TSTP Solution File: SEU152+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU152+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 : n012.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 17:51:15 EDT 2023
% Result : Theorem 0.20s 0.54s
% 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 : SEU152+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
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 17:03:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.54 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.54
% 0.20/0.54 % SZS status Theorem
% 0.20/0.54
% 0.20/0.54 % SZS output start Proof
% 0.20/0.54 Take the following subset of the input axioms:
% 0.20/0.55 fof(commutativity_k2_xboole_0, axiom, ![A, B]: set_union2(A, B)=set_union2(B, A)).
% 0.20/0.55 fof(l23_zfmisc_1, conjecture, ![A3, B2]: (in(A3, B2) => set_union2(singleton(A3), B2)=B2)).
% 0.20/0.55 fof(l2_zfmisc_1, lemma, ![A2, B2]: (subset(singleton(A2), B2) <=> in(A2, B2))).
% 0.20/0.55 fof(l32_xboole_1, lemma, ![B2, A2_2]: (set_difference(A2_2, B2)=empty_set <=> subset(A2_2, B2))).
% 0.20/0.55 fof(t1_boole, axiom, ![A3]: set_union2(A3, empty_set)=A3).
% 0.20/0.55 fof(t39_xboole_1, lemma, ![A3, B2]: set_union2(A3, set_difference(B2, A3))=set_union2(A3, B2)).
% 0.20/0.55
% 0.20/0.55 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.55 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.55 fresh(y, y, x1...xn) = u
% 0.20/0.55 C => fresh(s, t, x1...xn) = v
% 0.20/0.55 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.55 variables of u and v.
% 0.20/0.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.55 input problem has no model of domain size 1).
% 0.20/0.55
% 0.20/0.55 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.55
% 0.20/0.55 Axiom 1 (l23_zfmisc_1): in(a3, b) = true2.
% 0.20/0.55 Axiom 2 (commutativity_k2_xboole_0): set_union2(X, Y) = set_union2(Y, X).
% 0.20/0.55 Axiom 3 (t1_boole): set_union2(X, empty_set) = X.
% 0.20/0.55 Axiom 4 (t39_xboole_1): set_union2(X, set_difference(Y, X)) = set_union2(X, Y).
% 0.20/0.55 Axiom 5 (l2_zfmisc_1): fresh43(X, X, Y, Z) = true2.
% 0.20/0.55 Axiom 6 (l32_xboole_1_1): fresh40(X, X, Y, Z) = empty_set.
% 0.20/0.55 Axiom 7 (l2_zfmisc_1): fresh43(in(X, Y), true2, X, Y) = subset(singleton(X), Y).
% 0.20/0.55 Axiom 8 (l32_xboole_1_1): fresh40(subset(X, Y), true2, X, Y) = set_difference(X, Y).
% 0.20/0.55
% 0.20/0.55 Goal 1 (l23_zfmisc_1_1): set_union2(singleton(a3), b) = b.
% 0.20/0.55 Proof:
% 0.20/0.55 set_union2(singleton(a3), b)
% 0.20/0.55 = { by axiom 2 (commutativity_k2_xboole_0) }
% 0.20/0.55 set_union2(b, singleton(a3))
% 0.20/0.55 = { by axiom 4 (t39_xboole_1) R->L }
% 0.20/0.55 set_union2(b, set_difference(singleton(a3), b))
% 0.20/0.55 = { by axiom 8 (l32_xboole_1_1) R->L }
% 0.20/0.55 set_union2(b, fresh40(subset(singleton(a3), b), true2, singleton(a3), b))
% 0.20/0.55 = { by axiom 7 (l2_zfmisc_1) R->L }
% 0.20/0.55 set_union2(b, fresh40(fresh43(in(a3, b), true2, a3, b), true2, singleton(a3), b))
% 0.20/0.55 = { by axiom 1 (l23_zfmisc_1) }
% 0.20/0.55 set_union2(b, fresh40(fresh43(true2, true2, a3, b), true2, singleton(a3), b))
% 0.20/0.55 = { by axiom 5 (l2_zfmisc_1) }
% 0.20/0.55 set_union2(b, fresh40(true2, true2, singleton(a3), b))
% 0.20/0.55 = { by axiom 6 (l32_xboole_1_1) }
% 0.20/0.55 set_union2(b, empty_set)
% 0.20/0.55 = { by axiom 3 (t1_boole) }
% 0.20/0.55 b
% 0.20/0.55 % SZS output end Proof
% 0.20/0.55
% 0.20/0.55 RESULT: Theorem (the conjecture is true).
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