TSTP Solution File: SEU435+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU435+1 : TPTP v8.1.2. Released v3.4.0.
% 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 : n022.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 17:52:51 EDT 2023
% Result : Theorem 0.19s 0.50s
% Output : Proof 0.19s
% 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 : SEU435+1 : TPTP v8.1.2. Released v3.4.0.
% 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 : n022.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 18:51:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.50 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.50
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 Take the following subset of the input axioms:
% 0.19/0.50 fof(s8_domain_1__e1_46__relset_2, axiom, ![B, C, D, E, F, A2]: ((m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A2, B)))) & m1_subset_1(F, k1_zfmisc_1(D))) => m1_subset_1(a_6_0_relset_2(A2, B, C, D, E, F), k1_zfmisc_1(k1_zfmisc_1(E))))).
% 0.19/0.51 fof(t36_relset_2, conjecture, ![A, B2, C2]: (m1_subset_1(C2, k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A, B2)))) => ![D2, E2, F2]: (m1_subset_1(F2, k1_zfmisc_1(D2)) => m1_subset_1(a_6_0_relset_2(A, B2, C2, D2, E2, F2), k1_zfmisc_1(k1_zfmisc_1(E2)))))).
% 0.19/0.51
% 0.19/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.51 fresh(y, y, x1...xn) = u
% 0.19/0.51 C => fresh(s, t, x1...xn) = v
% 0.19/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.51 variables of u and v.
% 0.19/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.51 input problem has no model of domain size 1).
% 0.19/0.51
% 0.19/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.51
% 0.19/0.51 Axiom 1 (t36_relset_2_1): m1_subset_1(f, k1_zfmisc_1(d)) = true2.
% 0.19/0.51 Axiom 2 (t36_relset_2): m1_subset_1(c5, k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(a4, b5)))) = true2.
% 0.19/0.51 Axiom 3 (s8_domain_1__e1_46__relset_2): fresh12(X, X, Y, Z, W, V, U, T) = true2.
% 0.19/0.51 Axiom 4 (s8_domain_1__e1_46__relset_2): fresh13(X, X, Y, Z, W, V, U, T) = m1_subset_1(a_6_0_relset_2(Y, Z, W, V, U, T), k1_zfmisc_1(k1_zfmisc_1(U))).
% 0.19/0.51 Axiom 5 (s8_domain_1__e1_46__relset_2): fresh13(m1_subset_1(X, k1_zfmisc_1(Y)), true2, Z, W, V, Y, U, X) = fresh12(m1_subset_1(V, k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(Z, W)))), true2, Z, W, V, Y, U, X).
% 0.19/0.51
% 0.19/0.51 Goal 1 (t36_relset_2_2): m1_subset_1(a_6_0_relset_2(a4, b5, c5, d, e, f), k1_zfmisc_1(k1_zfmisc_1(e))) = true2.
% 0.19/0.51 Proof:
% 0.19/0.51 m1_subset_1(a_6_0_relset_2(a4, b5, c5, d, e, f), k1_zfmisc_1(k1_zfmisc_1(e)))
% 0.19/0.51 = { by axiom 4 (s8_domain_1__e1_46__relset_2) R->L }
% 0.19/0.51 fresh13(true2, true2, a4, b5, c5, d, e, f)
% 0.19/0.51 = { by axiom 1 (t36_relset_2_1) R->L }
% 0.19/0.51 fresh13(m1_subset_1(f, k1_zfmisc_1(d)), true2, a4, b5, c5, d, e, f)
% 0.19/0.51 = { by axiom 5 (s8_domain_1__e1_46__relset_2) }
% 0.19/0.51 fresh12(m1_subset_1(c5, k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(a4, b5)))), true2, a4, b5, c5, d, e, f)
% 0.19/0.51 = { by axiom 2 (t36_relset_2) }
% 0.19/0.51 fresh12(true2, true2, a4, b5, c5, d, e, f)
% 0.19/0.51 = { by axiom 3 (s8_domain_1__e1_46__relset_2) }
% 0.19/0.51 true2
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51
% 0.19/0.51 RESULT: Theorem (the conjecture is true).
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