TSTP Solution File: SEU150+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU150+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 : n003.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 0.58s
% 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 : SEU150+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % 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 : n003.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 : Wed Aug 23 19:36:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.58
% 0.20/0.58 % SZS status Theorem
% 0.20/0.58
% 0.20/0.58 % SZS output start Proof
% 0.20/0.58 Take the following subset of the input axioms:
% 0.20/0.58 fof(commutativity_k2_tarski, axiom, ![A, B]: unordered_pair(A, B)=unordered_pair(B, A)).
% 0.20/0.58 fof(d2_tarski, axiom, ![C, A2, B2]: (C=unordered_pair(A2, B2) <=> ![D]: (in(D, C) <=> (D=A2 | D=B2)))).
% 0.20/0.58 fof(l2_zfmisc_1, lemma, ![B2, A2_2]: (subset(singleton(A2_2), B2) <=> in(A2_2, B2))).
% 0.20/0.58 fof(t6_zfmisc_1, lemma, ![B2, A2_2]: (subset(singleton(A2_2), singleton(B2)) => A2_2=B2)).
% 0.20/0.58 fof(t9_zfmisc_1, conjecture, ![A3, B2, C2]: (singleton(A3)=unordered_pair(B2, C2) => B2=C2)).
% 0.20/0.58
% 0.20/0.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.58 fresh(y, y, x1...xn) = u
% 0.20/0.58 C => fresh(s, t, x1...xn) = v
% 0.20/0.58 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.58 variables of u and v.
% 0.20/0.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.58 input problem has no model of domain size 1).
% 0.20/0.58
% 0.20/0.58 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.58
% 0.20/0.58 Axiom 1 (commutativity_k2_tarski): unordered_pair(X, Y) = unordered_pair(Y, X).
% 0.20/0.58 Axiom 2 (t9_zfmisc_1): singleton(a) = unordered_pair(b, c).
% 0.20/0.58 Axiom 3 (d2_tarski_1): equiv4(X, Y, X) = true2.
% 0.20/0.58 Axiom 4 (d2_tarski_4): fresh74(X, X, Y, Z) = true2.
% 0.20/0.58 Axiom 5 (l2_zfmisc_1): fresh42(X, X, Y, Z) = true2.
% 0.20/0.58 Axiom 6 (t6_zfmisc_1): fresh2(X, X, Y, Z) = Z.
% 0.20/0.58 Axiom 7 (d2_tarski_4): fresh75(X, X, Y, Z, W, V) = in(V, W).
% 0.20/0.58 Axiom 8 (l2_zfmisc_1): fresh42(in(X, Y), true2, X, Y) = subset(singleton(X), Y).
% 0.20/0.58 Axiom 9 (t6_zfmisc_1): fresh2(subset(singleton(X), singleton(Y)), true2, X, Y) = X.
% 0.20/0.58 Axiom 10 (d2_tarski_4): fresh75(equiv4(X, Y, Z), true2, X, Y, W, Z) = fresh74(W, unordered_pair(X, Y), W, Z).
% 0.20/0.58
% 0.20/0.58 Lemma 11: in(X, unordered_pair(X, Y)) = true2.
% 0.20/0.58 Proof:
% 0.20/0.58 in(X, unordered_pair(X, Y))
% 0.20/0.58 = { by axiom 7 (d2_tarski_4) R->L }
% 0.20/0.58 fresh75(true2, true2, X, Y, unordered_pair(X, Y), X)
% 0.20/0.58 = { by axiom 3 (d2_tarski_1) R->L }
% 0.20/0.58 fresh75(equiv4(X, Y, X), true2, X, Y, unordered_pair(X, Y), X)
% 0.20/0.58 = { by axiom 10 (d2_tarski_4) }
% 0.20/0.58 fresh74(unordered_pair(X, Y), unordered_pair(X, Y), unordered_pair(X, Y), X)
% 0.20/0.58 = { by axiom 4 (d2_tarski_4) }
% 0.20/0.58 true2
% 0.20/0.58
% 0.20/0.58 Goal 1 (t9_zfmisc_1_1): b = c.
% 0.20/0.58 Proof:
% 0.20/0.58 b
% 0.20/0.58 = { by axiom 6 (t6_zfmisc_1) R->L }
% 0.20/0.58 fresh2(true2, true2, c, b)
% 0.20/0.58 = { by axiom 5 (l2_zfmisc_1) R->L }
% 0.20/0.58 fresh2(fresh42(true2, true2, c, singleton(a)), true2, c, b)
% 0.20/0.58 = { by lemma 11 R->L }
% 0.20/0.58 fresh2(fresh42(in(c, unordered_pair(c, b)), true2, c, singleton(a)), true2, c, b)
% 0.20/0.58 = { by axiom 1 (commutativity_k2_tarski) }
% 0.20/0.58 fresh2(fresh42(in(c, unordered_pair(b, c)), true2, c, singleton(a)), true2, c, b)
% 0.20/0.58 = { by axiom 2 (t9_zfmisc_1) R->L }
% 0.20/0.58 fresh2(fresh42(in(c, singleton(a)), true2, c, singleton(a)), true2, c, b)
% 0.20/0.58 = { by axiom 8 (l2_zfmisc_1) }
% 0.20/0.58 fresh2(subset(singleton(c), singleton(a)), true2, c, b)
% 0.20/0.59 = { by axiom 6 (t6_zfmisc_1) R->L }
% 0.20/0.59 fresh2(subset(singleton(c), singleton(fresh2(true2, true2, b, a))), true2, c, b)
% 0.20/0.59 = { by axiom 5 (l2_zfmisc_1) R->L }
% 0.20/0.59 fresh2(subset(singleton(c), singleton(fresh2(fresh42(true2, true2, b, singleton(a)), true2, b, a))), true2, c, b)
% 0.20/0.59 = { by lemma 11 R->L }
% 0.20/0.59 fresh2(subset(singleton(c), singleton(fresh2(fresh42(in(b, unordered_pair(b, c)), true2, b, singleton(a)), true2, b, a))), true2, c, b)
% 0.20/0.59 = { by axiom 2 (t9_zfmisc_1) R->L }
% 0.20/0.59 fresh2(subset(singleton(c), singleton(fresh2(fresh42(in(b, singleton(a)), true2, b, singleton(a)), true2, b, a))), true2, c, b)
% 0.20/0.59 = { by axiom 8 (l2_zfmisc_1) }
% 0.20/0.59 fresh2(subset(singleton(c), singleton(fresh2(subset(singleton(b), singleton(a)), true2, b, a))), true2, c, b)
% 0.20/0.59 = { by axiom 9 (t6_zfmisc_1) }
% 0.20/0.59 fresh2(subset(singleton(c), singleton(b)), true2, c, b)
% 0.20/0.59 = { by axiom 9 (t6_zfmisc_1) }
% 0.20/0.59 c
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59
% 0.20/0.59 RESULT: Theorem (the conjecture is true).
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