TSTP Solution File: SEU152+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU152+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 : n009.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 17:51:14 EDT 2023
% Result : Theorem 0.20s 0.38s
% 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+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
% 0.14/0.34 % Computer : n009.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 : Wed Aug 23 20:12:36 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.38 Command-line arguments: --no-flatten-goal
% 0.20/0.38
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 Take the following subset of the input axioms:
% 0.20/0.38 fof(l23_zfmisc_1, conjecture, ![A, B]: (in(A, B) => set_union2(singleton(A), B)=B)).
% 0.20/0.38 fof(l2_zfmisc_1, axiom, ![A2, B2]: (subset(singleton(A2), B2) <=> in(A2, B2))).
% 0.20/0.38 fof(t12_xboole_1, axiom, ![B2, A2_2]: (subset(A2_2, B2) => set_union2(A2_2, B2)=B2)).
% 0.20/0.38
% 0.20/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.38 fresh(y, y, x1...xn) = u
% 0.20/0.38 C => fresh(s, t, x1...xn) = v
% 0.20/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.38 variables of u and v.
% 0.20/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.39 input problem has no model of domain size 1).
% 0.20/0.39
% 0.20/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.39
% 0.20/0.39 Axiom 1 (l23_zfmisc_1): in(a, b) = true2.
% 0.20/0.39 Axiom 2 (t12_xboole_1): fresh(X, X, Y, Z) = Z.
% 0.20/0.39 Axiom 3 (l2_zfmisc_1): fresh2(X, X, Y, Z) = true2.
% 0.20/0.39 Axiom 4 (t12_xboole_1): fresh(subset(X, Y), true2, X, Y) = set_union2(X, Y).
% 0.20/0.39 Axiom 5 (l2_zfmisc_1): fresh2(in(X, Y), true2, X, Y) = subset(singleton(X), Y).
% 0.20/0.39
% 0.20/0.39 Goal 1 (l23_zfmisc_1_1): set_union2(singleton(a), b) = b.
% 0.20/0.39 Proof:
% 0.20/0.39 set_union2(singleton(a), b)
% 0.20/0.39 = { by axiom 4 (t12_xboole_1) R->L }
% 0.20/0.39 fresh(subset(singleton(a), b), true2, singleton(a), b)
% 0.20/0.39 = { by axiom 5 (l2_zfmisc_1) R->L }
% 0.20/0.39 fresh(fresh2(in(a, b), true2, a, b), true2, singleton(a), b)
% 0.20/0.39 = { by axiom 1 (l23_zfmisc_1) }
% 0.20/0.39 fresh(fresh2(true2, true2, a, b), true2, singleton(a), b)
% 0.20/0.39 = { by axiom 3 (l2_zfmisc_1) }
% 0.20/0.39 fresh(true2, true2, singleton(a), b)
% 0.20/0.39 = { by axiom 2 (t12_xboole_1) }
% 0.20/0.39 b
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39
% 0.20/0.39 RESULT: Theorem (the conjecture is true).
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