%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU449+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 : Sat Jun 21 05:28:00 AM UTC 2025
% Result : Theorem 7.35s 7.60s
% Output : Proof 7.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU449+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 07:26:56 EDT 2025
% 0.11/0.33 % CPUTime :
% 7.35/7.60 % SZS status Theorem
% 7.35/7.60 % SZS output start Proof
% 7.35/7.60 tff(r1_tarski_type, type, (
% 7.35/7.60 r1_tarski: ( $i * $i ) > $o)).
% 7.35/7.60 tff(k8_relset_2_type, type, (
% 7.35/7.60 k8_relset_2: ( $i * $i * $i * $i ) > $i)).
% 7.35/7.60 tff(k6_relset_1_type, type, (
% 7.35/7.60 k6_relset_1: ( $i * $i * $i ) > $i)).
% 7.35/7.60 tff(tptp_fun_E_4_type, type, (
% 7.35/7.60 tptp_fun_E_4: $i)).
% 7.35/7.60 tff(tptp_fun_B_1_type, type, (
% 7.35/7.60 tptp_fun_B_1: $i)).
% 7.35/7.60 tff(tptp_fun_A_2_type, type, (
% 7.35/7.60 tptp_fun_A_2: $i)).
% 7.35/7.60 tff(tptp_fun_C_0_type, type, (
% 7.35/7.60 tptp_fun_C_0: $i)).
% 7.35/7.60 tff(k8_setfam_1_type, type, (
% 7.35/7.60 k8_setfam_1: ( $i * $i ) > $i)).
% 7.35/7.60 tff(k4_relset_2_type, type, (
% 7.35/7.60 k4_relset_2: ( $i * $i * $i * $i ) > $i)).
% 7.35/7.60 tff(k3_pua2mss1_type, type, (
% 7.35/7.60 k3_pua2mss1: $i > $i)).
% 7.35/7.60 tff(k6_relset_2_type, type, (
% 7.35/7.60 k6_relset_2: ( $i * $i * $i ) > $i)).
% 7.35/7.60 tff(k1_zfmisc_1_type, type, (
% 7.35/7.60 k1_zfmisc_1: $i > $i)).
% 7.35/7.60 tff(k7_relset_2_type, type, (
% 7.35/7.60 k7_relset_2: ( $i * $i * $i * $i ) > $i)).
% 7.35/7.60 tff(m1_subset_1_type, type, (
% 7.35/7.60 m1_subset_1: ( $i * $i ) > $o)).
% 7.35/7.60 tff(k2_zfmisc_1_type, type, (
% 7.35/7.60 k2_zfmisc_1: ( $i * $i ) > $i)).
% 7.35/7.60 tff(m2_relset_1_type, type, (
% 7.35/7.60 m2_relset_1: ( $i * $i * $i ) > $o)).
% 7.35/7.60 tff(tptp_fun_D_3_type, type, (
% 7.35/7.60 tptp_fun_D_3: $i)).
% 7.35/7.60 tff(k4_relat_1_type, type, (
% 7.35/7.60 k4_relat_1: $i > $i)).
% 7.35/7.60 tff(m1_relset_1_type, type, (
% 7.35/7.60 m1_relset_1: ( $i * $i * $i ) > $o)).
% 7.35/7.60 tff(1,plain,
% 7.35/7.60 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 7.35/7.60 inference(bind,[status(th)],[])).
% 7.35/7.60 tff(2,plain,
% 7.35/7.60 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 7.35/7.60 inference(quant_intro,[status(thm)],[1])).
% 7.35/7.60 tff(3,plain,
% 7.35/7.60 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 7.35/7.60 inference(rewrite,[status(thm)],[])).
% 7.35/7.60 tff(4,plain,
% 7.35/7.60 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 7.35/7.60 inference(bind,[status(th)],[])).
% 7.35/7.60 tff(5,plain,
% 7.35/7.60 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 7.35/7.60 inference(quant_intro,[status(thm)],[4])).
% 7.35/7.60 tff(6,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 7.35/7.60 tff(7,plain,
% 7.35/7.60 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 7.35/7.60 inference(modus_ponens,[status(thm)],[6, 5])).
% 7.35/7.60 tff(8,plain,
% 7.35/7.60 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 7.35/7.60 inference(modus_ponens,[status(thm)],[7, 3])).
% 7.35/7.60 tff(9,plain,(
% 7.35/7.60 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 7.35/7.60 inference(skolemize,[status(sab)],[8])).
% 7.35/7.60 tff(10,plain,
% 7.35/7.60 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 7.35/7.60 inference(modus_ponens,[status(thm)],[9, 2])).
% 7.35/7.60 tff(11,plain,
% 7.35/7.60 ((m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4))) & r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4))) & r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))))))),
% 7.35/7.60 inference(rewrite,[status(thm)],[])).
% 7.35/7.60 tff(12,plain,
% 7.35/7.60 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, k8_relset_2(A, B, C, E), k6_relset_1(A, B, E))) & r1_tarski(D, k8_relset_2(A, B, k8_relset_2(B, A, D, k6_relset_1(A, B, E)), E))))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, k8_relset_2(A, B, C, E), k6_relset_1(A, B, E))) & r1_tarski(D, k8_relset_2(A, B, k8_relset_2(B, A, D, k6_relset_1(A, B, E)), E)))))))),
% 7.35/7.60 inference(rewrite,[status(thm)],[])).
% 7.35/7.60 tff(13,plain,
% 7.35/7.60 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(C, k8_relset_2(B, A, k8_relset_2(A, B, C, E), k6_relset_1(A, B, E))) & r1_tarski(D, k8_relset_2(A, B, k8_relset_2(B, A, D, k6_relset_1(A, B, E)), E))))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, k8_relset_2(A, B, C, E), k6_relset_1(A, B, E))) & r1_tarski(D, k8_relset_2(A, B, k8_relset_2(B, A, D, k6_relset_1(A, B, E)), E)))))))),
% 7.35/7.60 inference(rewrite,[status(thm)],[])).
% 7.35/7.60 tff(14,axiom,(~![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(C, k8_relset_2(B, A, k8_relset_2(A, B, C, E), k6_relset_1(A, B, E))) & r1_tarski(D, k8_relset_2(A, B, k8_relset_2(B, A, D, k6_relset_1(A, B, E)), E))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t63_relset_2')).
% 7.35/7.60 tff(15,plain,
% 7.35/7.60 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, k8_relset_2(A, B, C, E), k6_relset_1(A, B, E))) & r1_tarski(D, k8_relset_2(A, B, k8_relset_2(B, A, D, k6_relset_1(A, B, E)), E))))))),
% 7.35/7.60 inference(modus_ponens,[status(thm)],[14, 13])).
% 7.35/7.60 tff(16,plain,
% 7.35/7.60 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, k8_relset_2(A, B, C, E), k6_relset_1(A, B, E))) & r1_tarski(D, k8_relset_2(A, B, k8_relset_2(B, A, D, k6_relset_1(A, B, E)), E))))))),
% 7.35/7.60 inference(modus_ponens,[status(thm)],[15, 12])).
% 7.35/7.60 tff(17,plain,
% 7.35/7.60 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, k8_relset_2(A, B, C, E), k6_relset_1(A, B, E))) & r1_tarski(D, k8_relset_2(A, B, k8_relset_2(B, A, D, k6_relset_1(A, B, E)), E))))))),
% 7.35/7.60 inference(modus_ponens,[status(thm)],[16, 12])).
% 7.35/7.60 tff(18,plain,
% 7.35/7.60 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, k8_relset_2(A, B, C, E), k6_relset_1(A, B, E))) & r1_tarski(D, k8_relset_2(A, B, k8_relset_2(B, A, D, k6_relset_1(A, B, E)), E))))))),
% 7.35/7.60 inference(modus_ponens,[status(thm)],[17, 12])).
% 7.35/7.60 tff(19,plain,
% 7.35/7.60 (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4))) & r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4)))))),
% 7.35/7.60 inference(modus_ponens,[status(thm)],[18, 11])).
% 7.35/7.60 tff(20,plain,
% 7.35/7.60 (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4))) & r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))))),
% 7.35/7.60 inference(and_elim,[status(thm)],[19])).
% 7.35/7.60 tff(21,plain,
% 7.35/7.60 (m2_relset_1(E!4, A!2, B!1)),
% 7.35/7.61 inference(or_elim,[status(thm)],[20])).
% 7.35/7.61 tff(22,plain,
% 7.35/7.61 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 7.35/7.61 inference(rewrite,[status(thm)],[])).
% 7.35/7.61 tff(23,plain,
% 7.35/7.61 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 7.35/7.61 inference(quant_inst,[status(thm)],[])).
% 7.35/7.61 tff(24,plain,
% 7.35/7.61 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 7.35/7.61 inference(modus_ponens,[status(thm)],[23, 22])).
% 7.35/7.61 tff(25,plain,
% 7.35/7.61 (m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 7.35/7.61 inference(unit_resolution,[status(thm)],[24, 21, 10])).
% 7.35/7.61 tff(26,plain,
% 7.35/7.61 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 7.35/7.61 inference(bind,[status(th)],[])).
% 7.35/7.61 tff(27,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 7.35/7.61 inference(quant_intro,[status(thm)],[26])).
% 7.35/7.61 tff(28,plain,
% 7.35/7.61 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> (~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))), rewrite((~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> (((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))))), rewrite((((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 7.35/7.61 inference(bind,[status(th)],[])).
% 7.35/7.61 tff(29,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 7.35/7.61 inference(quant_intro,[status(thm)],[28])).
% 7.35/7.61 tff(30,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 7.35/7.61 inference(rewrite,[status(thm)],[])).
% 7.35/7.61 tff(31,plain,
% 7.35/7.61 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))))),
% 7.35/7.61 inference(bind,[status(th)],[])).
% 7.35/7.61 tff(32,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 7.35/7.61 inference(quant_intro,[status(thm)],[31])).
% 7.35/7.61 tff(33,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k8_relset_2')).
% 7.35/7.61 tff(34,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 7.35/7.61 inference(modus_ponens,[status(thm)],[33, 32])).
% 7.35/7.61 tff(35,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 7.35/7.61 inference(modus_ponens,[status(thm)],[34, 30])).
% 7.35/7.61 tff(36,plain,(
% 7.35/7.61 ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 7.35/7.61 inference(skolemize,[status(sab)],[35])).
% 7.35/7.61 tff(37,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 7.35/7.61 inference(modus_ponens,[status(thm)],[36, 29])).
% 7.35/7.61 tff(38,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 7.35/7.61 inference(modus_ponens,[status(thm)],[37, 27])).
% 7.35/7.61 tff(39,plain,
% 7.35/7.61 (m1_subset_1(C!0, k1_zfmisc_1(A!2))),
% 7.35/7.61 inference(and_elim,[status(thm)],[19])).
% 7.35/7.61 tff(40,plain,
% 7.35/7.61 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4)))),
% 7.35/7.61 inference(rewrite,[status(thm)],[])).
% 7.35/7.61 tff(41,plain,
% 7.35/7.61 (((k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) <=> ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4)))),
% 7.35/7.61 inference(rewrite,[status(thm)],[])).
% 7.35/7.61 tff(42,plain,
% 7.35/7.61 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4))))),
% 7.35/7.61 inference(monotonicity,[status(thm)],[41])).
% 7.35/7.61 tff(43,plain,
% 7.35/7.61 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4)))),
% 7.35/7.61 inference(transitivity,[status(thm)],[42, 40])).
% 7.35/7.61 tff(44,plain,
% 7.35/7.61 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))),
% 7.35/7.61 inference(quant_inst,[status(thm)],[])).
% 7.35/7.61 tff(45,plain,
% 7.35/7.61 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4))),
% 7.35/7.61 inference(modus_ponens,[status(thm)],[44, 43])).
% 7.35/7.61 tff(46,plain,
% 7.35/7.61 (k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4)),
% 7.35/7.61 inference(unit_resolution,[status(thm)],[45, 39, 38, 25])).
% 7.35/7.61 tff(47,plain,
% 7.35/7.61 (k7_relset_2(A!2, B!1, C!0, E!4) = k8_relset_2(A!2, B!1, C!0, E!4)),
% 7.35/7.61 inference(symmetry,[status(thm)],[46])).
% 7.35/7.61 tff(48,plain,
% 7.35/7.61 (^[A: $i, B: $i, C: $i] : refl(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))))),
% 7.35/7.61 inference(bind,[status(th)],[])).
% 7.35/7.61 tff(49,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))),
% 7.35/7.61 inference(quant_intro,[status(thm)],[48])).
% 7.35/7.61 tff(50,plain,
% 7.35/7.61 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))))),
% 7.35/7.61 inference(bind,[status(th)],[])).
% 7.35/7.61 tff(51,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))),
% 7.35/7.61 inference(quant_intro,[status(thm)],[50])).
% 7.35/7.61 tff(52,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))),
% 7.35/7.61 inference(transitivity,[status(thm)],[51, 49])).
% 7.35/7.61 tff(53,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))),
% 7.35/7.61 inference(rewrite,[status(thm)],[])).
% 7.35/7.61 tff(54,plain,
% 7.35/7.61 (^[A: $i, B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))) <=> ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))) <=> (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))))),
% 7.35/7.61 inference(bind,[status(th)],[])).
% 7.35/7.61 tff(55,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))),
% 7.35/7.61 inference(quant_intro,[status(thm)],[54])).
% 7.35/7.61 tff(56,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_relset_2')).
% 7.35/7.61 tff(57,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))),
% 7.35/7.61 inference(modus_ponens,[status(thm)],[56, 55])).
% 7.35/7.61 tff(58,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))),
% 7.35/7.61 inference(modus_ponens,[status(thm)],[57, 53])).
% 7.35/7.61 tff(59,plain,(
% 7.35/7.61 ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))),
% 7.35/7.61 inference(skolemize,[status(sab)],[58])).
% 7.35/7.61 tff(60,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))),
% 7.35/7.61 inference(modus_ponens,[status(thm)],[59, 52])).
% 7.35/7.61 tff(61,plain,
% 7.35/7.61 (((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, D) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, D), k3_pua2mss1(C!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, D) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, D), k3_pua2mss1(C!0))))))),
% 7.35/7.61 inference(rewrite,[status(thm)],[])).
% 7.35/7.61 tff(62,plain,
% 7.35/7.61 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, D) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, D), k3_pua2mss1(C!0))))))),
% 7.35/7.61 inference(quant_inst,[status(thm)],[])).
% 7.35/7.61 tff(63,plain,
% 7.35/7.61 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k7_relset_2(A, B, C, D) = k8_setfam_1(B, k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, D), k3_pua2mss1(C))))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, D) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, D), k3_pua2mss1(C!0)))))),
% 7.35/7.61 inference(modus_ponens,[status(thm)],[62, 61])).
% 7.35/7.61 tff(64,plain,
% 7.35/7.61 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, D) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, D), k3_pua2mss1(C!0)))))),
% 7.35/7.61 inference(unit_resolution,[status(thm)],[63, 39, 60])).
% 7.35/7.61 tff(65,plain,
% 7.35/7.61 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, D) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, D), k3_pua2mss1(C!0)))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, E!4) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, D) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, D), k3_pua2mss1(C!0)))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, E!4) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)))))),
% 7.35/7.61 inference(rewrite,[status(thm)],[])).
% 7.35/7.61 tff(66,plain,
% 7.35/7.61 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, D) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, D), k3_pua2mss1(C!0)))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, E!4) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)))))),
% 7.35/7.61 inference(quant_inst,[status(thm)],[])).
% 7.35/7.61 tff(67,plain,
% 7.35/7.61 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, D) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, D), k3_pua2mss1(C!0)))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, C!0, E!4) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))))),
% 7.35/7.61 inference(modus_ponens,[status(thm)],[66, 65])).
% 7.35/7.61 tff(68,plain,
% 7.35/7.61 (k7_relset_2(A!2, B!1, C!0, E!4) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)))),
% 7.35/7.61 inference(unit_resolution,[status(thm)],[67, 25, 64])).
% 7.35/7.61 tff(69,plain,
% 7.35/7.61 (k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))) = k7_relset_2(A!2, B!1, C!0, E!4)),
% 7.35/7.61 inference(symmetry,[status(thm)],[68])).
% 7.35/7.61 tff(70,plain,
% 7.35/7.61 (k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))) = k8_relset_2(A!2, B!1, C!0, E!4)),
% 7.35/7.61 inference(transitivity,[status(thm)],[69, 47])).
% 7.35/7.61 tff(71,plain,
% 7.35/7.61 (k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E!4)) = k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4))),
% 7.35/7.61 inference(monotonicity,[status(thm)],[70])).
% 7.35/7.61 tff(72,plain,
% 7.35/7.61 (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4)))),
% 7.35/7.61 inference(monotonicity,[status(thm)],[71])).
% 7.35/7.61 tff(73,plain,
% 7.35/7.61 (k8_relset_2(A!2, B!1, C!0, E!4) = k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)))),
% 7.35/7.61 inference(transitivity,[status(thm)],[46, 68])).
% 7.35/7.61 tff(74,plain,
% 7.35/7.61 (m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1)) <=> m1_subset_1(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k1_zfmisc_1(B!1))),
% 7.35/7.61 inference(monotonicity,[status(thm)],[73])).
% 7.35/7.61 tff(75,plain,
% 7.35/7.61 (^[A: $i, B: $i, C: $i, D: $i] : refl((m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 7.35/7.61 inference(bind,[status(th)],[])).
% 7.35/7.61 tff(76,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 7.35/7.61 inference(quant_intro,[status(thm)],[75])).
% 7.35/7.61 tff(77,plain,
% 7.35/7.61 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> (~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))), rewrite((~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> (((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))))), rewrite((((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 7.35/7.61 inference(bind,[status(th)],[])).
% 7.35/7.61 tff(78,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 7.35/7.61 inference(quant_intro,[status(thm)],[77])).
% 7.35/7.61 tff(79,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 7.35/7.61 inference(rewrite,[status(thm)],[])).
% 7.35/7.61 tff(80,plain,
% 7.35/7.61 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))))),
% 7.35/7.61 inference(bind,[status(th)],[])).
% 7.35/7.61 tff(81,plain,
% 7.35/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 7.35/7.61 inference(quant_intro,[status(thm)],[80])).
% 7.35/7.61 tff(82,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_relset_2')).
% 7.46/7.61 tff(83,plain,
% 7.46/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 7.46/7.61 inference(modus_ponens,[status(thm)],[82, 81])).
% 7.46/7.61 tff(84,plain,
% 7.46/7.61 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 7.46/7.61 inference(modus_ponens,[status(thm)],[83, 79])).
% 7.46/7.61 tff(85,plain,(
% 7.46/7.61 ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 7.46/7.61 inference(skolemize,[status(sab)],[84])).
% 7.46/7.61 tff(86,plain,
% 7.46/7.61 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 7.46/7.61 inference(modus_ponens,[status(thm)],[85, 78])).
% 7.46/7.61 tff(87,plain,
% 7.46/7.61 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 7.46/7.61 inference(modus_ponens,[status(thm)],[86, 76])).
% 7.46/7.61 tff(88,plain,
% 7.46/7.61 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1)))),
% 7.46/7.61 inference(rewrite,[status(thm)],[])).
% 7.46/7.61 tff(89,plain,
% 7.46/7.61 ((m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) <=> ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1)))),
% 7.46/7.61 inference(rewrite,[status(thm)],[])).
% 7.46/7.61 tff(90,plain,
% 7.46/7.61 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))))),
% 7.46/7.61 inference(monotonicity,[status(thm)],[89])).
% 7.46/7.61 tff(91,plain,
% 7.46/7.61 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1)))),
% 7.46/7.61 inference(transitivity,[status(thm)],[90, 88])).
% 7.46/7.61 tff(92,plain,
% 7.46/7.61 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))),
% 7.46/7.61 inference(quant_inst,[status(thm)],[])).
% 7.46/7.61 tff(93,plain,
% 7.46/7.61 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))),
% 7.46/7.61 inference(modus_ponens,[status(thm)],[92, 91])).
% 7.46/7.61 tff(94,plain,
% 7.46/7.61 (m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))),
% 7.46/7.61 inference(unit_resolution,[status(thm)],[93, 39, 87, 25])).
% 7.46/7.61 tff(95,plain,
% 7.46/7.61 (m1_subset_1(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k1_zfmisc_1(B!1))),
% 7.46/7.61 inference(modus_ponens,[status(thm)],[94, 74])).
% 7.46/7.61 tff(96,plain,
% 7.46/7.61 (^[A: $i, B: $i, C: $i] : refl(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))))),
% 7.46/7.61 inference(bind,[status(th)],[])).
% 7.46/7.61 tff(97,plain,
% 7.46/7.61 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))),
% 7.46/7.61 inference(quant_intro,[status(thm)],[96])).
% 7.46/7.61 tff(98,plain,
% 7.46/7.61 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))))),
% 7.46/7.61 inference(bind,[status(th)],[])).
% 7.46/7.61 tff(99,plain,
% 7.46/7.61 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))),
% 7.46/7.61 inference(quant_intro,[status(thm)],[98])).
% 7.46/7.61 tff(100,plain,
% 7.46/7.61 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))),
% 7.46/7.61 inference(transitivity,[status(thm)],[99, 97])).
% 7.46/7.61 tff(101,plain,
% 7.46/7.61 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))),
% 7.46/7.62 inference(rewrite,[status(thm)],[])).
% 7.46/7.62 tff(102,plain,
% 7.46/7.62 (^[A: $i, B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : rewrite((m2_relset_1(E, A, B) => (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))) <=> ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))), (![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))) <=> ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))), ((m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))) <=> (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))), rewrite((m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))), ((m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))) <=> ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))) <=> (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))))),
% 7.46/7.62 inference(bind,[status(th)],[])).
% 7.46/7.62 tff(103,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))),
% 7.46/7.62 inference(quant_intro,[status(thm)],[102])).
% 7.46/7.62 tff(104,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t61_relset_2')).
% 7.46/7.62 tff(105,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[104, 103])).
% 7.46/7.62 tff(106,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[105, 101])).
% 7.46/7.62 tff(107,plain,(
% 7.46/7.62 ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))),
% 7.46/7.62 inference(skolemize,[status(sab)],[106])).
% 7.46/7.62 tff(108,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[107, 100])).
% 7.46/7.62 tff(109,plain,
% 7.46/7.62 (((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, C!0, E))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, C!0, E))))))),
% 7.46/7.62 inference(rewrite,[status(thm)],[])).
% 7.46/7.62 tff(110,plain,
% 7.46/7.62 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, C!0, E))))))),
% 7.46/7.62 inference(quant_inst,[status(thm)],[])).
% 7.46/7.62 tff(111,plain,
% 7.46/7.62 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, C!0, E)))))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[110, 109])).
% 7.46/7.62 tff(112,plain,
% 7.46/7.62 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, C!0, E)))))),
% 7.46/7.62 inference(unit_resolution,[status(thm)],[111, 39, 108])).
% 7.46/7.62 tff(113,plain,
% 7.46/7.62 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, C!0, E)))))) | ((~m1_subset_1(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, C!0, E)))))) | (~m1_subset_1(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E)))))),
% 7.46/7.62 inference(rewrite,[status(thm)],[])).
% 7.46/7.62 tff(114,plain,
% 7.46/7.62 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, C!0, E)))))) | ((~m1_subset_1(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E)))))),
% 7.46/7.62 inference(quant_inst,[status(thm)],[])).
% 7.46/7.62 tff(115,plain,
% 7.46/7.62 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, C!0, E)))))) | (~m1_subset_1(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E))))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[114, 113])).
% 7.46/7.62 tff(116,plain,
% 7.46/7.62 (![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E))))),
% 7.46/7.62 inference(unit_resolution,[status(thm)],[115, 112, 95])).
% 7.46/7.62 tff(117,plain,
% 7.46/7.62 (((~![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E))))) | ((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E!4))))) <=> ((~![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E))))) | (~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E!4))))),
% 7.46/7.62 inference(rewrite,[status(thm)],[])).
% 7.46/7.62 tff(118,plain,
% 7.46/7.62 ((~![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E))))) | ((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E!4))))),
% 7.46/7.62 inference(quant_inst,[status(thm)],[])).
% 7.46/7.62 tff(119,plain,
% 7.46/7.62 ((~![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E))))) | (~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E!4)))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[118, 117])).
% 7.46/7.62 tff(120,plain,
% 7.46/7.62 (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E!4))),
% 7.46/7.62 inference(unit_resolution,[status(thm)],[119, 21, 116])).
% 7.46/7.62 tff(121,plain,
% 7.46/7.62 (r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E!4))),
% 7.46/7.62 inference(monotonicity,[status(thm)],[70])).
% 7.46/7.62 tff(122,plain,
% 7.46/7.62 (^[A: $i] : refl(r1_tarski(A, A) <=> r1_tarski(A, A))),
% 7.46/7.62 inference(bind,[status(th)],[])).
% 7.46/7.62 tff(123,plain,
% 7.46/7.62 (![A: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 7.46/7.62 inference(quant_intro,[status(thm)],[122])).
% 7.46/7.62 tff(124,plain,
% 7.46/7.62 (![A: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 7.46/7.62 inference(rewrite,[status(thm)],[])).
% 7.46/7.62 tff(125,plain,
% 7.46/7.62 (![A: $i, B: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 7.46/7.62 inference(elim_unused_vars,[status(thm)],[])).
% 7.46/7.62 tff(126,axiom,(![A: $i, B: $i] : r1_tarski(A, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 7.46/7.62 tff(127,plain,
% 7.46/7.62 (![A: $i] : r1_tarski(A, A)),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[126, 125])).
% 7.46/7.62 tff(128,plain,
% 7.46/7.62 (![A: $i] : r1_tarski(A, A)),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[127, 124])).
% 7.46/7.62 tff(129,plain,(
% 7.46/7.62 ![A: $i] : r1_tarski(A, A)),
% 7.46/7.62 inference(skolemize,[status(sab)],[128])).
% 7.46/7.62 tff(130,plain,
% 7.46/7.62 (![A: $i] : r1_tarski(A, A)),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[129, 123])).
% 7.46/7.62 tff(131,plain,
% 7.46/7.62 ((~![A: $i] : r1_tarski(A, A)) | r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))))),
% 7.46/7.62 inference(quant_inst,[status(thm)],[])).
% 7.46/7.62 tff(132,plain,
% 7.46/7.62 (r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))))),
% 7.46/7.62 inference(unit_resolution,[status(thm)],[131, 130])).
% 7.46/7.62 tff(133,plain,
% 7.46/7.62 (r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E!4))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[132, 121])).
% 7.46/7.62 tff(134,plain,
% 7.46/7.62 ((~(r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E!4)))) | r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E!4))) | (~r1_tarski(k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k8_relset_2(A!2, B!1, C!0, E!4)))),
% 7.46/7.62 inference(tautology,[status(thm)],[])).
% 7.46/7.62 tff(135,plain,
% 7.46/7.62 (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_setfam_1(B!1, k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))), k6_relset_1(A!2, B!1, E!4)))),
% 7.46/7.62 inference(unit_resolution,[status(thm)],[134, 133, 120])).
% 7.46/7.62 tff(136,plain,
% 7.46/7.62 (r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4)))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[135, 72])).
% 7.46/7.62 tff(137,plain,
% 7.46/7.62 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 7.46/7.62 inference(bind,[status(th)],[])).
% 7.46/7.62 tff(138,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 7.46/7.62 inference(quant_intro,[status(thm)],[137])).
% 7.46/7.62 tff(139,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 7.46/7.62 inference(rewrite,[status(thm)],[])).
% 7.46/7.62 tff(140,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 7.46/7.62 tff(141,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[140, 139])).
% 7.46/7.62 tff(142,plain,(
% 7.46/7.62 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 7.46/7.62 inference(skolemize,[status(sab)],[141])).
% 7.46/7.62 tff(143,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[142, 138])).
% 7.46/7.62 tff(144,plain,
% 7.46/7.62 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1))),
% 7.46/7.62 inference(quant_inst,[status(thm)],[])).
% 7.46/7.62 tff(145,plain,
% 7.46/7.62 (m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1)),
% 7.46/7.62 inference(unit_resolution,[status(thm)],[144, 143])).
% 7.46/7.62 tff(146,plain,
% 7.46/7.62 ((~(m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1))) | (~m2_relset_1(E!4, A!2, B!1)) | m1_relset_1(E!4, A!2, B!1)),
% 7.46/7.62 inference(tautology,[status(thm)],[])).
% 7.46/7.62 tff(147,plain,
% 7.46/7.62 ((~(m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1))) | m1_relset_1(E!4, A!2, B!1)),
% 7.46/7.62 inference(unit_resolution,[status(thm)],[146, 21])).
% 7.46/7.62 tff(148,plain,
% 7.46/7.62 (m1_relset_1(E!4, A!2, B!1)),
% 7.46/7.62 inference(unit_resolution,[status(thm)],[147, 145])).
% 7.46/7.62 tff(149,plain,
% 7.46/7.62 (^[A: $i, B: $i, C: $i] : refl(((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))))),
% 7.46/7.62 inference(bind,[status(th)],[])).
% 7.46/7.62 tff(150,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 7.46/7.62 inference(quant_intro,[status(thm)],[149])).
% 7.46/7.62 tff(151,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 7.46/7.62 inference(rewrite,[status(thm)],[])).
% 7.46/7.62 tff(152,plain,
% 7.46/7.62 (^[A: $i, B: $i, C: $i] : rewrite((m1_relset_1(C, A, B) => (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))))),
% 7.46/7.62 inference(bind,[status(th)],[])).
% 7.46/7.62 tff(153,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 7.46/7.62 inference(quant_intro,[status(thm)],[152])).
% 7.46/7.62 tff(154,axiom,(![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => (k6_relset_1(A, B, C) = k4_relat_1(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k6_relset_1')).
% 7.46/7.62 tff(155,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[154, 153])).
% 7.46/7.62 tff(156,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[155, 151])).
% 7.46/7.62 tff(157,plain,(
% 7.46/7.62 ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 7.46/7.62 inference(skolemize,[status(sab)],[156])).
% 7.46/7.62 tff(158,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[157, 150])).
% 7.46/7.62 tff(159,plain,
% 7.46/7.62 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | ((~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | (~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)))),
% 7.46/7.62 inference(rewrite,[status(thm)],[])).
% 7.46/7.62 tff(160,plain,
% 7.46/7.62 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | ((~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)))),
% 7.46/7.62 inference(quant_inst,[status(thm)],[])).
% 7.46/7.62 tff(161,plain,
% 7.46/7.62 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | (~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[160, 159])).
% 7.46/7.62 tff(162,plain,
% 7.46/7.62 (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)),
% 7.46/7.62 inference(unit_resolution,[status(thm)],[161, 158, 148])).
% 7.46/7.62 tff(163,plain,
% 7.46/7.62 (k4_relat_1(E!4) = k6_relset_1(A!2, B!1, E!4)),
% 7.46/7.62 inference(symmetry,[status(thm)],[162])).
% 7.46/7.62 tff(164,plain,
% 7.46/7.62 (k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)) = k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4))),
% 7.46/7.62 inference(monotonicity,[status(thm)],[163])).
% 7.46/7.62 tff(165,plain,
% 7.46/7.62 (k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)) = k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4))),
% 7.46/7.62 inference(symmetry,[status(thm)],[164])).
% 7.46/7.62 tff(166,plain,
% 7.46/7.62 (m1_subset_1(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k1_zfmisc_1(A!2)) <=> m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2))),
% 7.46/7.62 inference(monotonicity,[status(thm)],[165])).
% 7.46/7.62 tff(167,plain,
% 7.46/7.62 (m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2)) <=> m1_subset_1(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k1_zfmisc_1(A!2))),
% 7.46/7.62 inference(symmetry,[status(thm)],[166])).
% 7.46/7.62 tff(168,plain,
% 7.46/7.62 (m2_relset_1(k4_relat_1(E!4), B!1, A!2) <=> m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 7.46/7.62 inference(monotonicity,[status(thm)],[163])).
% 7.46/7.62 tff(169,plain,
% 7.46/7.62 (m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2) <=> m2_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 7.46/7.62 inference(symmetry,[status(thm)],[168])).
% 7.46/7.62 tff(170,plain,
% 7.46/7.62 (^[A: $i, B: $i, C: $i] : refl(((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)))),
% 7.46/7.62 inference(bind,[status(th)],[])).
% 7.46/7.62 tff(171,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 7.46/7.62 inference(quant_intro,[status(thm)],[170])).
% 7.46/7.62 tff(172,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 7.46/7.62 inference(rewrite,[status(thm)],[])).
% 7.46/7.62 tff(173,plain,
% 7.46/7.62 (^[A: $i, B: $i, C: $i] : rewrite((m1_relset_1(C, A, B) => m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)))),
% 7.46/7.62 inference(bind,[status(th)],[])).
% 7.46/7.62 tff(174,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 7.46/7.62 inference(quant_intro,[status(thm)],[173])).
% 7.46/7.62 tff(175,axiom,(![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => m2_relset_1(k6_relset_1(A, B, C), B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_relset_1')).
% 7.46/7.62 tff(176,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[175, 174])).
% 7.46/7.62 tff(177,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[176, 172])).
% 7.46/7.62 tff(178,plain,(
% 7.46/7.62 ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 7.46/7.62 inference(skolemize,[status(sab)],[177])).
% 7.46/7.62 tff(179,plain,
% 7.46/7.62 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[178, 171])).
% 7.46/7.62 tff(180,plain,
% 7.46/7.62 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | ((~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | (~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2))),
% 7.46/7.62 inference(rewrite,[status(thm)],[])).
% 7.46/7.62 tff(181,plain,
% 7.46/7.62 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | ((~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2))),
% 7.46/7.62 inference(quant_inst,[status(thm)],[])).
% 7.46/7.62 tff(182,plain,
% 7.46/7.62 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | (~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 7.46/7.62 inference(modus_ponens,[status(thm)],[181, 180])).
% 7.46/7.62 tff(183,plain,
% 7.46/7.62 (m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 7.46/7.63 inference(unit_resolution,[status(thm)],[182, 179, 148])).
% 7.46/7.63 tff(184,plain,
% 7.46/7.63 (m2_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 7.46/7.63 inference(modus_ponens,[status(thm)],[183, 169])).
% 7.46/7.63 tff(185,plain,
% 7.46/7.63 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(k4_relat_1(E!4), B!1, A!2)) | m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(k4_relat_1(E!4), B!1, A!2)) | m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2))))),
% 7.46/7.63 inference(rewrite,[status(thm)],[])).
% 7.46/7.63 tff(186,plain,
% 7.46/7.63 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(k4_relat_1(E!4), B!1, A!2)) | m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2))))),
% 7.46/7.63 inference(quant_inst,[status(thm)],[])).
% 7.46/7.63 tff(187,plain,
% 7.46/7.63 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(k4_relat_1(E!4), B!1, A!2)) | m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))),
% 7.46/7.63 inference(modus_ponens,[status(thm)],[186, 185])).
% 7.46/7.63 tff(188,plain,
% 7.46/7.63 ((~m2_relset_1(k4_relat_1(E!4), B!1, A!2)) | m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))),
% 7.46/7.63 inference(unit_resolution,[status(thm)],[187, 10])).
% 7.46/7.63 tff(189,plain,
% 7.46/7.63 (m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))),
% 7.46/7.63 inference(unit_resolution,[status(thm)],[188, 184])).
% 7.46/7.63 tff(190,plain,
% 7.46/7.63 (m1_subset_1(D!3, k1_zfmisc_1(B!1))),
% 7.46/7.63 inference(and_elim,[status(thm)],[19])).
% 7.46/7.63 tff(191,plain,
% 7.46/7.63 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (~m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))) | m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (~m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))) | m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2)))),
% 7.46/7.63 inference(rewrite,[status(thm)],[])).
% 7.46/7.63 tff(192,plain,
% 7.46/7.63 ((m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2)) | (~m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1)))) <=> ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (~m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))) | m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2)))),
% 7.46/7.63 inference(rewrite,[status(thm)],[])).
% 7.46/7.63 tff(193,plain,
% 7.46/7.63 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2)) | (~m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (~m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))) | m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2))))),
% 7.46/7.63 inference(monotonicity,[status(thm)],[192])).
% 7.46/7.63 tff(194,plain,
% 7.46/7.63 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2)) | (~m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (~m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))) | m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2)))),
% 7.46/7.63 inference(transitivity,[status(thm)],[193, 191])).
% 7.46/7.63 tff(195,plain,
% 7.46/7.63 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2)) | (~m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))))),
% 7.46/7.63 inference(quant_inst,[status(thm)],[])).
% 7.46/7.63 tff(196,plain,
% 7.46/7.63 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (~m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))) | m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2))),
% 7.46/7.63 inference(modus_ponens,[status(thm)],[195, 194])).
% 7.46/7.63 tff(197,plain,
% 7.46/7.63 ((~m1_subset_1(k4_relat_1(E!4), k1_zfmisc_1(k2_zfmisc_1(B!1, A!2)))) | m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2))),
% 7.46/7.63 inference(unit_resolution,[status(thm)],[196, 190, 87])).
% 7.46/7.63 tff(198,plain,
% 7.46/7.63 (m1_subset_1(k8_relset_2(B!1, A!2, D!3, k4_relat_1(E!4)), k1_zfmisc_1(A!2))),
% 7.46/7.63 inference(unit_resolution,[status(thm)],[197, 189])).
% 7.46/7.63 tff(199,plain,
% 7.46/7.63 (m1_subset_1(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k1_zfmisc_1(A!2))),
% 7.46/7.63 inference(modus_ponens,[status(thm)],[198, 167])).
% 7.46/7.63 tff(200,plain,
% 7.46/7.63 (((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))) | ((~m1_subset_1(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))) | (~m1_subset_1(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E))))))),
% 7.46/7.63 inference(rewrite,[status(thm)],[])).
% 7.46/7.63 tff(201,plain,
% 7.46/7.63 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))) | ((~m1_subset_1(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E))))))),
% 7.46/7.63 inference(quant_inst,[status(thm)],[])).
% 7.46/7.63 tff(202,plain,
% 7.46/7.63 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(C, k8_relset_2(B, A, D, k6_relset_1(A, B, E))) <=> r1_tarski(D, k8_relset_2(A, B, C, E))))))) | (~m1_subset_1(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E)))))),
% 7.46/7.63 inference(modus_ponens,[status(thm)],[201, 200])).
% 7.46/7.63 tff(203,plain,
% 7.46/7.63 ((~m1_subset_1(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E)))))),
% 7.46/7.63 inference(unit_resolution,[status(thm)],[202, 108])).
% 7.46/7.63 tff(204,plain,
% 7.46/7.63 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E)))))),
% 7.46/7.63 inference(unit_resolution,[status(thm)],[203, 199])).
% 7.46/7.63 tff(205,plain,
% 7.46/7.63 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E)))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E)))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E)))))),
% 7.46/7.63 inference(rewrite,[status(thm)],[])).
% 7.46/7.63 tff(206,plain,
% 7.46/7.63 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E)))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E)))))),
% 7.46/7.63 inference(quant_inst,[status(thm)],[])).
% 7.46/7.63 tff(207,plain,
% 7.46/7.63 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E)))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E))))),
% 7.46/7.63 inference(modus_ponens,[status(thm)],[206, 205])).
% 7.46/7.63 tff(208,plain,
% 7.46/7.63 (![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E))))),
% 7.46/7.63 inference(unit_resolution,[status(thm)],[207, 190, 204])).
% 7.46/7.63 tff(209,plain,
% 7.46/7.63 (((~![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E))))) | ((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))))) <=> ((~![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E))))) | (~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))))),
% 7.46/7.63 inference(rewrite,[status(thm)],[])).
% 7.46/7.63 tff(210,plain,
% 7.46/7.63 ((~![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E))))) | ((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))))),
% 7.46/7.63 inference(quant_inst,[status(thm)],[])).
% 7.46/7.63 tff(211,plain,
% 7.46/7.63 ((~![E: $i] : ((~m2_relset_1(E, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E))))) | (~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4)))),
% 7.46/7.63 inference(modus_ponens,[status(thm)],[210, 209])).
% 7.46/7.63 tff(212,plain,
% 7.46/7.63 (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))),
% 7.46/7.63 inference(unit_resolution,[status(thm)],[211, 21, 208])).
% 7.46/7.63 tff(213,plain,
% 7.46/7.63 ((~![A: $i] : r1_tarski(A, A)) | r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)))),
% 7.46/7.63 inference(quant_inst,[status(thm)],[])).
% 7.46/7.63 tff(214,plain,
% 7.46/7.63 (r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)))),
% 7.46/7.63 inference(unit_resolution,[status(thm)],[213, 130])).
% 7.46/7.63 tff(215,plain,
% 7.46/7.63 ((~(r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4)))) | (~r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)))) | r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))),
% 7.46/7.66 inference(tautology,[status(thm)],[])).
% 7.46/7.66 tff(216,plain,
% 7.46/7.66 ((~(r1_tarski(k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4))) <=> r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4)))) | r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))),
% 7.46/7.66 inference(unit_resolution,[status(thm)],[215, 214])).
% 7.46/7.66 tff(217,plain,
% 7.46/7.66 (r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))),
% 7.46/7.66 inference(unit_resolution,[status(thm)],[216, 212])).
% 7.46/7.66 tff(218,plain,
% 7.46/7.66 ((~(~((~r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4)))) | (~r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4)))))) <=> ((~r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4)))) | (~r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))))),
% 7.46/7.66 inference(rewrite,[status(thm)],[])).
% 7.46/7.66 tff(219,plain,
% 7.46/7.66 ((r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4))) & r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))) <=> (~((~r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4)))) | (~r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4)))))),
% 7.46/7.66 inference(rewrite,[status(thm)],[])).
% 7.46/7.66 tff(220,plain,
% 7.46/7.66 ((~(r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4))) & r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4)))) <=> (~(~((~r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4)))) | (~r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))))))),
% 7.46/7.66 inference(monotonicity,[status(thm)],[219])).
% 7.46/7.66 tff(221,plain,
% 7.46/7.66 ((~(r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4))) & r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4)))) <=> ((~r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4)))) | (~r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4))))),
% 7.46/7.66 inference(transitivity,[status(thm)],[220, 218])).
% 7.46/7.66 tff(222,plain,
% 7.46/7.66 (~(r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4))) & r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4)))),
% 7.46/7.66 inference(or_elim,[status(thm)],[20])).
% 7.46/7.66 tff(223,plain,
% 7.46/7.66 ((~r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4)))) | (~r1_tarski(D!3, k8_relset_2(A!2, B!1, k8_relset_2(B!1, A!2, D!3, k6_relset_1(A!2, B!1, E!4)), E!4)))),
% 7.46/7.66 inference(modus_ponens,[status(thm)],[222, 221])).
% 7.46/7.66 tff(224,plain,
% 7.46/7.66 (~r1_tarski(C!0, k8_relset_2(B!1, A!2, k8_relset_2(A!2, B!1, C!0, E!4), k6_relset_1(A!2, B!1, E!4)))),
% 7.46/7.66 inference(unit_resolution,[status(thm)],[223, 217])).
% 7.46/7.66 tff(225,plain,
% 7.46/7.66 ($false),
% 7.46/7.66 inference(unit_resolution,[status(thm)],[224, 136])).
% 7.46/7.66 % SZS output end Proof
% 7.46/7.66 % E exiting
%------------------------------------------------------------------------------