TSTP Solution File: SEU451+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU451+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 : n016.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 17:53:00 EDT 2023
% Result : Theorem 23.05s 3.36s
% Output : Proof 23.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU451+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
% 0.14/0.34 % Computer : n016.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 17:41:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 23.05/3.36 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 23.05/3.36
% 23.05/3.36 % SZS status Theorem
% 23.05/3.36
% 23.05/3.37 % SZS output start Proof
% 23.05/3.37 Take the following subset of the input axioms:
% 23.05/3.37 fof(dt_k6_partfun1, axiom, ![A]: (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))).
% 23.05/3.37 fof(dt_m2_relset_1, axiom, ![B, C, A2]: (m2_relset_1(C, A2, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A2, B))))).
% 23.05/3.37 fof(redefinition_k7_relset_1, axiom, ![D, E, F, B2, C2, A2_2]: ((m1_relset_1(E, A2_2, B2) & m1_relset_1(F, C2, D)) => k7_relset_1(A2_2, B2, C2, D, E, F)=k5_relat_1(E, F))).
% 23.05/3.37 fof(redefinition_k9_relset_2, axiom, ![B2, C2, A2_2, D2, E2]: ((m1_subset_1(D2, k1_zfmisc_1(k2_zfmisc_1(A2_2, B2))) & m1_subset_1(E2, k1_zfmisc_1(k2_zfmisc_1(B2, C2)))) => k9_relset_2(A2_2, B2, C2, D2, E2)=k5_relat_1(D2, E2))).
% 23.05/3.37 fof(redefinition_m2_relset_1, axiom, ![B2, C2, A2_2]: (m2_relset_1(C2, A2_2, B2) <=> m1_relset_1(C2, A2_2, B2))).
% 23.05/3.37 fof(t23_funct_2, axiom, ![B2, C2, A2_2]: (m2_relset_1(C2, A2_2, B2) => (k7_relset_1(A2_2, A2_2, A2_2, B2, k6_partfun1(A2_2), C2)=C2 & k7_relset_1(A2_2, B2, B2, B2, C2, k6_partfun1(B2))=C2))).
% 23.05/3.37 fof(t65_relset_2, conjecture, ![A3, B2, C2]: (m2_relset_1(C2, A3, B2) => k9_relset_2(A3, A3, B2, k6_partfun1(A3), C2)=k9_relset_2(A3, B2, B2, C2, k6_partfun1(B2)))).
% 23.05/3.37
% 23.05/3.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 23.05/3.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 23.05/3.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 23.05/3.37 fresh(y, y, x1...xn) = u
% 23.05/3.37 C => fresh(s, t, x1...xn) = v
% 23.05/3.37 where fresh is a fresh function symbol and x1..xn are the free
% 23.05/3.37 variables of u and v.
% 23.05/3.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 23.05/3.37 input problem has no model of domain size 1).
% 23.05/3.37
% 23.05/3.37 The encoding turns the above axioms into the following unit equations and goals:
% 23.05/3.37
% 23.05/3.37 Axiom 1 (t65_relset_2): m2_relset_1(c4, a4, b5) = true2.
% 23.05/3.37 Axiom 2 (dt_k6_partfun1): m2_relset_1(k6_partfun1(X), X, X) = true2.
% 23.05/3.37 Axiom 3 (dt_m2_relset_1): fresh26(X, X, Y, Z, W) = true2.
% 23.05/3.37 Axiom 4 (redefinition_m2_relset_1): fresh12(X, X, Y, Z, W) = true2.
% 23.05/3.37 Axiom 5 (t23_funct_2_1): fresh4(X, X, Y, Z, W) = W.
% 23.05/3.37 Axiom 6 (t23_funct_2): fresh3(X, X, Y, Z, W) = W.
% 23.05/3.37 Axiom 7 (redefinition_k9_relset_2): fresh14(X, X, Y, Z, W, V, U) = k9_relset_2(Y, Z, W, V, U).
% 23.05/3.37 Axiom 8 (redefinition_k9_relset_2): fresh13(X, X, Y, Z, W, V, U) = k5_relat_1(V, U).
% 23.05/3.37 Axiom 9 (dt_m2_relset_1): fresh26(m2_relset_1(X, Y, Z), true2, Y, Z, X) = m1_subset_1(X, k1_zfmisc_1(k2_zfmisc_1(Y, Z))).
% 23.05/3.37 Axiom 10 (redefinition_k7_relset_1): fresh16(X, X, Y, Z, W, V, U, T) = k5_relat_1(U, T).
% 23.05/3.37 Axiom 11 (redefinition_k7_relset_1): fresh15(X, X, Y, Z, W, V, U, T) = k7_relset_1(Y, Z, W, V, U, T).
% 23.05/3.37 Axiom 12 (redefinition_m2_relset_1): fresh12(m2_relset_1(X, Y, Z), true2, Y, Z, X) = m1_relset_1(X, Y, Z).
% 23.05/3.37 Axiom 13 (t23_funct_2_1): fresh4(m2_relset_1(X, Y, Z), true2, Y, Z, X) = k7_relset_1(Y, Z, Z, Z, X, k6_partfun1(Z)).
% 23.05/3.37 Axiom 14 (t23_funct_2): fresh3(m2_relset_1(X, Y, Z), true2, Y, Z, X) = k7_relset_1(Y, Y, Y, Z, k6_partfun1(Y), X).
% 23.05/3.37 Axiom 15 (redefinition_k7_relset_1): fresh15(m1_relset_1(X, Y, Z), true2, W, V, Y, Z, U, X) = fresh16(m1_relset_1(U, W, V), true2, W, V, Y, Z, U, X).
% 23.05/3.37 Axiom 16 (redefinition_k9_relset_2): fresh14(m1_subset_1(X, k1_zfmisc_1(k2_zfmisc_1(Y, Z))), true2, W, Y, Z, V, X) = fresh13(m1_subset_1(V, k1_zfmisc_1(k2_zfmisc_1(W, Y))), true2, W, Y, Z, V, X).
% 23.05/3.37
% 23.05/3.37 Lemma 17: m1_relset_1(c4, a4, b5) = true2.
% 23.05/3.37 Proof:
% 23.05/3.37 m1_relset_1(c4, a4, b5)
% 23.05/3.37 = { by axiom 12 (redefinition_m2_relset_1) R->L }
% 23.05/3.37 fresh12(m2_relset_1(c4, a4, b5), true2, a4, b5, c4)
% 23.05/3.37 = { by axiom 1 (t65_relset_2) }
% 23.05/3.37 fresh12(true2, true2, a4, b5, c4)
% 23.05/3.37 = { by axiom 4 (redefinition_m2_relset_1) }
% 23.05/3.37 true2
% 23.05/3.37
% 23.05/3.37 Lemma 18: m1_relset_1(k6_partfun1(X), X, X) = true2.
% 23.05/3.37 Proof:
% 23.05/3.37 m1_relset_1(k6_partfun1(X), X, X)
% 23.05/3.37 = { by axiom 12 (redefinition_m2_relset_1) R->L }
% 23.05/3.37 fresh12(m2_relset_1(k6_partfun1(X), X, X), true2, X, X, k6_partfun1(X))
% 23.05/3.37 = { by axiom 2 (dt_k6_partfun1) }
% 23.05/3.37 fresh12(true2, true2, X, X, k6_partfun1(X))
% 23.05/3.37 = { by axiom 4 (redefinition_m2_relset_1) }
% 23.05/3.37 true2
% 23.05/3.37
% 23.05/3.37 Lemma 19: m1_subset_1(c4, k1_zfmisc_1(k2_zfmisc_1(a4, b5))) = true2.
% 23.05/3.37 Proof:
% 23.05/3.37 m1_subset_1(c4, k1_zfmisc_1(k2_zfmisc_1(a4, b5)))
% 23.05/3.37 = { by axiom 9 (dt_m2_relset_1) R->L }
% 23.05/3.37 fresh26(m2_relset_1(c4, a4, b5), true2, a4, b5, c4)
% 23.05/3.37 = { by axiom 1 (t65_relset_2) }
% 23.05/3.37 fresh26(true2, true2, a4, b5, c4)
% 23.05/3.37 = { by axiom 3 (dt_m2_relset_1) }
% 23.05/3.37 true2
% 23.05/3.37
% 23.05/3.37 Lemma 20: m1_subset_1(k6_partfun1(X), k1_zfmisc_1(k2_zfmisc_1(X, X))) = true2.
% 23.05/3.37 Proof:
% 23.05/3.37 m1_subset_1(k6_partfun1(X), k1_zfmisc_1(k2_zfmisc_1(X, X)))
% 23.05/3.37 = { by axiom 9 (dt_m2_relset_1) R->L }
% 23.05/3.37 fresh26(m2_relset_1(k6_partfun1(X), X, X), true2, X, X, k6_partfun1(X))
% 23.05/3.37 = { by axiom 2 (dt_k6_partfun1) }
% 23.05/3.37 fresh26(true2, true2, X, X, k6_partfun1(X))
% 23.05/3.37 = { by axiom 3 (dt_m2_relset_1) }
% 23.05/3.37 true2
% 23.05/3.37
% 23.05/3.37 Goal 1 (t65_relset_2_1): k9_relset_2(a4, a4, b5, k6_partfun1(a4), c4) = k9_relset_2(a4, b5, b5, c4, k6_partfun1(b5)).
% 23.05/3.37 Proof:
% 23.05/3.37 k9_relset_2(a4, a4, b5, k6_partfun1(a4), c4)
% 23.05/3.37 = { by axiom 7 (redefinition_k9_relset_2) R->L }
% 23.05/3.37 fresh14(true2, true2, a4, a4, b5, k6_partfun1(a4), c4)
% 23.05/3.37 = { by lemma 19 R->L }
% 23.05/3.37 fresh14(m1_subset_1(c4, k1_zfmisc_1(k2_zfmisc_1(a4, b5))), true2, a4, a4, b5, k6_partfun1(a4), c4)
% 23.05/3.37 = { by axiom 16 (redefinition_k9_relset_2) }
% 23.05/3.37 fresh13(m1_subset_1(k6_partfun1(a4), k1_zfmisc_1(k2_zfmisc_1(a4, a4))), true2, a4, a4, b5, k6_partfun1(a4), c4)
% 23.05/3.37 = { by lemma 20 }
% 23.05/3.37 fresh13(true2, true2, a4, a4, b5, k6_partfun1(a4), c4)
% 23.05/3.37 = { by axiom 8 (redefinition_k9_relset_2) }
% 23.05/3.37 k5_relat_1(k6_partfun1(a4), c4)
% 23.05/3.37 = { by axiom 10 (redefinition_k7_relset_1) R->L }
% 23.05/3.37 fresh16(true2, true2, a4, a4, a4, b5, k6_partfun1(a4), c4)
% 23.05/3.37 = { by lemma 18 R->L }
% 23.05/3.37 fresh16(m1_relset_1(k6_partfun1(a4), a4, a4), true2, a4, a4, a4, b5, k6_partfun1(a4), c4)
% 23.05/3.37 = { by axiom 15 (redefinition_k7_relset_1) R->L }
% 23.05/3.37 fresh15(m1_relset_1(c4, a4, b5), true2, a4, a4, a4, b5, k6_partfun1(a4), c4)
% 23.05/3.37 = { by lemma 17 }
% 23.05/3.37 fresh15(true2, true2, a4, a4, a4, b5, k6_partfun1(a4), c4)
% 23.05/3.37 = { by axiom 11 (redefinition_k7_relset_1) }
% 23.05/3.37 k7_relset_1(a4, a4, a4, b5, k6_partfun1(a4), c4)
% 23.05/3.37 = { by axiom 14 (t23_funct_2) R->L }
% 23.05/3.37 fresh3(m2_relset_1(c4, a4, b5), true2, a4, b5, c4)
% 23.05/3.37 = { by axiom 1 (t65_relset_2) }
% 23.05/3.37 fresh3(true2, true2, a4, b5, c4)
% 23.05/3.37 = { by axiom 6 (t23_funct_2) }
% 23.05/3.37 c4
% 23.05/3.37 = { by axiom 5 (t23_funct_2_1) R->L }
% 23.05/3.37 fresh4(true2, true2, a4, b5, c4)
% 23.05/3.37 = { by axiom 1 (t65_relset_2) R->L }
% 23.05/3.37 fresh4(m2_relset_1(c4, a4, b5), true2, a4, b5, c4)
% 23.05/3.37 = { by axiom 13 (t23_funct_2_1) }
% 23.05/3.37 k7_relset_1(a4, b5, b5, b5, c4, k6_partfun1(b5))
% 23.05/3.37 = { by axiom 11 (redefinition_k7_relset_1) R->L }
% 23.05/3.37 fresh15(true2, true2, a4, b5, b5, b5, c4, k6_partfun1(b5))
% 23.05/3.37 = { by lemma 18 R->L }
% 23.05/3.37 fresh15(m1_relset_1(k6_partfun1(b5), b5, b5), true2, a4, b5, b5, b5, c4, k6_partfun1(b5))
% 23.05/3.37 = { by axiom 15 (redefinition_k7_relset_1) }
% 23.05/3.37 fresh16(m1_relset_1(c4, a4, b5), true2, a4, b5, b5, b5, c4, k6_partfun1(b5))
% 23.05/3.37 = { by lemma 17 }
% 23.05/3.37 fresh16(true2, true2, a4, b5, b5, b5, c4, k6_partfun1(b5))
% 23.05/3.37 = { by axiom 10 (redefinition_k7_relset_1) }
% 23.05/3.37 k5_relat_1(c4, k6_partfun1(b5))
% 23.05/3.37 = { by axiom 8 (redefinition_k9_relset_2) R->L }
% 23.05/3.37 fresh13(true2, true2, a4, b5, b5, c4, k6_partfun1(b5))
% 23.05/3.37 = { by lemma 19 R->L }
% 23.05/3.37 fresh13(m1_subset_1(c4, k1_zfmisc_1(k2_zfmisc_1(a4, b5))), true2, a4, b5, b5, c4, k6_partfun1(b5))
% 23.05/3.37 = { by axiom 16 (redefinition_k9_relset_2) R->L }
% 23.05/3.37 fresh14(m1_subset_1(k6_partfun1(b5), k1_zfmisc_1(k2_zfmisc_1(b5, b5))), true2, a4, b5, b5, c4, k6_partfun1(b5))
% 23.05/3.37 = { by lemma 20 }
% 23.05/3.37 fresh14(true2, true2, a4, b5, b5, c4, k6_partfun1(b5))
% 23.05/3.37 = { by axiom 7 (redefinition_k9_relset_2) }
% 23.05/3.37 k9_relset_2(a4, b5, b5, c4, k6_partfun1(b5))
% 23.05/3.37 % SZS output end Proof
% 23.05/3.37
% 23.05/3.37 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------