TSTP Solution File: SEU450+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU450+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 : n020.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 17:52:59 EDT 2023
% Result : Theorem 16.02s 2.52s
% Output : Proof 16.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU450+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 : n020.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 17:51:30 EDT 2023
% 0.13/0.34 % CPUTime :
% 16.02/2.52 Command-line arguments: --ground-connectedness --complete-subsets
% 16.02/2.52
% 16.02/2.52 % SZS status Theorem
% 16.02/2.52
% 16.73/2.57 % SZS output start Proof
% 16.73/2.57 Take the following subset of the input axioms:
% 16.73/2.57 fof(cc1_relset_1, axiom, ![A, B, C]: (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C))).
% 16.73/2.57 fof(d10_xboole_0, axiom, ![A2, B2]: (A2=B2 <=> (r1_tarski(A2, B2) & r1_tarski(B2, A2)))).
% 16.73/2.57 fof(dt_k6_relset_1, axiom, ![B2, C2, A2_2]: (m1_relset_1(C2, A2_2, B2) => m2_relset_1(k6_relset_1(A2_2, B2, C2), B2, A2_2))).
% 16.73/2.57 fof(dt_k8_relset_2, axiom, ![D, B2, C2, A2_2]: ((m1_subset_1(C2, k1_zfmisc_1(A2_2)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A2_2, B2)))) => m1_subset_1(k8_relset_2(A2_2, B2, C2, D), k1_zfmisc_1(B2)))).
% 16.73/2.57 fof(dt_m2_relset_1, axiom, ![B2, C2, A2_2]: (m2_relset_1(C2, A2_2, B2) => m1_subset_1(C2, k1_zfmisc_1(k2_zfmisc_1(A2_2, B2))))).
% 16.73/2.57 fof(involutiveness_k4_relat_1, axiom, ![A2_2]: (v1_relat_1(A2_2) => k4_relat_1(k4_relat_1(A2_2))=A2_2)).
% 16.73/2.57 fof(redefinition_k6_relset_1, axiom, ![B2, C2, A2_2]: (m1_relset_1(C2, A2_2, B2) => k6_relset_1(A2_2, B2, C2)=k4_relat_1(C2))).
% 16.73/2.57 fof(redefinition_m2_relset_1, axiom, ![B2, C2, A2_2]: (m2_relset_1(C2, A2_2, B2) <=> m1_relset_1(C2, A2_2, B2))).
% 16.73/2.57 fof(t32_relset_2, axiom, ![B2, C2, A2_2]: (m1_subset_1(C2, k1_zfmisc_1(A2_2)) => ![D2]: (m1_subset_1(D2, k1_zfmisc_1(A2_2)) => ![E]: (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A2_2, B2))) => (r1_tarski(C2, D2) => r1_tarski(k8_relset_2(A2_2, B2, D2, E), k8_relset_2(A2_2, B2, C2, E))))))).
% 16.73/2.57 fof(t61_relset_2, axiom, ![B2, C2, A2_2]: (m1_subset_1(C2, k1_zfmisc_1(A2_2)) => ![D2]: (m1_subset_1(D2, k1_zfmisc_1(B2)) => ![E2]: (m2_relset_1(E2, A2_2, B2) => (r1_tarski(C2, k8_relset_2(B2, A2_2, D2, k6_relset_1(A2_2, B2, E2))) <=> r1_tarski(D2, k8_relset_2(A2_2, B2, C2, E2))))))).
% 16.73/2.57 fof(t64_relset_2, conjecture, ![A3, B2, C2]: (m1_subset_1(C2, k1_zfmisc_1(A3)) => ![D2]: (m1_subset_1(D2, k1_zfmisc_1(B2)) => ![E2]: (m2_relset_1(E2, A3, B2) => (k8_relset_2(A3, B2, C2, E2)=k8_relset_2(A3, B2, k8_relset_2(B2, A3, k8_relset_2(A3, B2, C2, E2), k6_relset_1(A3, B2, E2)), E2) & k8_relset_2(B2, A3, D2, k6_relset_1(A3, B2, E2))=k8_relset_2(B2, A3, k8_relset_2(A3, B2, k8_relset_2(B2, A3, D2, k6_relset_1(A3, B2, E2)), E2), k6_relset_1(A3, B2, E2))))))).
% 16.73/2.57
% 16.73/2.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.73/2.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.73/2.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.73/2.57 fresh(y, y, x1...xn) = u
% 16.73/2.57 C => fresh(s, t, x1...xn) = v
% 16.73/2.57 where fresh is a fresh function symbol and x1..xn are the free
% 16.73/2.57 variables of u and v.
% 16.73/2.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.73/2.57 input problem has no model of domain size 1).
% 16.73/2.57
% 16.73/2.57 The encoding turns the above axioms into the following unit equations and goals:
% 16.73/2.57
% 16.73/2.57 Axiom 1 (d10_xboole_0): r1_tarski(X, X) = true2.
% 16.73/2.57 Axiom 2 (cc1_relset_1): fresh37(X, X, Y) = true2.
% 16.73/2.57 Axiom 3 (involutiveness_k4_relat_1): fresh4(X, X, Y) = Y.
% 16.73/2.57 Axiom 4 (t64_relset_2_2): m2_relset_1(e, a4, b5) = true2.
% 16.73/2.57 Axiom 5 (t64_relset_2): m1_subset_1(c4, k1_zfmisc_1(a4)) = true2.
% 16.73/2.57 Axiom 6 (t64_relset_2_1): m1_subset_1(d, k1_zfmisc_1(b5)) = true2.
% 16.73/2.57 Axiom 7 (d10_xboole_0_1): fresh6(X, X, Y, Z) = Y.
% 16.73/2.57 Axiom 8 (d10_xboole_0_1): fresh5(X, X, Y, Z) = Z.
% 16.73/2.57 Axiom 9 (involutiveness_k4_relat_1): fresh4(v1_relat_1(X), true2, X) = k4_relat_1(k4_relat_1(X)).
% 16.73/2.57 Axiom 10 (dt_k6_relset_1): fresh31(X, X, Y, Z, W) = true2.
% 16.73/2.57 Axiom 11 (dt_m2_relset_1): fresh23(X, X, Y, Z, W) = true2.
% 16.73/2.57 Axiom 12 (redefinition_k6_relset_1): fresh18(X, X, Y, Z, W) = k4_relat_1(W).
% 16.73/2.57 Axiom 13 (redefinition_m2_relset_1): fresh14(X, X, Y, Z, W) = true2.
% 16.73/2.57 Axiom 14 (dt_k8_relset_2): fresh26(X, X, Y, Z, W, V) = true2.
% 16.73/2.57 Axiom 15 (d10_xboole_0_1): fresh6(r1_tarski(X, Y), true2, Y, X) = fresh5(r1_tarski(Y, X), true2, Y, X).
% 16.73/2.57 Axiom 16 (t32_relset_2): fresh49(X, X, Y, Z, W, V, U) = true2.
% 16.73/2.57 Axiom 17 (t61_relset_2_1): fresh45(X, X, Y, Z, W, V, U) = true2.
% 16.73/2.57 Axiom 18 (dt_k8_relset_2): fresh27(X, X, Y, Z, W, V) = m1_subset_1(k8_relset_2(Y, Z, W, V), k1_zfmisc_1(Z)).
% 16.73/2.57 Axiom 19 (cc1_relset_1): fresh37(m1_subset_1(X, k1_zfmisc_1(k2_zfmisc_1(Y, Z))), true2, X) = v1_relat_1(X).
% 16.73/2.57 Axiom 20 (dt_k6_relset_1): fresh31(m1_relset_1(X, Y, Z), true2, Y, Z, X) = m2_relset_1(k6_relset_1(Y, Z, X), Z, Y).
% 16.73/2.57 Axiom 21 (dt_m2_relset_1): fresh23(m2_relset_1(X, Y, Z), true2, Y, Z, X) = m1_subset_1(X, k1_zfmisc_1(k2_zfmisc_1(Y, Z))).
% 16.73/2.57 Axiom 22 (redefinition_k6_relset_1): fresh18(m1_relset_1(X, Y, Z), true2, Y, Z, X) = k6_relset_1(Y, Z, X).
% 16.73/2.57 Axiom 23 (redefinition_m2_relset_1): fresh14(m2_relset_1(X, Y, Z), true2, Y, Z, X) = m1_relset_1(X, Y, Z).
% 16.73/2.57 Axiom 24 (t61_relset_2_1): fresh43(X, X, Y, Z, W, V, U) = r1_tarski(W, k8_relset_2(Z, Y, V, k6_relset_1(Y, Z, U))).
% 16.73/2.57 Axiom 25 (t32_relset_2): fresh48(X, X, Y, Z, W, V, U) = fresh49(m1_subset_1(W, k1_zfmisc_1(Y)), true2, Y, Z, W, V, U).
% 16.73/2.57 Axiom 26 (t32_relset_2): fresh46(X, X, Y, Z, W, V, U) = fresh47(m1_subset_1(V, k1_zfmisc_1(Y)), true2, Y, Z, W, V, U).
% 16.73/2.57 Axiom 27 (t61_relset_2_1): fresh44(X, X, Y, Z, W, V, U) = fresh45(m1_subset_1(W, k1_zfmisc_1(Y)), true2, Y, Z, W, V, U).
% 16.73/2.58 Axiom 28 (t61_relset_2_1): fresh42(X, X, Y, Z, W, V, U) = fresh43(m1_subset_1(V, k1_zfmisc_1(Z)), true2, Y, Z, W, V, U).
% 16.73/2.58 Axiom 29 (t32_relset_2): fresh47(X, X, Y, Z, W, V, U) = r1_tarski(k8_relset_2(Y, Z, V, U), k8_relset_2(Y, Z, W, U)).
% 16.73/2.58 Axiom 30 (dt_k8_relset_2): fresh27(m1_subset_1(X, k1_zfmisc_1(k2_zfmisc_1(Y, Z))), true2, Y, Z, W, X) = fresh26(m1_subset_1(W, k1_zfmisc_1(Y)), true2, Y, Z, W, X).
% 16.73/2.58 Axiom 31 (t32_relset_2): fresh46(r1_tarski(X, Y), true2, Z, W, X, Y, V) = fresh48(m1_subset_1(V, k1_zfmisc_1(k2_zfmisc_1(Z, W))), true2, Z, W, X, Y, V).
% 16.73/2.58 Axiom 32 (t61_relset_2_1): fresh42(r1_tarski(X, k8_relset_2(Y, Z, W, V)), true2, Y, Z, W, X, V) = fresh44(m2_relset_1(V, Y, Z), true2, Y, Z, W, X, V).
% 16.73/2.58
% 16.73/2.58 Lemma 33: m1_relset_1(e, a4, b5) = true2.
% 16.73/2.58 Proof:
% 16.73/2.58 m1_relset_1(e, a4, b5)
% 16.73/2.58 = { by axiom 23 (redefinition_m2_relset_1) R->L }
% 16.73/2.58 fresh14(m2_relset_1(e, a4, b5), true2, a4, b5, e)
% 16.73/2.58 = { by axiom 4 (t64_relset_2_2) }
% 16.73/2.58 fresh14(true2, true2, a4, b5, e)
% 16.73/2.58 = { by axiom 13 (redefinition_m2_relset_1) }
% 16.73/2.58 true2
% 16.73/2.58
% 16.73/2.58 Lemma 34: m1_subset_1(e, k1_zfmisc_1(k2_zfmisc_1(a4, b5))) = true2.
% 16.73/2.58 Proof:
% 16.73/2.58 m1_subset_1(e, k1_zfmisc_1(k2_zfmisc_1(a4, b5)))
% 16.73/2.58 = { by axiom 21 (dt_m2_relset_1) R->L }
% 16.73/2.58 fresh23(m2_relset_1(e, a4, b5), true2, a4, b5, e)
% 16.73/2.58 = { by axiom 4 (t64_relset_2_2) }
% 16.73/2.58 fresh23(true2, true2, a4, b5, e)
% 16.73/2.58 = { by axiom 11 (dt_m2_relset_1) }
% 16.73/2.58 true2
% 16.73/2.58
% 16.73/2.58 Lemma 35: fresh27(U, U, Y, Z, W, V) = fresh27(X, X, Y, Z, W, V).
% 16.73/2.58 Proof:
% 16.73/2.58 fresh27(U, U, Y, Z, W, V)
% 16.73/2.58 = { by axiom 18 (dt_k8_relset_2) }
% 16.73/2.58 m1_subset_1(k8_relset_2(Y, Z, W, V), k1_zfmisc_1(Z))
% 16.73/2.58 = { by axiom 18 (dt_k8_relset_2) R->L }
% 16.73/2.58 fresh27(X, X, Y, Z, W, V)
% 16.73/2.58
% 16.73/2.58 Lemma 36: m2_relset_1(k6_relset_1(a4, b5, e), b5, a4) = true2.
% 16.73/2.58 Proof:
% 16.73/2.58 m2_relset_1(k6_relset_1(a4, b5, e), b5, a4)
% 16.73/2.58 = { by axiom 20 (dt_k6_relset_1) R->L }
% 16.73/2.58 fresh31(m1_relset_1(e, a4, b5), true2, a4, b5, e)
% 16.73/2.58 = { by lemma 33 }
% 16.73/2.58 fresh31(true2, true2, a4, b5, e)
% 16.73/2.58 = { by axiom 10 (dt_k6_relset_1) }
% 16.73/2.58 true2
% 16.73/2.58
% 16.73/2.58 Lemma 37: fresh26(m1_subset_1(X, k1_zfmisc_1(a4)), true2, a4, b5, X, e) = fresh27(Y, Y, a4, b5, X, e).
% 16.73/2.58 Proof:
% 16.73/2.58 fresh26(m1_subset_1(X, k1_zfmisc_1(a4)), true2, a4, b5, X, e)
% 16.73/2.58 = { by axiom 30 (dt_k8_relset_2) R->L }
% 16.73/2.58 fresh27(m1_subset_1(e, k1_zfmisc_1(k2_zfmisc_1(a4, b5))), true2, a4, b5, X, e)
% 16.73/2.58 = { by lemma 34 }
% 16.73/2.58 fresh27(true2, true2, a4, b5, X, e)
% 16.73/2.58 = { by lemma 35 R->L }
% 16.73/2.58 fresh27(Y, Y, a4, b5, X, e)
% 16.73/2.58
% 16.73/2.58 Lemma 38: m1_subset_1(k8_relset_2(a4, b5, c4, e), k1_zfmisc_1(b5)) = true2.
% 16.73/2.58 Proof:
% 16.73/2.58 m1_subset_1(k8_relset_2(a4, b5, c4, e), k1_zfmisc_1(b5))
% 16.73/2.58 = { by axiom 18 (dt_k8_relset_2) R->L }
% 16.73/2.58 fresh27(X, X, a4, b5, c4, e)
% 16.73/2.58 = { by lemma 37 R->L }
% 16.73/2.58 fresh26(m1_subset_1(c4, k1_zfmisc_1(a4)), true2, a4, b5, c4, e)
% 16.73/2.58 = { by axiom 5 (t64_relset_2) }
% 16.73/2.58 fresh26(true2, true2, a4, b5, c4, e)
% 16.73/2.58 = { by axiom 14 (dt_k8_relset_2) }
% 16.73/2.58 true2
% 16.73/2.58
% 16.73/2.58 Lemma 39: m1_subset_1(k6_relset_1(a4, b5, e), k1_zfmisc_1(k2_zfmisc_1(b5, a4))) = true2.
% 16.73/2.58 Proof:
% 16.73/2.58 m1_subset_1(k6_relset_1(a4, b5, e), k1_zfmisc_1(k2_zfmisc_1(b5, a4)))
% 16.73/2.58 = { by axiom 21 (dt_m2_relset_1) R->L }
% 16.73/2.58 fresh23(m2_relset_1(k6_relset_1(a4, b5, e), b5, a4), true2, b5, a4, k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by lemma 36 }
% 16.73/2.58 fresh23(true2, true2, b5, a4, k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by axiom 11 (dt_m2_relset_1) }
% 16.73/2.58 true2
% 16.73/2.58
% 16.73/2.58 Lemma 40: fresh26(m1_subset_1(X, k1_zfmisc_1(b5)), true2, b5, a4, X, k6_relset_1(a4, b5, e)) = fresh27(Y, Y, b5, a4, X, k6_relset_1(a4, b5, e)).
% 16.73/2.58 Proof:
% 16.73/2.58 fresh26(m1_subset_1(X, k1_zfmisc_1(b5)), true2, b5, a4, X, k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by axiom 30 (dt_k8_relset_2) R->L }
% 16.73/2.58 fresh27(m1_subset_1(k6_relset_1(a4, b5, e), k1_zfmisc_1(k2_zfmisc_1(b5, a4))), true2, b5, a4, X, k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by lemma 39 }
% 16.73/2.58 fresh27(true2, true2, b5, a4, X, k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by lemma 35 R->L }
% 16.73/2.58 fresh27(Y, Y, b5, a4, X, k6_relset_1(a4, b5, e))
% 16.73/2.58
% 16.73/2.58 Lemma 41: m1_subset_1(k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k1_zfmisc_1(a4)) = true2.
% 16.73/2.58 Proof:
% 16.73/2.58 m1_subset_1(k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k1_zfmisc_1(a4))
% 16.73/2.58 = { by axiom 18 (dt_k8_relset_2) R->L }
% 16.73/2.58 fresh27(X, X, b5, a4, d, k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by lemma 40 R->L }
% 16.73/2.58 fresh26(m1_subset_1(d, k1_zfmisc_1(b5)), true2, b5, a4, d, k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by axiom 6 (t64_relset_2_1) }
% 16.73/2.58 fresh26(true2, true2, b5, a4, d, k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by axiom 14 (dt_k8_relset_2) }
% 16.73/2.58 true2
% 16.73/2.58
% 16.73/2.58 Lemma 42: fresh43(X, X, b5, a4, Y, Z, k6_relset_1(a4, b5, e)) = r1_tarski(Y, k8_relset_2(a4, b5, Z, e)).
% 16.73/2.58 Proof:
% 16.73/2.58 fresh43(X, X, b5, a4, Y, Z, k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by axiom 24 (t61_relset_2_1) }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, k6_relset_1(b5, a4, k6_relset_1(a4, b5, e))))
% 16.73/2.58 = { by axiom 22 (redefinition_k6_relset_1) R->L }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, fresh18(m1_relset_1(k6_relset_1(a4, b5, e), b5, a4), true2, b5, a4, k6_relset_1(a4, b5, e))))
% 16.73/2.58 = { by axiom 23 (redefinition_m2_relset_1) R->L }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, fresh18(fresh14(m2_relset_1(k6_relset_1(a4, b5, e), b5, a4), true2, b5, a4, k6_relset_1(a4, b5, e)), true2, b5, a4, k6_relset_1(a4, b5, e))))
% 16.73/2.58 = { by lemma 36 }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, fresh18(fresh14(true2, true2, b5, a4, k6_relset_1(a4, b5, e)), true2, b5, a4, k6_relset_1(a4, b5, e))))
% 16.73/2.58 = { by axiom 13 (redefinition_m2_relset_1) }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, fresh18(true2, true2, b5, a4, k6_relset_1(a4, b5, e))))
% 16.73/2.58 = { by axiom 12 (redefinition_k6_relset_1) }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, k4_relat_1(k6_relset_1(a4, b5, e))))
% 16.73/2.58 = { by axiom 22 (redefinition_k6_relset_1) R->L }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, k4_relat_1(fresh18(m1_relset_1(e, a4, b5), true2, a4, b5, e))))
% 16.73/2.58 = { by lemma 33 }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, k4_relat_1(fresh18(true2, true2, a4, b5, e))))
% 16.73/2.58 = { by axiom 12 (redefinition_k6_relset_1) }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, k4_relat_1(k4_relat_1(e))))
% 16.73/2.58 = { by axiom 9 (involutiveness_k4_relat_1) R->L }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, fresh4(v1_relat_1(e), true2, e)))
% 16.73/2.58 = { by axiom 19 (cc1_relset_1) R->L }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, fresh4(fresh37(m1_subset_1(e, k1_zfmisc_1(k2_zfmisc_1(a4, b5))), true2, e), true2, e)))
% 16.73/2.58 = { by lemma 34 }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, fresh4(fresh37(true2, true2, e), true2, e)))
% 16.73/2.58 = { by axiom 2 (cc1_relset_1) }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, fresh4(true2, true2, e)))
% 16.73/2.58 = { by axiom 3 (involutiveness_k4_relat_1) }
% 16.73/2.58 r1_tarski(Y, k8_relset_2(a4, b5, Z, e))
% 16.73/2.58
% 16.73/2.58 Lemma 43: m1_subset_1(k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k1_zfmisc_1(b5)) = true2.
% 16.73/2.58 Proof:
% 16.73/2.58 m1_subset_1(k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k1_zfmisc_1(b5))
% 16.73/2.58 = { by axiom 18 (dt_k8_relset_2) R->L }
% 16.73/2.58 fresh27(X, X, a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e)
% 16.73/2.58 = { by lemma 37 R->L }
% 16.73/2.58 fresh26(m1_subset_1(k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k1_zfmisc_1(a4)), true2, a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e)
% 16.73/2.58 = { by lemma 41 }
% 16.73/2.58 fresh26(true2, true2, a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e)
% 16.73/2.58 = { by axiom 14 (dt_k8_relset_2) }
% 16.73/2.58 true2
% 16.73/2.58
% 16.73/2.58 Lemma 44: m1_subset_1(k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k1_zfmisc_1(a4)) = true2.
% 16.73/2.58 Proof:
% 16.73/2.58 m1_subset_1(k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k1_zfmisc_1(a4))
% 16.73/2.58 = { by axiom 18 (dt_k8_relset_2) R->L }
% 16.73/2.58 fresh27(X, X, b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by lemma 40 R->L }
% 16.73/2.58 fresh26(m1_subset_1(k8_relset_2(a4, b5, c4, e), k1_zfmisc_1(b5)), true2, b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by lemma 38 }
% 16.73/2.58 fresh26(true2, true2, b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))
% 16.73/2.58 = { by axiom 14 (dt_k8_relset_2) }
% 16.73/2.58 true2
% 16.73/2.58
% 16.73/2.58 Goal 1 (t64_relset_2_3): tuple3(k8_relset_2(a4, b5, c4, e), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))) = tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e))).
% 16.73/2.58 Proof:
% 16.73/2.58 tuple3(k8_relset_2(a4, b5, c4, e), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.73/2.58 = { by axiom 7 (d10_xboole_0_1) R->L }
% 16.73/2.58 tuple3(fresh6(true2, true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.73/2.58 = { by axiom 16 (t32_relset_2) R->L }
% 16.73/2.58 tuple3(fresh6(fresh49(true2, true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.73/2.58 = { by axiom 5 (t64_relset_2) R->L }
% 16.73/2.58 tuple3(fresh6(fresh49(m1_subset_1(c4, k1_zfmisc_1(a4)), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.73/2.58 = { by axiom 25 (t32_relset_2) R->L }
% 16.73/2.58 tuple3(fresh6(fresh48(true2, true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.73/2.58 = { by lemma 34 R->L }
% 16.73/2.58 tuple3(fresh6(fresh48(m1_subset_1(e, k1_zfmisc_1(k2_zfmisc_1(a4, b5))), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.73/2.58 = { by axiom 31 (t32_relset_2) R->L }
% 16.73/2.58 tuple3(fresh6(fresh46(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.73/2.58 = { by axiom 24 (t61_relset_2_1) R->L }
% 16.73/2.58 tuple3(fresh6(fresh46(fresh43(true2, true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.73/2.58 = { by lemma 38 R->L }
% 16.73/2.58 tuple3(fresh6(fresh46(fresh43(m1_subset_1(k8_relset_2(a4, b5, c4, e), k1_zfmisc_1(b5)), true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.73/2.58 = { by axiom 28 (t61_relset_2_1) R->L }
% 16.73/2.58 tuple3(fresh6(fresh46(fresh42(true2, true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.58 = { by axiom 1 (d10_xboole_0) R->L }
% 16.99/2.58 tuple3(fresh6(fresh46(fresh42(r1_tarski(k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, c4, e)), true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.58 = { by axiom 32 (t61_relset_2_1) }
% 16.99/2.58 tuple3(fresh6(fresh46(fresh44(m2_relset_1(e, a4, b5), true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.58 = { by axiom 4 (t64_relset_2_2) }
% 16.99/2.58 tuple3(fresh6(fresh46(fresh44(true2, true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.58 = { by axiom 27 (t61_relset_2_1) }
% 16.99/2.58 tuple3(fresh6(fresh46(fresh45(m1_subset_1(c4, k1_zfmisc_1(a4)), true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.58 = { by axiom 5 (t64_relset_2) }
% 16.99/2.58 tuple3(fresh6(fresh46(fresh45(true2, true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.58 = { by axiom 17 (t61_relset_2_1) }
% 16.99/2.58 tuple3(fresh6(fresh46(true2, true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by axiom 26 (t32_relset_2) }
% 16.99/2.59 tuple3(fresh6(fresh47(m1_subset_1(k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k1_zfmisc_1(a4)), true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by lemma 44 }
% 16.99/2.59 tuple3(fresh6(fresh47(true2, true2, a4, b5, c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by axiom 29 (t32_relset_2) }
% 16.99/2.59 tuple3(fresh6(r1_tarski(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), k8_relset_2(a4, b5, c4, e)), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by axiom 15 (d10_xboole_0_1) }
% 16.99/2.59 tuple3(fresh5(r1_tarski(k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by lemma 42 R->L }
% 16.99/2.59 tuple3(fresh5(fresh43(true2, true2, b5, a4, k8_relset_2(a4, b5, c4, e), k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by lemma 44 R->L }
% 16.99/2.59 tuple3(fresh5(fresh43(m1_subset_1(k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k1_zfmisc_1(a4)), true2, b5, a4, k8_relset_2(a4, b5, c4, e), k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by axiom 28 (t61_relset_2_1) R->L }
% 16.99/2.59 tuple3(fresh5(fresh42(true2, true2, b5, a4, k8_relset_2(a4, b5, c4, e), k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by axiom 1 (d10_xboole_0) R->L }
% 16.99/2.59 tuple3(fresh5(fresh42(r1_tarski(k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), true2, b5, a4, k8_relset_2(a4, b5, c4, e), k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by axiom 32 (t61_relset_2_1) }
% 16.99/2.59 tuple3(fresh5(fresh44(m2_relset_1(k6_relset_1(a4, b5, e), b5, a4), true2, b5, a4, k8_relset_2(a4, b5, c4, e), k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by lemma 36 }
% 16.99/2.59 tuple3(fresh5(fresh44(true2, true2, b5, a4, k8_relset_2(a4, b5, c4, e), k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by axiom 27 (t61_relset_2_1) }
% 16.99/2.59 tuple3(fresh5(fresh45(m1_subset_1(k8_relset_2(a4, b5, c4, e), k1_zfmisc_1(b5)), true2, b5, a4, k8_relset_2(a4, b5, c4, e), k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by lemma 38 }
% 16.99/2.59 tuple3(fresh5(fresh45(true2, true2, b5, a4, k8_relset_2(a4, b5, c4, e), k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by axiom 17 (t61_relset_2_1) }
% 16.99/2.59 tuple3(fresh5(true2, true2, k8_relset_2(a4, b5, c4, e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by axiom 8 (d10_xboole_0_1) }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)))
% 16.99/2.59 = { by axiom 8 (d10_xboole_0_1) R->L }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(true2, true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 16 (t32_relset_2) R->L }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh49(true2, true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 6 (t64_relset_2_1) R->L }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh49(m1_subset_1(d, k1_zfmisc_1(b5)), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 25 (t32_relset_2) R->L }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh48(true2, true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by lemma 39 R->L }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh48(m1_subset_1(k6_relset_1(a4, b5, e), k1_zfmisc_1(k2_zfmisc_1(b5, a4))), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 31 (t32_relset_2) R->L }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh46(r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e)), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by lemma 42 R->L }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh46(fresh43(true2, true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by lemma 41 R->L }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh46(fresh43(m1_subset_1(k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k1_zfmisc_1(a4)), true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 28 (t61_relset_2_1) R->L }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh46(fresh42(true2, true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 1 (d10_xboole_0) R->L }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh46(fresh42(r1_tarski(k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))), true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 32 (t61_relset_2_1) }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh46(fresh44(m2_relset_1(k6_relset_1(a4, b5, e), b5, a4), true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by lemma 36 }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh46(fresh44(true2, true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 27 (t61_relset_2_1) }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh46(fresh45(m1_subset_1(d, k1_zfmisc_1(b5)), true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 6 (t64_relset_2_1) }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh46(fresh45(true2, true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 17 (t61_relset_2_1) }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh46(true2, true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 26 (t32_relset_2) }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh47(m1_subset_1(k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k1_zfmisc_1(b5)), true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by lemma 43 }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(fresh47(true2, true2, b5, a4, d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 29 (t32_relset_2) }
% 16.99/2.59 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh5(r1_tarski(k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.59 = { by axiom 15 (d10_xboole_0_1) R->L }
% 16.99/2.60 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh6(r1_tarski(k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e))), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.60 = { by axiom 24 (t61_relset_2_1) R->L }
% 16.99/2.60 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh6(fresh43(true2, true2, a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), e), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.60 = { by lemma 43 R->L }
% 16.99/2.60 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh6(fresh43(m1_subset_1(k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k1_zfmisc_1(b5)), true2, a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), e), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.60 = { by axiom 28 (t61_relset_2_1) R->L }
% 16.99/2.60 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh6(fresh42(true2, true2, a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), e), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.60 = { by axiom 1 (d10_xboole_0) R->L }
% 16.99/2.60 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh6(fresh42(r1_tarski(k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e)), true2, a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), e), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.60 = { by axiom 32 (t61_relset_2_1) }
% 16.99/2.60 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh6(fresh44(m2_relset_1(e, a4, b5), true2, a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), e), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.60 = { by axiom 4 (t64_relset_2_2) }
% 16.99/2.60 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh6(fresh44(true2, true2, a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), e), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.60 = { by axiom 27 (t61_relset_2_1) }
% 16.99/2.60 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh6(fresh45(m1_subset_1(k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k1_zfmisc_1(a4)), true2, a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), e), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.60 = { by lemma 41 }
% 16.99/2.60 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh6(fresh45(true2, true2, a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), e), true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.60 = { by axiom 17 (t61_relset_2_1) }
% 16.99/2.60 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), fresh6(true2, true2, k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)), k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e))))
% 16.99/2.60 = { by axiom 7 (d10_xboole_0_1) }
% 16.99/2.60 tuple3(k8_relset_2(a4, b5, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e)), e), k8_relset_2(b5, a4, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e), k6_relset_1(a4, b5, e)))
% 16.99/2.60 % SZS output end Proof
% 16.99/2.60
% 16.99/2.60 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------