, X, Y) = in(X, Y).
% 19.77/2.91
% 19.77/2.91 Goal 1 (t10_ordinal1): in(a, succ(a)) = true2.
% 19.77/2.91 Proof:
% 19.77/2.91 in(a, succ(a))
% 19.77/2.91 = { by axiom 5 (l2_zfmisc_1_1) R->L }
% 19.77/2.91 fresh216(subset(singleton(a), succ(a)), true2, a, succ(a))
% 19.77/2.91 = { by axiom 3 (d1_ordinal1) }
% 19.77/2.91 fresh216(subset(singleton(a), set_union2(a, singleton(a))), true2, a, succ(a))
% 19.77/2.91 = { by axiom 1 (commutativity_k2_xboole_0) R->L }
% 19.77/2.91 fresh216(subset(singleton(a), set_union2(singleton(a), a)), true2, a, succ(a))
% 19.77/2.91 = { by axiom 2 (t7_xboole_1) }
% 19.77/2.91 fresh216(true2, true2, a, succ(a))
% 19.77/2.91 = { by axiom 4 (l2_zfmisc_1_1) }
% 19.77/2.91 true2
% 19.77/2.91 % SZS output end Proof
% 19.77/2.91
% 19.77/2.91 RESULT: Theorem (the conjecture is true).
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