TSTP Solution File: SET904+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET904+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n010.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 15:33:41 EDT 2023
% Result : Theorem 0.13s 0.40s
% 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 : SET904+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n010.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 : Sat Aug 26 11:07:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.40 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.13/0.40
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Take the following subset of the input axioms:
% 0.20/0.40 fof(l21_zfmisc_1, axiom, ![B, A2]: (subset(set_union2(singleton(A2), B), B) => in(A2, B))).
% 0.20/0.40 fof(t45_zfmisc_1, conjecture, ![A, B2]: (subset(set_union2(singleton(A), B2), B2) => in(A, B2))).
% 0.20/0.40
% 0.20/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40 fresh(y, y, x1...xn) = u
% 0.20/0.40 C => fresh(s, t, x1...xn) = v
% 0.20/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40 variables of u and v.
% 0.20/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40 input problem has no model of domain size 1).
% 0.20/0.40
% 0.20/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.40
% 0.20/0.40 Axiom 1 (l21_zfmisc_1): fresh(X, X, Y, Z) = true2.
% 0.20/0.40 Axiom 2 (t45_zfmisc_1): subset(set_union2(singleton(a), b), b) = true2.
% 0.20/0.40 Axiom 3 (l21_zfmisc_1): fresh(subset(set_union2(singleton(X), Y), Y), true2, X, Y) = in(X, Y).
% 0.20/0.40
% 0.20/0.40 Goal 1 (t45_zfmisc_1_1): in(a, b) = true2.
% 0.20/0.40 Proof:
% 0.20/0.40 in(a, b)
% 0.20/0.40 = { by axiom 3 (l21_zfmisc_1) R->L }
% 0.20/0.40 fresh(subset(set_union2(singleton(a), b), b), true2, a, b)
% 0.20/0.40 = { by axiom 2 (t45_zfmisc_1) }
% 0.20/0.40 fresh(true2, true2, a, b)
% 0.20/0.40 = { by axiom 1 (l21_zfmisc_1) }
% 0.20/0.40 true2
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40
% 0.20/0.40 RESULT: Theorem (the conjecture is true).
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