TSTP Solution File: SEU449+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU449+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 : n032.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 7.32s 1.26s
% Output : Proof 7.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU449+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Wed Aug 23 20:39:11 EDT 2023
% 0.10/0.29 % CPUTime :
% 7.32/1.26 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 7.32/1.26
% 7.32/1.26 % SZS status Theorem
% 7.32/1.26
% 7.49/1.27 % SZS output start Proof
% 7.49/1.27 Take the following subset of the input axioms:
% 7.49/1.28 fof(cc1_relset_1, axiom, ![A, B, C]: (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C))).
% 7.49/1.28 fof(dt_k6_relset_1, axiom, ![A2, B2, C2]: (m1_relset_1(C2, A2, B2) => m2_relset_1(k6_relset_1(A2, B2, C2), B2, A2))).
% 7.49/1.28 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)))).
% 7.49/1.28 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))))).
% 7.49/1.28 fof(involutiveness_k4_relat_1, axiom, ![A2_2]: (v1_relat_1(A2_2) => k4_relat_1(k4_relat_1(A2_2))=A2_2)).
% 7.49/1.28 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))).
% 7.49/1.28 fof(redefinition_m2_relset_1, axiom, ![B2, C2, A2_2]: (m2_relset_1(C2, A2_2, B2) <=> m1_relset_1(C2, A2_2, B2))).
% 7.49/1.28 fof(reflexivity_r1_tarski, axiom, ![A3, B2]: r1_tarski(A3, A3)).
% 7.49/1.28 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)) => ![E]: (m2_relset_1(E, A2_2, B2) => (r1_tarski(C2, k8_relset_2(B2, A2_2, D2, k6_relset_1(A2_2, B2, E))) <=> r1_tarski(D2, k8_relset_2(A2_2, B2, C2, E))))))).
% 7.49/1.28 fof(t63_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) => (r1_tarski(C2, k8_relset_2(B2, A3, k8_relset_2(A3, B2, C2, E2), k6_relset_1(A3, B2, E2))) & r1_tarski(D2, k8_relset_2(A3, B2, k8_relset_2(B2, A3, D2, k6_relset_1(A3, B2, E2)), E2))))))).
% 7.49/1.28
% 7.49/1.28 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.49/1.28 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.49/1.28 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.49/1.28 fresh(y, y, x1...xn) = u
% 7.49/1.28 C => fresh(s, t, x1...xn) = v
% 7.49/1.28 where fresh is a fresh function symbol and x1..xn are the free
% 7.49/1.28 variables of u and v.
% 7.49/1.28 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.49/1.28 input problem has no model of domain size 1).
% 7.49/1.28
% 7.49/1.28 The encoding turns the above axioms into the following unit equations and goals:
% 7.49/1.28
% 7.49/1.28 Axiom 1 (reflexivity_r1_tarski): r1_tarski(X, X) = true2.
% 7.49/1.28 Axiom 2 (t63_relset_2): m1_subset_1(c4, k1_zfmisc_1(a4)) = true2.
% 7.49/1.28 Axiom 3 (t63_relset_2_1): m1_subset_1(d, k1_zfmisc_1(b5)) = true2.
% 7.49/1.28 Axiom 4 (t63_relset_2_2): m2_relset_1(e, a4, b5) = true2.
% 7.49/1.28 Axiom 5 (cc1_relset_1): fresh35(X, X, Y) = true2.
% 7.49/1.28 Axiom 6 (involutiveness_k4_relat_1): fresh4(X, X, Y) = Y.
% 7.49/1.28 Axiom 7 (involutiveness_k4_relat_1): fresh4(v1_relat_1(X), true2, X) = k4_relat_1(k4_relat_1(X)).
% 7.49/1.28 Axiom 8 (dt_k6_relset_1): fresh29(X, X, Y, Z, W) = true2.
% 7.49/1.28 Axiom 9 (dt_m2_relset_1): fresh21(X, X, Y, Z, W) = true2.
% 7.49/1.28 Axiom 10 (redefinition_k6_relset_1): fresh16(X, X, Y, Z, W) = k4_relat_1(W).
% 7.49/1.28 Axiom 11 (redefinition_m2_relset_1): fresh12(X, X, Y, Z, W) = true2.
% 7.49/1.28 Axiom 12 (dt_k8_relset_2): fresh24(X, X, Y, Z, W, V) = true2.
% 7.49/1.28 Axiom 13 (dt_k8_relset_2): fresh25(X, X, Y, Z, W, V) = m1_subset_1(k8_relset_2(Y, Z, W, V), k1_zfmisc_1(Z)).
% 7.49/1.28 Axiom 14 (t61_relset_2_1): fresh43(X, X, Y, Z, W, V, U) = true2.
% 7.49/1.28 Axiom 15 (cc1_relset_1): fresh35(m1_subset_1(X, k1_zfmisc_1(k2_zfmisc_1(Y, Z))), true2, X) = v1_relat_1(X).
% 7.49/1.28 Axiom 16 (dt_k6_relset_1): fresh29(m1_relset_1(X, Y, Z), true2, Y, Z, X) = m2_relset_1(k6_relset_1(Y, Z, X), Z, Y).
% 7.49/1.28 Axiom 17 (dt_m2_relset_1): fresh21(m2_relset_1(X, Y, Z), true2, Y, Z, X) = m1_subset_1(X, k1_zfmisc_1(k2_zfmisc_1(Y, Z))).
% 7.49/1.28 Axiom 18 (redefinition_k6_relset_1): fresh16(m1_relset_1(X, Y, Z), true2, Y, Z, X) = k6_relset_1(Y, Z, X).
% 7.49/1.28 Axiom 19 (redefinition_m2_relset_1): fresh12(m2_relset_1(X, Y, Z), true2, Y, Z, X) = m1_relset_1(X, Y, Z).
% 7.49/1.28 Axiom 20 (t61_relset_2_1): fresh41(X, X, Y, Z, W, V, U) = r1_tarski(W, k8_relset_2(Z, Y, V, k6_relset_1(Y, Z, U))).
% 7.49/1.28 Axiom 21 (t61_relset_2_1): fresh42(X, X, Y, Z, W, V, U) = fresh43(m1_subset_1(W, k1_zfmisc_1(Y)), true2, Y, Z, W, V, U).
% 7.49/1.28 Axiom 22 (t61_relset_2_1): fresh40(X, X, Y, Z, W, V, U) = fresh41(m1_subset_1(V, k1_zfmisc_1(Z)), true2, Y, Z, W, V, U).
% 7.49/1.28 Axiom 23 (dt_k8_relset_2): fresh25(m1_subset_1(X, k1_zfmisc_1(k2_zfmisc_1(Y, Z))), true2, Y, Z, W, X) = fresh24(m1_subset_1(W, k1_zfmisc_1(Y)), true2, Y, Z, W, X).
% 7.49/1.28 Axiom 24 (t61_relset_2_1): fresh40(r1_tarski(X, k8_relset_2(Y, Z, W, V)), true2, Y, Z, W, X, V) = fresh42(m2_relset_1(V, Y, Z), true2, Y, Z, W, X, V).
% 7.49/1.28
% 7.49/1.28 Lemma 25: m1_relset_1(e, a4, b5) = true2.
% 7.49/1.28 Proof:
% 7.49/1.28 m1_relset_1(e, a4, b5)
% 7.49/1.28 = { by axiom 19 (redefinition_m2_relset_1) R->L }
% 7.49/1.28 fresh12(m2_relset_1(e, a4, b5), true2, a4, b5, e)
% 7.49/1.28 = { by axiom 4 (t63_relset_2_2) }
% 7.49/1.28 fresh12(true2, true2, a4, b5, e)
% 7.49/1.28 = { by axiom 11 (redefinition_m2_relset_1) }
% 7.49/1.28 true2
% 7.49/1.28
% 7.49/1.28 Lemma 26: m1_subset_1(e, k1_zfmisc_1(k2_zfmisc_1(a4, b5))) = true2.
% 7.49/1.28 Proof:
% 7.49/1.28 m1_subset_1(e, k1_zfmisc_1(k2_zfmisc_1(a4, b5)))
% 7.49/1.28 = { by axiom 17 (dt_m2_relset_1) R->L }
% 7.49/1.28 fresh21(m2_relset_1(e, a4, b5), true2, a4, b5, e)
% 7.49/1.28 = { by axiom 4 (t63_relset_2_2) }
% 7.49/1.28 fresh21(true2, true2, a4, b5, e)
% 7.49/1.28 = { by axiom 9 (dt_m2_relset_1) }
% 7.49/1.28 true2
% 7.49/1.28
% 7.49/1.28 Lemma 27: m2_relset_1(k6_relset_1(a4, b5, e), b5, a4) = true2.
% 7.49/1.28 Proof:
% 7.49/1.28 m2_relset_1(k6_relset_1(a4, b5, e), b5, a4)
% 7.49/1.28 = { by axiom 16 (dt_k6_relset_1) R->L }
% 7.49/1.28 fresh29(m1_relset_1(e, a4, b5), true2, a4, b5, e)
% 7.49/1.28 = { by lemma 25 }
% 7.49/1.28 fresh29(true2, true2, a4, b5, e)
% 7.49/1.28 = { by axiom 8 (dt_k6_relset_1) }
% 7.49/1.28 true2
% 7.49/1.28
% 7.49/1.28 Goal 1 (t63_relset_2_3): tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e))) = tuple2(true2, true2).
% 7.49/1.28 Proof:
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), e)))
% 7.49/1.28 = { by axiom 6 (involutiveness_k4_relat_1) R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), fresh4(true2, true2, e))))
% 7.49/1.28 = { by axiom 5 (cc1_relset_1) R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), fresh4(fresh35(true2, true2, e), true2, e))))
% 7.49/1.28 = { by lemma 26 R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), fresh4(fresh35(m1_subset_1(e, k1_zfmisc_1(k2_zfmisc_1(a4, b5))), true2, e), true2, e))))
% 7.49/1.28 = { by axiom 15 (cc1_relset_1) }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), fresh4(v1_relat_1(e), true2, e))))
% 7.49/1.28 = { by axiom 7 (involutiveness_k4_relat_1) }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k4_relat_1(k4_relat_1(e)))))
% 7.49/1.28 = { by axiom 10 (redefinition_k6_relset_1) R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k4_relat_1(fresh16(true2, true2, a4, b5, e)))))
% 7.49/1.28 = { by lemma 25 R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k4_relat_1(fresh16(m1_relset_1(e, a4, b5), true2, a4, b5, e)))))
% 7.49/1.28 = { by axiom 18 (redefinition_k6_relset_1) }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k4_relat_1(k6_relset_1(a4, b5, e)))))
% 7.49/1.28 = { by axiom 10 (redefinition_k6_relset_1) R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), fresh16(true2, true2, b5, a4, k6_relset_1(a4, b5, e)))))
% 7.49/1.28 = { by axiom 11 (redefinition_m2_relset_1) R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), fresh16(fresh12(true2, true2, b5, a4, k6_relset_1(a4, b5, e)), true2, b5, a4, k6_relset_1(a4, b5, e)))))
% 7.49/1.28 = { by lemma 27 R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), fresh16(fresh12(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)))))
% 7.49/1.28 = { by axiom 19 (redefinition_m2_relset_1) }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), fresh16(m1_relset_1(k6_relset_1(a4, b5, e), b5, a4), true2, b5, a4, k6_relset_1(a4, b5, e)))))
% 7.49/1.28 = { by axiom 18 (redefinition_k6_relset_1) }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), r1_tarski(d, k8_relset_2(a4, b5, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(b5, a4, k6_relset_1(a4, b5, e)))))
% 7.49/1.28 = { by axiom 20 (t61_relset_2_1) R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh41(true2, true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)))
% 7.49/1.28 = { by axiom 12 (dt_k8_relset_2) R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh41(fresh24(true2, true2, 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)))
% 7.49/1.28 = { by axiom 3 (t63_relset_2_1) R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh41(fresh24(m1_subset_1(d, k1_zfmisc_1(b5)), true2, 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)))
% 7.49/1.28 = { by axiom 23 (dt_k8_relset_2) R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh41(fresh25(m1_subset_1(k6_relset_1(a4, b5, e), k1_zfmisc_1(k2_zfmisc_1(b5, a4))), true2, 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)))
% 7.49/1.28 = { by axiom 17 (dt_m2_relset_1) R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh41(fresh25(fresh21(m2_relset_1(k6_relset_1(a4, b5, e), b5, a4), true2, b5, a4, k6_relset_1(a4, b5, e)), true2, 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)))
% 7.49/1.28 = { by lemma 27 }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh41(fresh25(fresh21(true2, true2, b5, a4, k6_relset_1(a4, b5, e)), true2, 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)))
% 7.49/1.28 = { by axiom 9 (dt_m2_relset_1) }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh41(fresh25(true2, true2, 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)))
% 7.49/1.28 = { by axiom 13 (dt_k8_relset_2) }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh41(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)))
% 7.49/1.28 = { by axiom 22 (t61_relset_2_1) R->L }
% 7.49/1.28 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh40(true2, true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)))
% 7.49/1.28 = { by axiom 1 (reflexivity_r1_tarski) R->L }
% 7.49/1.29 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh40(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)))
% 7.49/1.29 = { by axiom 24 (t61_relset_2_1) }
% 7.49/1.29 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh42(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)))
% 7.49/1.29 = { by lemma 27 }
% 7.49/1.29 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh42(true2, true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)))
% 7.49/1.29 = { by axiom 21 (t61_relset_2_1) }
% 7.49/1.29 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh43(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)))
% 7.49/1.29 = { by axiom 3 (t63_relset_2_1) }
% 7.49/1.29 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), fresh43(true2, true2, b5, a4, d, k8_relset_2(b5, a4, d, k6_relset_1(a4, b5, e)), k6_relset_1(a4, b5, e)))
% 7.49/1.29 = { by axiom 14 (t61_relset_2_1) }
% 7.49/1.29 tuple2(r1_tarski(c4, k8_relset_2(b5, a4, k8_relset_2(a4, b5, c4, e), k6_relset_1(a4, b5, e))), true2)
% 7.49/1.29 = { by axiom 20 (t61_relset_2_1) R->L }
% 7.49/1.29 tuple2(fresh41(true2, true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2)
% 7.49/1.29 = { by axiom 12 (dt_k8_relset_2) R->L }
% 7.49/1.29 tuple2(fresh41(fresh24(true2, true2, a4, b5, c4, e), true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2)
% 7.49/1.29 = { by axiom 2 (t63_relset_2) R->L }
% 7.49/1.29 tuple2(fresh41(fresh24(m1_subset_1(c4, k1_zfmisc_1(a4)), true2, a4, b5, c4, e), true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2)
% 7.49/1.29 = { by axiom 23 (dt_k8_relset_2) R->L }
% 7.49/1.29 tuple2(fresh41(fresh25(m1_subset_1(e, k1_zfmisc_1(k2_zfmisc_1(a4, b5))), true2, a4, b5, c4, e), true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2)
% 7.49/1.29 = { by lemma 26 }
% 7.49/1.29 tuple2(fresh41(fresh25(true2, true2, a4, b5, c4, e), true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2)
% 7.49/1.29 = { by axiom 13 (dt_k8_relset_2) }
% 7.49/1.29 tuple2(fresh41(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)
% 7.49/1.29 = { by axiom 22 (t61_relset_2_1) R->L }
% 7.49/1.29 tuple2(fresh40(true2, true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2)
% 7.49/1.29 = { by axiom 1 (reflexivity_r1_tarski) R->L }
% 7.49/1.29 tuple2(fresh40(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)
% 7.49/1.29 = { by axiom 24 (t61_relset_2_1) }
% 7.49/1.29 tuple2(fresh42(m2_relset_1(e, a4, b5), true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2)
% 7.49/1.29 = { by axiom 4 (t63_relset_2_2) }
% 7.49/1.29 tuple2(fresh42(true2, true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2)
% 7.49/1.29 = { by axiom 21 (t61_relset_2_1) }
% 7.49/1.29 tuple2(fresh43(m1_subset_1(c4, k1_zfmisc_1(a4)), true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2)
% 7.49/1.29 = { by axiom 2 (t63_relset_2) }
% 7.49/1.29 tuple2(fresh43(true2, true2, a4, b5, c4, k8_relset_2(a4, b5, c4, e), e), true2)
% 7.49/1.29 = { by axiom 14 (t61_relset_2_1) }
% 7.49/1.29 tuple2(true2, true2)
% 7.49/1.29 % SZS output end Proof
% 7.49/1.29
% 7.49/1.29 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------