TSTP Solution File: SEU149+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU149+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 17:51:13 EDT 2023
% Result : Theorem 0.20s 0.57s
% 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
% 0.00/0.13 % Problem : SEU149+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 15:08:42 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.57 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.57
% 0.20/0.57 % SZS status Theorem
% 0.20/0.57
% 0.20/0.57 % SZS output start Proof
% 0.20/0.57 Take the following subset of the input axioms:
% 0.20/0.57 fof(d2_tarski, axiom, ![B, C, A2]: (C=unordered_pair(A2, B) <=> ![D]: (in(D, C) <=> (D=A2 | D=B)))).
% 0.20/0.57 fof(l2_zfmisc_1, lemma, ![B2, A2_2]: (subset(singleton(A2_2), B2) <=> in(A2_2, B2))).
% 0.20/0.57 fof(t6_zfmisc_1, lemma, ![B2, A2_2]: (subset(singleton(A2_2), singleton(B2)) => A2_2=B2)).
% 0.20/0.57 fof(t8_zfmisc_1, conjecture, ![A, B2, C2]: (singleton(A)=unordered_pair(B2, C2) => A=B2)).
% 0.20/0.57
% 0.20/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.57 fresh(y, y, x1...xn) = u
% 0.20/0.57 C => fresh(s, t, x1...xn) = v
% 0.20/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.57 variables of u and v.
% 0.20/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.57 input problem has no model of domain size 1).
% 0.20/0.57
% 0.20/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.57
% 0.20/0.57 Axiom 1 (t8_zfmisc_1): singleton(a) = unordered_pair(b, c).
% 0.20/0.57 Axiom 2 (d2_tarski_1): equiv4(X, Y, X) = true2.
% 0.20/0.57 Axiom 3 (t6_zfmisc_1): fresh(X, X, Y, Z) = Z.
% 0.20/0.57 Axiom 4 (d2_tarski_4): fresh73(X, X, Y, Z) = true2.
% 0.20/0.57 Axiom 5 (l2_zfmisc_1): fresh41(X, X, Y, Z) = true2.
% 0.20/0.57 Axiom 6 (d2_tarski_4): fresh74(X, X, Y, Z, W, V) = in(V, W).
% 0.20/0.57 Axiom 7 (l2_zfmisc_1): fresh41(in(X, Y), true2, X, Y) = subset(singleton(X), Y).
% 0.20/0.57 Axiom 8 (t6_zfmisc_1): fresh(subset(singleton(X), singleton(Y)), true2, X, Y) = X.
% 0.20/0.57 Axiom 9 (d2_tarski_4): fresh74(equiv4(X, Y, Z), true2, X, Y, W, Z) = fresh73(W, unordered_pair(X, Y), W, Z).
% 0.20/0.57
% 0.20/0.57 Goal 1 (t8_zfmisc_1_1): a = b.
% 0.20/0.57 Proof:
% 0.20/0.57 a
% 0.20/0.57 = { by axiom 3 (t6_zfmisc_1) R->L }
% 0.20/0.57 fresh(true2, true2, b, a)
% 0.20/0.57 = { by axiom 5 (l2_zfmisc_1) R->L }
% 0.20/0.57 fresh(fresh41(true2, true2, b, singleton(a)), true2, b, a)
% 0.20/0.57 = { by axiom 4 (d2_tarski_4) R->L }
% 0.20/0.57 fresh(fresh41(fresh73(unordered_pair(b, c), unordered_pair(b, c), unordered_pair(b, c), b), true2, b, singleton(a)), true2, b, a)
% 0.20/0.57 = { by axiom 9 (d2_tarski_4) R->L }
% 0.20/0.57 fresh(fresh41(fresh74(equiv4(b, c, b), true2, b, c, unordered_pair(b, c), b), true2, b, singleton(a)), true2, b, a)
% 0.20/0.57 = { by axiom 2 (d2_tarski_1) }
% 0.20/0.57 fresh(fresh41(fresh74(true2, true2, b, c, unordered_pair(b, c), b), true2, b, singleton(a)), true2, b, a)
% 0.20/0.57 = { by axiom 6 (d2_tarski_4) }
% 0.20/0.57 fresh(fresh41(in(b, unordered_pair(b, c)), true2, b, singleton(a)), true2, b, a)
% 0.20/0.57 = { by axiom 1 (t8_zfmisc_1) R->L }
% 0.20/0.57 fresh(fresh41(in(b, singleton(a)), true2, b, singleton(a)), true2, b, a)
% 0.20/0.57 = { by axiom 7 (l2_zfmisc_1) }
% 0.20/0.57 fresh(subset(singleton(b), singleton(a)), true2, b, a)
% 0.20/0.57 = { by axiom 8 (t6_zfmisc_1) }
% 0.20/0.57 b
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Theorem (the conjecture is true).
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