%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU428+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:27:54 AM UTC 2025
% Result : Theorem 4.26s 4.44s
% Output : Proof 4.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU428+1 : TPTP v9.0.0. Released v3.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:15:22 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.26/4.44 % SZS status Theorem
% 4.26/4.44 % SZS output start Proof
% 4.26/4.44 tff(k4_subset_1_type, type, (
% 4.26/4.44 k4_subset_1: ( $i * $i * $i ) > $i)).
% 4.26/4.44 tff(k9_relat_1_type, type, (
% 4.26/4.44 k9_relat_1: ( $i * $i ) > $i)).
% 4.26/4.44 tff(k3_pua2mss1_type, type, (
% 4.26/4.44 k3_pua2mss1: $i > $i)).
% 4.26/4.44 tff(tptp_fun_C_0_type, type, (
% 4.26/4.44 tptp_fun_C_0: $i)).
% 4.26/4.44 tff(k5_relset_2_type, type, (
% 4.26/4.44 k5_relset_2: ( $i * $i ) > $i)).
% 4.26/4.44 tff(tptp_fun_E_4_type, type, (
% 4.26/4.44 tptp_fun_E_4: $i)).
% 4.26/4.44 tff(tptp_fun_A_2_type, type, (
% 4.26/4.44 tptp_fun_A_2: $i)).
% 4.26/4.44 tff(tptp_fun_D_3_type, type, (
% 4.26/4.44 tptp_fun_D_3: $i)).
% 4.26/4.44 tff(k1_zfmisc_1_type, type, (
% 4.26/4.44 k1_zfmisc_1: $i > $i)).
% 4.26/4.44 tff(tptp_fun_B_1_type, type, (
% 4.26/4.44 tptp_fun_B_1: $i)).
% 4.26/4.44 tff(k4_relset_2_type, type, (
% 4.26/4.44 k4_relset_2: ( $i * $i * $i * $i ) > $i)).
% 4.26/4.44 tff(k2_xboole_0_type, type, (
% 4.26/4.44 k2_xboole_0: ( $i * $i ) > $i)).
% 4.26/4.44 tff(k6_relset_2_type, type, (
% 4.26/4.44 k6_relset_2: ( $i * $i * $i ) > $i)).
% 4.26/4.44 tff(m1_subset_1_type, type, (
% 4.26/4.44 m1_subset_1: ( $i * $i ) > $o)).
% 4.26/4.44 tff(k2_zfmisc_1_type, type, (
% 4.26/4.44 k2_zfmisc_1: ( $i * $i ) > $i)).
% 4.26/4.44 tff(m2_relset_1_type, type, (
% 4.26/4.44 m2_relset_1: ( $i * $i * $i ) > $o)).
% 4.26/4.45 tff(k5_subset_1_type, type, (
% 4.26/4.45 k5_subset_1: ( $i * $i * $i ) > $i)).
% 4.26/4.45 tff(k8_relset_2_type, type, (
% 4.26/4.45 k8_relset_2: ( $i * $i * $i * $i ) > $i)).
% 4.26/4.45 tff(v1_funct_2_type, type, (
% 4.26/4.45 v1_funct_2: ( $i * $i * $i ) > $o)).
% 4.26/4.45 tff(v1_funct_1_type, type, (
% 4.26/4.45 v1_funct_1: $i > $o)).
% 4.26/4.45 tff(v1_relat_1_type, type, (
% 4.26/4.45 v1_relat_1: $i > $o)).
% 4.26/4.45 tff(k8_setfam_1_type, type, (
% 4.26/4.45 k8_setfam_1: ( $i * $i ) > $i)).
% 4.26/4.45 tff(k7_relset_2_type, type, (
% 4.26/4.45 k7_relset_2: ( $i * $i * $i * $i ) > $i)).
% 4.26/4.45 tff(1,plain,
% 4.26/4.45 (^[A: $i, B: $i, C: $i] : refl(((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C))))),
% 4.26/4.45 inference(bind,[status(th)],[])).
% 4.26/4.45 tff(2,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C)))),
% 4.26/4.45 inference(quant_intro,[status(thm)],[1])).
% 4.26/4.45 tff(3,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C)))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(4,plain,
% 4.26/4.45 (^[A: $i, B: $i, C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (k6_relset_2(A, B, C) = k5_relset_2(B, C))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C))))),
% 4.26/4.45 inference(bind,[status(th)],[])).
% 4.26/4.45 tff(5,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (k6_relset_2(A, B, C) = k5_relset_2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C)))),
% 4.26/4.45 inference(quant_intro,[status(thm)],[4])).
% 4.26/4.45 tff(6,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (k6_relset_2(A, B, C) = k5_relset_2(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k6_relset_2')).
% 4.26/4.45 tff(7,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C)))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[6, 5])).
% 4.26/4.45 tff(8,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C)))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[7, 3])).
% 4.26/4.45 tff(9,plain,(
% 4.26/4.45 ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C)))),
% 4.26/4.45 inference(skolemize,[status(sab)],[8])).
% 4.26/4.45 tff(10,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C)))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[9, 2])).
% 4.26/4.45 tff(11,plain,
% 4.26/4.45 ((m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(D!3, 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, k4_subset_1(A!2, C!0, D!3), E!4) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4))))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, 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, k4_subset_1(A!2, C!0, D!3), E!4) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4))))))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(12,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k5_subset_1(B, k8_relset_2(A, B, C, E), k8_relset_2(A, B, D, E))))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k5_subset_1(B, k8_relset_2(A, B, C, E), k8_relset_2(A, B, D, E)))))))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(13,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(A)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k5_subset_1(B, k8_relset_2(A, B, C, E), k8_relset_2(A, B, D, E))))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k5_subset_1(B, k8_relset_2(A, B, C, E), k8_relset_2(A, B, D, E)))))))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 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(A)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k5_subset_1(B, k8_relset_2(A, B, C, E), k8_relset_2(A, B, D, E))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t27_relset_2')).
% 4.26/4.45 tff(15,plain,
% 4.26/4.45 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k5_subset_1(B, k8_relset_2(A, B, C, E), k8_relset_2(A, B, D, E))))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[14, 13])).
% 4.26/4.45 tff(16,plain,
% 4.26/4.45 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k5_subset_1(B, k8_relset_2(A, B, C, E), k8_relset_2(A, B, D, E))))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[15, 12])).
% 4.26/4.45 tff(17,plain,
% 4.26/4.45 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k5_subset_1(B, k8_relset_2(A, B, C, E), k8_relset_2(A, B, D, E))))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[16, 12])).
% 4.26/4.45 tff(18,plain,
% 4.26/4.45 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k5_subset_1(B, k8_relset_2(A, B, C, E), k8_relset_2(A, B, D, E))))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[17, 12])).
% 4.26/4.45 tff(19,plain,
% 4.26/4.45 (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, 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, k4_subset_1(A!2, C!0, D!3), E!4) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[18, 11])).
% 4.26/4.45 tff(20,plain,
% 4.26/4.45 (~((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4))))),
% 4.26/4.45 inference(and_elim,[status(thm)],[19])).
% 4.26/4.45 tff(21,plain,
% 4.26/4.45 (m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 4.26/4.45 inference(or_elim,[status(thm)],[20])).
% 4.26/4.45 tff(22,plain,
% 4.26/4.45 (((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C)))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k6_relset_2(B!1, A!2, E!4) = k5_relset_2(A!2, E!4)))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k6_relset_2(B!1, A!2, E!4) = k5_relset_2(A!2, E!4)))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(23,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C)))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k6_relset_2(B!1, A!2, E!4) = k5_relset_2(A!2, E!4)))),
% 4.26/4.45 inference(quant_inst,[status(thm)],[])).
% 4.26/4.45 tff(24,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (k6_relset_2(A, B, C) = k5_relset_2(B, C)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k6_relset_2(B!1, A!2, E!4) = k5_relset_2(A!2, E!4))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[23, 22])).
% 4.26/4.45 tff(25,plain,
% 4.26/4.45 (k6_relset_2(B!1, A!2, E!4) = k5_relset_2(A!2, E!4)),
% 4.26/4.45 inference(unit_resolution,[status(thm)],[24, 21, 10])).
% 4.26/4.45 tff(26,plain,
% 4.26/4.45 (k5_relset_2(A!2, E!4) = k6_relset_2(B!1, A!2, E!4)),
% 4.26/4.45 inference(symmetry,[status(thm)],[25])).
% 4.26/4.45 tff(27,plain,
% 4.26/4.45 (m2_relset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1)) <=> m2_relset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))),
% 4.26/4.45 inference(monotonicity,[status(thm)],[26])).
% 4.26/4.45 tff(28,plain,
% 4.26/4.45 (m2_relset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1)) <=> m2_relset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))),
% 4.26/4.45 inference(symmetry,[status(thm)],[27])).
% 4.26/4.45 tff(29,plain,
% 4.26/4.45 (^[A: $i, B: $i, C: $i] : refl(((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))))))),
% 4.26/4.45 inference(bind,[status(th)],[])).
% 4.26/4.45 tff(30,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))))),
% 4.26/4.45 inference(quant_intro,[status(thm)],[29])).
% 4.26/4.45 tff(31,plain,
% 4.26/4.45 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))))))),
% 4.26/4.45 inference(bind,[status(th)],[])).
% 4.26/4.45 tff(32,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))))),
% 4.26/4.45 inference(quant_intro,[status(thm)],[31])).
% 4.26/4.45 tff(33,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(34,plain,
% 4.26/4.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) <=> (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))), ((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => ((v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))) <=> (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))))), rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))), ((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => ((v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))))),
% 4.26/4.45 inference(bind,[status(th)],[])).
% 4.26/4.45 tff(35,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => ((v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))),
% 4.26/4.45 inference(quant_intro,[status(thm)],[34])).
% 4.26/4.45 tff(36,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => ((v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_relset_2')).
% 4.26/4.45 tff(37,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[36, 35])).
% 4.26/4.45 tff(38,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[37, 33])).
% 4.26/4.45 tff(39,plain,(
% 4.26/4.45 ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (v1_funct_1(k6_relset_2(A, B, C)) & v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A)) & m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))),
% 4.26/4.45 inference(skolemize,[status(sab)],[38])).
% 4.26/4.45 tff(40,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[39, 32])).
% 4.26/4.45 tff(41,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[40, 30])).
% 4.26/4.45 tff(42,plain,
% 4.26/4.45 (((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~v1_funct_1(k6_relset_2(B!1, A!2, E!4))) | (~v1_funct_2(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))) | (~m2_relset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~v1_funct_1(k6_relset_2(B!1, A!2, E!4))) | (~v1_funct_2(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))) | (~m2_relset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(43,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~v1_funct_1(k6_relset_2(B!1, A!2, E!4))) | (~v1_funct_2(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))) | (~m2_relset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))))),
% 4.26/4.45 inference(quant_inst,[status(thm)],[])).
% 4.26/4.45 tff(44,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~v1_funct_1(k6_relset_2(A, B, C))) | (~v1_funct_2(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))) | (~m2_relset_1(k6_relset_2(A, B, C), k1_zfmisc_1(B), k1_zfmisc_1(A))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~v1_funct_1(k6_relset_2(B!1, A!2, E!4))) | (~v1_funct_2(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))) | (~m2_relset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1)))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[43, 42])).
% 4.26/4.45 tff(45,plain,
% 4.26/4.45 (~((~v1_funct_1(k6_relset_2(B!1, A!2, E!4))) | (~v1_funct_2(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))) | (~m2_relset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))),
% 4.26/4.45 inference(unit_resolution,[status(thm)],[44, 21, 41])).
% 4.26/4.45 tff(46,plain,
% 4.26/4.45 (((~v1_funct_1(k6_relset_2(B!1, A!2, E!4))) | (~v1_funct_2(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))) | (~m2_relset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1)))) | m2_relset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))),
% 4.26/4.45 inference(tautology,[status(thm)],[])).
% 4.26/4.45 tff(47,plain,
% 4.26/4.45 (m2_relset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))),
% 4.26/4.45 inference(unit_resolution,[status(thm)],[46, 45])).
% 4.26/4.45 tff(48,plain,
% 4.26/4.45 (m2_relset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[47, 28])).
% 4.26/4.45 tff(49,plain,
% 4.26/4.45 (^[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)))))),
% 4.26/4.45 inference(bind,[status(th)],[])).
% 4.26/4.45 tff(50,plain,
% 4.26/4.45 (![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))))),
% 4.26/4.45 inference(quant_intro,[status(thm)],[49])).
% 4.26/4.45 tff(51,plain,
% 4.26/4.45 (![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))))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(52,plain,
% 4.26/4.45 (^[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)))))),
% 4.26/4.45 inference(bind,[status(th)],[])).
% 4.26/4.45 tff(53,plain,
% 4.26/4.45 (![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))))),
% 4.26/4.45 inference(quant_intro,[status(thm)],[52])).
% 4.26/4.45 tff(54,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/sandbox2/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 4.26/4.45 tff(55,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[54, 53])).
% 4.26/4.45 tff(56,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[55, 51])).
% 4.26/4.45 tff(57,plain,(
% 4.26/4.45 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 4.26/4.45 inference(skolemize,[status(sab)],[56])).
% 4.26/4.45 tff(58,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[57, 50])).
% 4.26/4.45 tff(59,plain,
% 4.26/4.45 (((~![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(k5_relset_2(A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))) | m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(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(k5_relset_2(A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))) | m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1)))))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(60,plain,
% 4.26/4.45 ((~![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(k5_relset_2(A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))) | m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1)))))),
% 4.26/4.45 inference(quant_inst,[status(thm)],[])).
% 4.26/4.45 tff(61,plain,
% 4.26/4.45 ((~![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(k5_relset_2(A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))) | m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 4.26/4.45 tff(62,plain,
% 4.26/4.45 ((~m2_relset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))) | m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))),
% 4.26/4.45 inference(unit_resolution,[status(thm)],[61, 58])).
% 4.26/4.45 tff(63,plain,
% 4.26/4.45 (m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))),
% 4.26/4.45 inference(unit_resolution,[status(thm)],[62, 48])).
% 4.26/4.45 tff(64,plain,
% 4.26/4.45 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D))))),
% 4.26/4.45 inference(bind,[status(th)],[])).
% 4.26/4.45 tff(65,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.26/4.45 inference(quant_intro,[status(thm)],[64])).
% 4.26/4.45 tff(66,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(67,plain,
% 4.26/4.45 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B)))) => (k4_relset_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D))))),
% 4.26/4.45 inference(bind,[status(th)],[])).
% 4.26/4.45 tff(68,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B)))) => (k4_relset_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.26/4.45 inference(quant_intro,[status(thm)],[67])).
% 4.26/4.45 tff(69,axiom,(![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B)))) => (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_relset_2')).
% 4.26/4.45 tff(70,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[69, 68])).
% 4.26/4.45 tff(71,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[70, 66])).
% 4.26/4.45 tff(72,plain,(
% 4.26/4.45 ![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.26/4.45 inference(skolemize,[status(sab)],[71])).
% 4.26/4.45 tff(73,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[72, 65])).
% 4.26/4.45 tff(74,plain,
% 4.26/4.45 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(75,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))))),
% 4.26/4.45 inference(quant_inst,[status(thm)],[])).
% 4.26/4.45 tff(76,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[75, 74])).
% 4.26/4.45 tff(77,plain,
% 4.26/4.45 ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)))),
% 4.26/4.45 inference(unit_resolution,[status(thm)],[76, 73])).
% 4.26/4.45 tff(78,plain,
% 4.26/4.45 (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))),
% 4.26/4.45 inference(unit_resolution,[status(thm)],[77, 63])).
% 4.26/4.45 tff(79,plain,
% 4.26/4.45 (k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)) = k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))),
% 4.26/4.45 inference(symmetry,[status(thm)],[78])).
% 4.26/4.45 tff(80,plain,
% 4.26/4.45 (m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1))) <=> m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.45 inference(monotonicity,[status(thm)],[79])).
% 4.26/4.45 tff(81,plain,
% 4.26/4.45 (m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1))) <=> m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.45 inference(symmetry,[status(thm)],[80])).
% 4.26/4.45 tff(82,plain,
% 4.26/4.45 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))),
% 4.26/4.45 inference(bind,[status(th)],[])).
% 4.26/4.45 tff(83,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 4.26/4.45 inference(quant_intro,[status(thm)],[82])).
% 4.26/4.45 tff(84,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(85,plain,
% 4.26/4.45 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B)))) => m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))),
% 4.26/4.45 inference(bind,[status(th)],[])).
% 4.26/4.45 tff(86,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B)))) => m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 4.26/4.45 inference(quant_intro,[status(thm)],[85])).
% 4.26/4.45 tff(87,axiom,(![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B)))) => m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_relset_2')).
% 4.26/4.45 tff(88,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 4.26/4.45 tff(89,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[88, 84])).
% 4.26/4.45 tff(90,plain,(
% 4.26/4.45 ![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 4.26/4.45 inference(skolemize,[status(sab)],[89])).
% 4.26/4.45 tff(91,plain,
% 4.26/4.45 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[90, 83])).
% 4.26/4.45 tff(92,plain,
% 4.26/4.45 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1))))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(93,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1))))),
% 4.26/4.45 inference(quant_inst,[status(thm)],[])).
% 4.26/4.45 tff(94,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[93, 92])).
% 4.26/4.45 tff(95,plain,
% 4.26/4.45 ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.45 inference(unit_resolution,[status(thm)],[94, 91])).
% 4.26/4.45 tff(96,plain,
% 4.26/4.45 (m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.45 inference(unit_resolution,[status(thm)],[95, 63])).
% 4.26/4.45 tff(97,plain,
% 4.26/4.45 (m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[96, 81])).
% 4.26/4.45 tff(98,plain,
% 4.26/4.45 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))),
% 4.26/4.45 inference(rewrite,[status(thm)],[])).
% 4.26/4.45 tff(99,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))),
% 4.26/4.45 inference(quant_inst,[status(thm)],[])).
% 4.26/4.45 tff(100,plain,
% 4.26/4.45 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))),
% 4.26/4.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 4.26/4.45 tff(101,plain,
% 4.26/4.45 ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))),
% 4.26/4.45 inference(unit_resolution,[status(thm)],[100, 73])).
% 4.26/4.45 tff(102,plain,
% 4.26/4.45 (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))),
% 4.26/4.45 inference(unit_resolution,[status(thm)],[101, 63])).
% 4.26/4.45 tff(103,plain,
% 4.26/4.45 (k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)) = k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))),
% 4.26/4.45 inference(symmetry,[status(thm)],[102])).
% 4.26/4.45 tff(104,plain,
% 4.26/4.45 (m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1))) <=> m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.45 inference(monotonicity,[status(thm)],[103])).
% 4.26/4.45 tff(105,plain,
% 4.26/4.45 (m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1))) <=> m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.45 inference(symmetry,[status(thm)],[104])).
% 4.26/4.45 tff(106,plain,
% 4.26/4.45 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1))))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(107,plain,
% 4.26/4.46 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1))))),
% 4.26/4.46 inference(quant_inst,[status(thm)],[])).
% 4.26/4.46 tff(108,plain,
% 4.26/4.46 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[107, 106])).
% 4.26/4.46 tff(109,plain,
% 4.26/4.46 ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.46 inference(unit_resolution,[status(thm)],[108, 91])).
% 4.26/4.46 tff(110,plain,
% 4.26/4.46 (m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.46 inference(unit_resolution,[status(thm)],[109, 63])).
% 4.26/4.46 tff(111,plain,
% 4.26/4.46 (m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[110, 105])).
% 4.26/4.46 tff(112,plain,
% 4.26/4.46 (^[A: $i, B: $i, C: $i] : refl(((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(113,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[112])).
% 4.26/4.46 tff(114,plain,
% 4.26/4.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> (((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))))), rewrite((((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(115,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[114])).
% 4.26/4.46 tff(116,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(117,plain,
% 4.26/4.46 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(118,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[117])).
% 4.26/4.46 tff(119,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_subset_1')).
% 4.26/4.46 tff(120,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[119, 118])).
% 4.26/4.46 tff(121,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[120, 116])).
% 4.26/4.46 tff(122,plain,(
% 4.26/4.46 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 4.26/4.46 inference(skolemize,[status(sab)],[121])).
% 4.26/4.46 tff(123,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[122, 115])).
% 4.26/4.46 tff(124,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[123, 113])).
% 4.26/4.46 tff(125,plain,
% 4.26/4.46 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(126,plain,
% 4.26/4.46 (((k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1))))) <=> ((~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(127,plain,
% 4.26/4.46 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))))),
% 4.26/4.46 inference(monotonicity,[status(thm)],[126])).
% 4.26/4.46 tff(128,plain,
% 4.26/4.46 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))))),
% 4.26/4.46 inference(transitivity,[status(thm)],[127, 125])).
% 4.26/4.46 tff(129,plain,
% 4.26/4.46 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))))),
% 4.26/4.46 inference(quant_inst,[status(thm)],[])).
% 4.26/4.46 tff(130,plain,
% 4.26/4.46 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | (k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[129, 128])).
% 4.26/4.46 tff(131,plain,
% 4.26/4.46 (k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))),
% 4.26/4.46 inference(unit_resolution,[status(thm)],[130, 124, 111, 97])).
% 4.26/4.46 tff(132,plain,
% 4.26/4.46 (k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))),
% 4.26/4.46 inference(symmetry,[status(thm)],[131])).
% 4.26/4.46 tff(133,plain,
% 4.26/4.46 (^[A: $i, B: $i, C: $i] : refl((v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(134,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[133])).
% 4.26/4.46 tff(135,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(136,plain,
% 4.26/4.46 (^[A: $i, B: $i, C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(137,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[136])).
% 4.26/4.46 tff(138,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_relset_1')).
% 4.26/4.46 tff(139,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[138, 137])).
% 4.26/4.46 tff(140,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[139, 135])).
% 4.26/4.46 tff(141,plain,(
% 4.26/4.46 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.26/4.46 inference(skolemize,[status(sab)],[140])).
% 4.26/4.46 tff(142,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[141, 134])).
% 4.26/4.46 tff(143,plain,
% 4.26/4.46 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(144,plain,
% 4.26/4.46 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 4.26/4.46 inference(quant_inst,[status(thm)],[])).
% 4.26/4.46 tff(145,plain,
% 4.26/4.46 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[144, 143])).
% 4.26/4.46 tff(146,plain,
% 4.26/4.46 (v1_relat_1(E!4)),
% 4.26/4.46 inference(unit_resolution,[status(thm)],[145, 21, 142])).
% 4.26/4.46 tff(147,plain,
% 4.26/4.46 (^[A: $i, B: $i] : refl(((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B)))))) <=> ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B)))))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(148,plain,
% 4.26/4.46 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B)))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[147])).
% 4.26/4.46 tff(149,plain,
% 4.26/4.46 (^[A: $i, B: $i] : rewrite(((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))) <=> ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B)))))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(150,plain,
% 4.26/4.46 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[149])).
% 4.26/4.46 tff(151,plain,
% 4.26/4.46 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(152,plain,
% 4.26/4.46 (^[A: $i, B: $i] : rewrite((v1_relat_1(B) => (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))) <=> ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(153,plain,
% 4.26/4.46 (![A: $i, B: $i] : (v1_relat_1(B) => (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[152])).
% 4.26/4.46 tff(154,axiom,(![A: $i, B: $i] : (v1_relat_1(B) => (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_relset_2')).
% 4.26/4.46 tff(155,plain,
% 4.26/4.46 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[154, 153])).
% 4.26/4.46 tff(156,plain,
% 4.26/4.46 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[155, 151])).
% 4.26/4.46 tff(157,plain,(
% 4.26/4.46 ![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 4.26/4.46 inference(skolemize,[status(sab)],[156])).
% 4.26/4.46 tff(158,plain,
% 4.26/4.46 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[157, 150])).
% 4.26/4.46 tff(159,plain,
% 4.26/4.46 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[158, 148])).
% 4.26/4.46 tff(160,plain,
% 4.26/4.46 (((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | ((~v1_relat_1(E!4)) | (~((~v1_relat_1(k5_relset_2(A!2, E!4))) | (~v1_funct_1(k5_relset_2(A!2, E!4))))))) <=> ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | (~v1_relat_1(E!4)) | (~((~v1_relat_1(k5_relset_2(A!2, E!4))) | (~v1_funct_1(k5_relset_2(A!2, E!4))))))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(161,plain,
% 4.26/4.46 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | ((~v1_relat_1(E!4)) | (~((~v1_relat_1(k5_relset_2(A!2, E!4))) | (~v1_funct_1(k5_relset_2(A!2, E!4))))))),
% 4.26/4.46 inference(quant_inst,[status(thm)],[])).
% 4.26/4.46 tff(162,plain,
% 4.26/4.46 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | (~v1_relat_1(E!4)) | (~((~v1_relat_1(k5_relset_2(A!2, E!4))) | (~v1_funct_1(k5_relset_2(A!2, E!4)))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[161, 160])).
% 4.26/4.46 tff(163,plain,
% 4.26/4.46 (~((~v1_relat_1(k5_relset_2(A!2, E!4))) | (~v1_funct_1(k5_relset_2(A!2, E!4))))),
% 4.26/4.46 inference(unit_resolution,[status(thm)],[162, 159, 146])).
% 4.26/4.46 tff(164,plain,
% 4.26/4.46 (((~v1_relat_1(k5_relset_2(A!2, E!4))) | (~v1_funct_1(k5_relset_2(A!2, E!4)))) | v1_relat_1(k5_relset_2(A!2, E!4))),
% 4.26/4.46 inference(tautology,[status(thm)],[])).
% 4.26/4.46 tff(165,plain,
% 4.26/4.46 (v1_relat_1(k5_relset_2(A!2, E!4))),
% 4.26/4.46 inference(unit_resolution,[status(thm)],[164, 163])).
% 4.26/4.46 tff(166,plain,
% 4.26/4.46 (^[A: $i, B: $i, C: $i] : refl(((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B)))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(167,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[166])).
% 4.26/4.46 tff(168,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(169,plain,
% 4.26/4.46 (^[A: $i, B: $i, C: $i] : rewrite((v1_relat_1(C) => (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B)))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(170,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[169])).
% 4.26/4.46 tff(171,axiom,(![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t153_relat_1')).
% 4.26/4.46 tff(172,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[171, 170])).
% 4.26/4.46 tff(173,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[172, 168])).
% 4.26/4.46 tff(174,plain,(
% 4.26/4.46 ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))),
% 4.26/4.46 inference(skolemize,[status(sab)],[173])).
% 4.26/4.46 tff(175,plain,
% 4.26/4.46 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[174, 167])).
% 4.26/4.46 tff(176,plain,
% 4.26/4.46 (((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))) | ((~v1_relat_1(k5_relset_2(A!2, E!4))) | (k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))) | (~v1_relat_1(k5_relset_2(A!2, E!4))) | (k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(177,plain,
% 4.26/4.46 ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))) | ((~v1_relat_1(k5_relset_2(A!2, E!4))) | (k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))))),
% 4.26/4.46 inference(quant_inst,[status(thm)],[])).
% 4.26/4.46 tff(178,plain,
% 4.26/4.46 ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(C, k2_xboole_0(A, B)) = k2_xboole_0(k9_relat_1(C, A), k9_relat_1(C, B))))) | (~v1_relat_1(k5_relset_2(A!2, E!4))) | (k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[177, 176])).
% 4.26/4.46 tff(179,plain,
% 4.26/4.46 (k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0))) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))),
% 4.26/4.46 inference(unit_resolution,[status(thm)],[178, 175, 165])).
% 4.26/4.46 tff(180,plain,
% 4.26/4.46 (^[A: $i, B: $i] : refl((k2_xboole_0(A, B) = k2_xboole_0(B, A)) <=> (k2_xboole_0(A, B) = k2_xboole_0(B, A)))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(181,plain,
% 4.26/4.46 (![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[180])).
% 4.26/4.46 tff(182,plain,
% 4.26/4.46 (![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(183,axiom,(![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 4.26/4.46 tff(184,plain,
% 4.26/4.46 (![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[183, 182])).
% 4.26/4.46 tff(185,plain,(
% 4.26/4.46 ![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 4.26/4.46 inference(skolemize,[status(sab)],[184])).
% 4.26/4.46 tff(186,plain,
% 4.26/4.46 (![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[185, 181])).
% 4.26/4.46 tff(187,plain,
% 4.26/4.46 ((~![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))) | (k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3)) = k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0)))),
% 4.26/4.46 inference(quant_inst,[status(thm)],[])).
% 4.26/4.46 tff(188,plain,
% 4.26/4.46 (k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3)) = k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0))),
% 4.26/4.46 inference(unit_resolution,[status(thm)],[187, 186])).
% 4.26/4.46 tff(189,plain,
% 4.26/4.46 (k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0)) = k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))),
% 4.26/4.46 inference(symmetry,[status(thm)],[188])).
% 4.26/4.46 tff(190,plain,
% 4.26/4.46 (k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0))) = k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3)))),
% 4.26/4.46 inference(monotonicity,[status(thm)],[189])).
% 4.26/4.46 tff(191,plain,
% 4.26/4.46 (k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))) = k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0)))),
% 4.26/4.46 inference(symmetry,[status(thm)],[190])).
% 4.26/4.46 tff(192,plain,
% 4.26/4.46 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))) = k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))) = k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3)))))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(193,plain,
% 4.26/4.46 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))) = k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3)))))),
% 4.26/4.46 inference(quant_inst,[status(thm)],[])).
% 4.26/4.46 tff(194,plain,
% 4.26/4.46 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | (k4_relset_2(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))) = k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[193, 192])).
% 4.26/4.46 tff(195,plain,
% 4.26/4.46 (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))) = k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3)))),
% 4.26/4.46 inference(unit_resolution,[status(thm)],[194, 73, 63])).
% 4.26/4.46 tff(196,plain,
% 4.26/4.46 (^[A: $i, B: $i] : refl((k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B))) <=> (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(197,plain,
% 4.26/4.46 (![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B))) <=> ![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B)))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[196])).
% 4.26/4.46 tff(198,plain,
% 4.26/4.46 (![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B))) <=> ![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B)))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(199,axiom,(![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_relset_2')).
% 4.26/4.46 tff(200,plain,
% 4.26/4.46 (![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B)))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[199, 198])).
% 4.26/4.46 tff(201,plain,(
% 4.26/4.46 ![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B)))),
% 4.26/4.46 inference(skolemize,[status(sab)],[200])).
% 4.26/4.46 tff(202,plain,
% 4.26/4.46 (![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B)))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[201, 197])).
% 4.26/4.46 tff(203,plain,
% 4.26/4.46 ((~![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B)))) | (k3_pua2mss1(k2_xboole_0(C!0, D!3)) = k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3)))),
% 4.26/4.46 inference(quant_inst,[status(thm)],[])).
% 4.26/4.46 tff(204,plain,
% 4.26/4.46 (k3_pua2mss1(k2_xboole_0(C!0, D!3)) = k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))),
% 4.26/4.46 inference(unit_resolution,[status(thm)],[203, 202])).
% 4.26/4.46 tff(205,plain,
% 4.26/4.46 (k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3)))),
% 4.26/4.46 inference(monotonicity,[status(thm)],[25, 204])).
% 4.26/4.46 tff(206,plain,
% 4.26/4.46 (k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))),
% 4.26/4.46 inference(transitivity,[status(thm)],[205, 195, 191, 179, 132])).
% 4.26/4.46 tff(207,plain,
% 4.26/4.46 (^[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)))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(208,plain,
% 4.26/4.46 (![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))))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[207])).
% 4.26/4.46 tff(209,plain,
% 4.26/4.46 (^[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))))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(210,plain,
% 4.26/4.46 (![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))))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[209])).
% 4.26/4.46 tff(211,plain,
% 4.26/4.46 (![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)))),
% 4.26/4.46 inference(rewrite,[status(thm)],[])).
% 4.26/4.46 tff(212,plain,
% 4.26/4.46 (^[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))))),
% 4.26/4.46 inference(bind,[status(th)],[])).
% 4.26/4.46 tff(213,plain,
% 4.26/4.46 (![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)))),
% 4.26/4.46 inference(quant_intro,[status(thm)],[212])).
% 4.26/4.46 tff(214,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/sandbox2/benchmark/theBenchmark.p','dt_k8_relset_2')).
% 4.26/4.46 tff(215,plain,
% 4.26/4.46 (![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)))),
% 4.26/4.46 inference(modus_ponens,[status(thm)],[214, 213])).
% 4.26/4.46 tff(216,plain,
% 4.26/4.46 (![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)))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[215, 211])).
% 4.26/4.47 tff(217,plain,(
% 4.26/4.47 ![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)))),
% 4.26/4.47 inference(skolemize,[status(sab)],[216])).
% 4.26/4.47 tff(218,plain,
% 4.26/4.47 (![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))))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[217, 210])).
% 4.26/4.47 tff(219,plain,
% 4.26/4.47 (![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))))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[218, 208])).
% 4.26/4.47 tff(220,plain,
% 4.26/4.47 (m1_subset_1(C!0, k1_zfmisc_1(A!2))),
% 4.26/4.47 inference(and_elim,[status(thm)],[19])).
% 4.26/4.47 tff(221,plain,
% 4.26/4.47 (((~![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)))),
% 4.26/4.47 inference(rewrite,[status(thm)],[])).
% 4.26/4.47 tff(222,plain,
% 4.26/4.47 ((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)))),
% 4.26/4.47 inference(rewrite,[status(thm)],[])).
% 4.26/4.47 tff(223,plain,
% 4.26/4.47 (((~![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))))),
% 4.26/4.47 inference(monotonicity,[status(thm)],[222])).
% 4.26/4.47 tff(224,plain,
% 4.26/4.47 (((~![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)))),
% 4.26/4.47 inference(transitivity,[status(thm)],[223, 221])).
% 4.26/4.47 tff(225,plain,
% 4.26/4.47 ((~![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))))),
% 4.26/4.47 inference(quant_inst,[status(thm)],[])).
% 4.26/4.47 tff(226,plain,
% 4.26/4.47 ((~![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))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[225, 224])).
% 4.26/4.47 tff(227,plain,
% 4.26/4.47 (m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))),
% 4.26/4.47 inference(unit_resolution,[status(thm)],[226, 220, 21, 219])).
% 4.26/4.47 tff(228,plain,
% 4.26/4.47 (m1_subset_1(D!3, k1_zfmisc_1(A!2))),
% 4.26/4.47 inference(and_elim,[status(thm)],[19])).
% 4.26/4.47 tff(229,plain,
% 4.26/4.47 (((~![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(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, D!3, 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(D!3, 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, D!3, E!4), k1_zfmisc_1(B!1)))),
% 4.26/4.47 inference(rewrite,[status(thm)],[])).
% 4.26/4.47 tff(230,plain,
% 4.26/4.47 ((m1_subset_1(k8_relset_2(A!2, B!1, D!3, 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(D!3, k1_zfmisc_1(A!2)))) <=> ((~m1_subset_1(D!3, 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, D!3, E!4), k1_zfmisc_1(B!1)))),
% 4.26/4.47 inference(rewrite,[status(thm)],[])).
% 4.26/4.47 tff(231,plain,
% 4.26/4.47 (((~![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, D!3, 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(D!3, 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(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, D!3, E!4), k1_zfmisc_1(B!1))))),
% 4.26/4.47 inference(monotonicity,[status(thm)],[230])).
% 4.26/4.47 tff(232,plain,
% 4.26/4.47 (((~![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, D!3, 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(D!3, 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(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, D!3, E!4), k1_zfmisc_1(B!1)))),
% 4.26/4.47 inference(transitivity,[status(thm)],[231, 229])).
% 4.26/4.47 tff(233,plain,
% 4.26/4.47 ((~![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, D!3, 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(D!3, k1_zfmisc_1(A!2))))),
% 4.26/4.47 inference(quant_inst,[status(thm)],[])).
% 4.26/4.47 tff(234,plain,
% 4.26/4.47 ((~![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(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, D!3, E!4), k1_zfmisc_1(B!1))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[233, 232])).
% 4.26/4.47 tff(235,plain,
% 4.26/4.47 (m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(B!1))),
% 4.26/4.47 inference(unit_resolution,[status(thm)],[234, 228, 21, 219])).
% 4.26/4.47 tff(236,plain,
% 4.26/4.47 (^[A: $i, B: $i, C: $i] : refl(((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))),
% 4.26/4.47 inference(bind,[status(th)],[])).
% 4.26/4.47 tff(237,plain,
% 4.26/4.47 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.47 inference(quant_intro,[status(thm)],[236])).
% 4.26/4.47 tff(238,plain,
% 4.26/4.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> (((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))))), rewrite((((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))))),
% 4.26/4.47 inference(bind,[status(th)],[])).
% 4.26/4.47 tff(239,plain,
% 4.26/4.47 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.47 inference(quant_intro,[status(thm)],[238])).
% 4.26/4.47 tff(240,plain,
% 4.26/4.47 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))),
% 4.26/4.47 inference(rewrite,[status(thm)],[])).
% 4.26/4.47 tff(241,plain,
% 4.26/4.47 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))))),
% 4.26/4.47 inference(bind,[status(th)],[])).
% 4.26/4.47 tff(242,plain,
% 4.26/4.47 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))),
% 4.26/4.47 inference(quant_intro,[status(thm)],[241])).
% 4.26/4.47 tff(243,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k5_subset_1')).
% 4.26/4.47 tff(244,plain,
% 4.26/4.47 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[243, 242])).
% 4.26/4.47 tff(245,plain,
% 4.26/4.47 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[244, 240])).
% 4.26/4.47 tff(246,plain,(
% 4.26/4.47 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))),
% 4.26/4.47 inference(skolemize,[status(sab)],[245])).
% 4.26/4.47 tff(247,plain,
% 4.26/4.47 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[246, 239])).
% 4.26/4.47 tff(248,plain,
% 4.26/4.47 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[247, 237])).
% 4.26/4.47 tff(249,plain,
% 4.26/4.47 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((~m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(B!1))) | (~m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))) | (k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(B!1))) | (~m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))) | (k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4))))),
% 4.26/4.47 inference(rewrite,[status(thm)],[])).
% 4.26/4.47 tff(250,plain,
% 4.26/4.47 (((k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4))) | (~m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(B!1))) | (~m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1)))) <=> ((~m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(B!1))) | (~m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))) | (k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4))))),
% 4.26/4.47 inference(rewrite,[status(thm)],[])).
% 4.26/4.47 tff(251,plain,
% 4.26/4.47 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4))) | (~m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(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] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((~m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(B!1))) | (~m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))) | (k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4)))))),
% 4.26/4.47 inference(monotonicity,[status(thm)],[250])).
% 4.26/4.47 tff(252,plain,
% 4.26/4.47 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4))) | (~m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(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] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(B!1))) | (~m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))) | (k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4))))),
% 4.26/4.47 inference(transitivity,[status(thm)],[251, 249])).
% 4.26/4.47 tff(253,plain,
% 4.26/4.47 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4))) | (~m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(B!1))) | (~m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))))),
% 4.26/4.47 inference(quant_inst,[status(thm)],[])).
% 4.26/4.47 tff(254,plain,
% 4.26/4.47 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(B!1))) | (~m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))) | (k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4)))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[253, 252])).
% 4.26/4.47 tff(255,plain,
% 4.26/4.47 ((~m1_subset_1(k8_relset_2(A!2, B!1, D!3, E!4), k1_zfmisc_1(B!1))) | (~m1_subset_1(k8_relset_2(A!2, B!1, C!0, E!4), k1_zfmisc_1(B!1))) | (k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4)))),
% 4.26/4.47 inference(unit_resolution,[status(thm)],[254, 248])).
% 4.26/4.47 tff(256,plain,
% 4.26/4.47 (k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4))),
% 4.26/4.47 inference(unit_resolution,[status(thm)],[255, 235, 227])).
% 4.26/4.47 tff(257,plain,
% 4.26/4.47 (k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4)) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4))),
% 4.26/4.47 inference(symmetry,[status(thm)],[256])).
% 4.26/4.47 tff(258,plain,
% 4.26/4.47 (^[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)))))),
% 4.26/4.47 inference(bind,[status(th)],[])).
% 4.26/4.47 tff(259,plain,
% 4.26/4.47 (![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))))),
% 4.26/4.47 inference(quant_intro,[status(thm)],[258])).
% 4.26/4.47 tff(260,plain,
% 4.26/4.47 (^[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))))))),
% 4.26/4.47 inference(bind,[status(th)],[])).
% 4.26/4.47 tff(261,plain,
% 4.26/4.47 (![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))))),
% 4.26/4.47 inference(quant_intro,[status(thm)],[260])).
% 4.26/4.47 tff(262,plain,
% 4.26/4.47 (![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)))),
% 4.26/4.47 inference(rewrite,[status(thm)],[])).
% 4.26/4.47 tff(263,plain,
% 4.26/4.47 (^[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))))),
% 4.26/4.47 inference(bind,[status(th)],[])).
% 4.26/4.47 tff(264,plain,
% 4.26/4.47 (![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)))),
% 4.26/4.47 inference(quant_intro,[status(thm)],[263])).
% 4.26/4.47 tff(265,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/sandbox2/benchmark/theBenchmark.p','redefinition_k8_relset_2')).
% 4.26/4.47 tff(266,plain,
% 4.26/4.47 (![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)))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[265, 264])).
% 4.26/4.47 tff(267,plain,
% 4.26/4.47 (![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)))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[266, 262])).
% 4.26/4.47 tff(268,plain,(
% 4.26/4.47 ![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)))),
% 4.26/4.47 inference(skolemize,[status(sab)],[267])).
% 4.26/4.47 tff(269,plain,
% 4.26/4.47 (![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))))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[268, 261])).
% 4.26/4.47 tff(270,plain,
% 4.26/4.47 (![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))))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[269, 259])).
% 4.26/4.47 tff(271,plain,
% 4.26/4.47 (((~![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)))),
% 4.26/4.47 inference(rewrite,[status(thm)],[])).
% 4.26/4.47 tff(272,plain,
% 4.26/4.47 (((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)))),
% 4.26/4.47 inference(rewrite,[status(thm)],[])).
% 4.26/4.47 tff(273,plain,
% 4.26/4.47 (((~![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))))),
% 4.26/4.47 inference(monotonicity,[status(thm)],[272])).
% 4.26/4.47 tff(274,plain,
% 4.26/4.47 (((~![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)))),
% 4.26/4.47 inference(transitivity,[status(thm)],[273, 271])).
% 4.26/4.47 tff(275,plain,
% 4.26/4.47 ((~![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))))),
% 4.26/4.47 inference(quant_inst,[status(thm)],[])).
% 4.26/4.47 tff(276,plain,
% 4.26/4.47 ((~![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))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[275, 274])).
% 4.26/4.47 tff(277,plain,
% 4.26/4.47 (k8_relset_2(A!2, B!1, C!0, E!4) = k7_relset_2(A!2, B!1, C!0, E!4)),
% 4.26/4.47 inference(unit_resolution,[status(thm)],[276, 220, 21, 270])).
% 4.26/4.47 tff(278,plain,
% 4.26/4.47 (k7_relset_2(A!2, B!1, C!0, E!4) = k8_relset_2(A!2, B!1, C!0, E!4)),
% 4.26/4.47 inference(symmetry,[status(thm)],[277])).
% 4.26/4.47 tff(279,plain,
% 4.26/4.47 (^[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)))))))),
% 4.26/4.47 inference(bind,[status(th)],[])).
% 4.26/4.47 tff(280,plain,
% 4.26/4.47 (![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))))))),
% 4.26/4.47 inference(quant_intro,[status(thm)],[279])).
% 4.26/4.47 tff(281,plain,
% 4.26/4.47 (^[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)))))))),
% 4.26/4.47 inference(bind,[status(th)],[])).
% 4.26/4.47 tff(282,plain,
% 4.26/4.47 (![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))))))),
% 4.26/4.47 inference(quant_intro,[status(thm)],[281])).
% 4.26/4.47 tff(283,plain,
% 4.26/4.47 (![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))))))),
% 4.26/4.47 inference(transitivity,[status(thm)],[282, 280])).
% 4.26/4.47 tff(284,plain,
% 4.26/4.47 (![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))))))),
% 4.26/4.47 inference(rewrite,[status(thm)],[])).
% 4.26/4.47 tff(285,plain,
% 4.26/4.47 (^[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))))))))),
% 4.26/4.47 inference(bind,[status(th)],[])).
% 4.26/4.47 tff(286,plain,
% 4.26/4.47 (![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))))))),
% 4.26/4.47 inference(quant_intro,[status(thm)],[285])).
% 4.26/4.47 tff(287,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/sandbox2/benchmark/theBenchmark.p','d4_relset_2')).
% 4.26/4.47 tff(288,plain,
% 4.26/4.47 (![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))))))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[287, 286])).
% 4.26/4.47 tff(289,plain,
% 4.26/4.47 (![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))))))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[288, 284])).
% 4.26/4.47 tff(290,plain,(
% 4.26/4.47 ![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))))))),
% 4.26/4.47 inference(skolemize,[status(sab)],[289])).
% 4.26/4.47 tff(291,plain,
% 4.26/4.47 (![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))))))),
% 4.26/4.47 inference(modus_ponens,[status(thm)],[290, 283])).
% 4.26/4.47 tff(292,plain,
% 4.26/4.47 (((~![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))))))),
% 4.26/4.48 inference(rewrite,[status(thm)],[])).
% 4.26/4.48 tff(293,plain,
% 4.26/4.48 ((~![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))))))),
% 4.26/4.48 inference(quant_inst,[status(thm)],[])).
% 4.26/4.48 tff(294,plain,
% 4.26/4.48 ((~![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)))))),
% 4.26/4.48 inference(modus_ponens,[status(thm)],[293, 292])).
% 4.26/4.48 tff(295,plain,
% 4.26/4.48 (![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)))))),
% 4.26/4.48 inference(unit_resolution,[status(thm)],[294, 220, 291])).
% 4.26/4.48 tff(296,plain,
% 4.26/4.48 (((~![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)))))),
% 4.26/4.48 inference(rewrite,[status(thm)],[])).
% 4.26/4.48 tff(297,plain,
% 4.26/4.48 ((~![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)))))),
% 4.26/4.48 inference(quant_inst,[status(thm)],[])).
% 4.26/4.48 tff(298,plain,
% 4.26/4.48 ((~![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))))),
% 4.26/4.48 inference(modus_ponens,[status(thm)],[297, 296])).
% 4.26/4.48 tff(299,plain,
% 4.26/4.48 (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)))),
% 4.26/4.48 inference(unit_resolution,[status(thm)],[298, 21, 295])).
% 4.26/4.48 tff(300,plain,
% 4.26/4.48 (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)),
% 4.26/4.48 inference(symmetry,[status(thm)],[299])).
% 4.26/4.48 tff(301,plain,
% 4.26/4.48 (k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))),
% 4.26/4.48 inference(monotonicity,[status(thm)],[25])).
% 4.26/4.48 tff(302,plain,
% 4.26/4.48 (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)) = k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))),
% 4.26/4.48 inference(symmetry,[status(thm)],[301])).
% 4.26/4.48 tff(303,plain,
% 4.26/4.48 (k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)) = k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))),
% 4.26/4.48 inference(transitivity,[status(thm)],[103, 302])).
% 4.26/4.48 tff(304,plain,
% 4.26/4.48 (k8_setfam_1(B!1, k9_relat_1(k5_relset_2(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)))),
% 4.26/4.48 inference(monotonicity,[status(thm)],[303])).
% 4.26/4.48 tff(305,plain,
% 4.26/4.48 (k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))) = k8_relset_2(A!2, B!1, C!0, E!4)),
% 4.26/4.48 inference(transitivity,[status(thm)],[304, 300, 278])).
% 4.26/4.48 tff(306,plain,
% 4.26/4.48 (((~![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(D!3, 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, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, 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(D!3, 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, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, E!4)))),
% 4.26/4.48 inference(rewrite,[status(thm)],[])).
% 4.26/4.48 tff(307,plain,
% 4.26/4.48 (((k8_relset_2(A!2, B!1, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2)))) <=> ((~m1_subset_1(D!3, 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, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, E!4)))),
% 4.26/4.48 inference(rewrite,[status(thm)],[])).
% 4.26/4.48 tff(308,plain,
% 4.26/4.48 (((~![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, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(D!3, 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(D!3, 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, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, E!4))))),
% 4.26/4.48 inference(monotonicity,[status(thm)],[307])).
% 4.26/4.48 tff(309,plain,
% 4.26/4.48 (((~![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, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(D!3, 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(D!3, 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, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, E!4)))),
% 4.26/4.48 inference(transitivity,[status(thm)],[308, 306])).
% 4.26/4.48 tff(310,plain,
% 4.26/4.48 ((~![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, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))))),
% 4.26/4.48 inference(quant_inst,[status(thm)],[])).
% 4.26/4.48 tff(311,plain,
% 4.26/4.48 ((~![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(D!3, 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, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, E!4))),
% 4.26/4.48 inference(modus_ponens,[status(thm)],[310, 309])).
% 4.26/4.48 tff(312,plain,
% 4.26/4.48 (k8_relset_2(A!2, B!1, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, E!4)),
% 4.26/4.48 inference(unit_resolution,[status(thm)],[311, 228, 21, 270])).
% 4.26/4.48 tff(313,plain,
% 4.26/4.48 (k7_relset_2(A!2, B!1, D!3, E!4) = k8_relset_2(A!2, B!1, D!3, E!4)),
% 4.26/4.48 inference(symmetry,[status(thm)],[312])).
% 4.26/4.48 tff(314,plain,
% 4.26/4.48 (((~![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(D!3, 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, D!3, 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(D!3))))))) <=> ((~![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(D!3, 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, D!3, 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(D!3))))))),
% 4.26/4.48 inference(rewrite,[status(thm)],[])).
% 4.26/4.48 tff(315,plain,
% 4.26/4.48 ((~![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(D!3, 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, D!3, 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(D!3))))))),
% 4.26/4.48 inference(quant_inst,[status(thm)],[])).
% 4.26/4.48 tff(316,plain,
% 4.26/4.48 ((~![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(D!3, 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, D!3, 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(D!3)))))),
% 4.26/4.48 inference(modus_ponens,[status(thm)],[315, 314])).
% 4.26/4.48 tff(317,plain,
% 4.26/4.48 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, D!3, 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(D!3)))))),
% 4.26/4.48 inference(unit_resolution,[status(thm)],[316, 228, 291])).
% 4.26/4.48 tff(318,plain,
% 4.26/4.48 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, D!3, 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(D!3)))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, D!3, 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(D!3)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, D!3, 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(D!3)))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, D!3, 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(D!3)))))),
% 4.26/4.48 inference(rewrite,[status(thm)],[])).
% 4.26/4.48 tff(319,plain,
% 4.26/4.48 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, D!3, 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(D!3)))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, D!3, 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(D!3)))))),
% 4.26/4.48 inference(quant_inst,[status(thm)],[])).
% 4.26/4.48 tff(320,plain,
% 4.26/4.48 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, D!3, 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(D!3)))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, D!3, 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(D!3))))),
% 4.26/4.48 inference(modus_ponens,[status(thm)],[319, 318])).
% 4.26/4.48 tff(321,plain,
% 4.26/4.48 (k7_relset_2(A!2, B!1, D!3, 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(D!3)))),
% 4.26/4.48 inference(unit_resolution,[status(thm)],[320, 21, 317])).
% 4.26/4.48 tff(322,plain,
% 4.26/4.48 (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(D!3))) = k7_relset_2(A!2, B!1, D!3, E!4)),
% 4.26/4.48 inference(symmetry,[status(thm)],[321])).
% 4.26/4.48 tff(323,plain,
% 4.26/4.48 (k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(D!3)) = k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))),
% 4.26/4.48 inference(monotonicity,[status(thm)],[25])).
% 4.26/4.48 tff(324,plain,
% 4.26/4.48 (k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)) = k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(D!3))),
% 4.26/4.48 inference(symmetry,[status(thm)],[323])).
% 4.26/4.48 tff(325,plain,
% 4.26/4.48 (k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)) = k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(D!3))),
% 4.26/4.48 inference(transitivity,[status(thm)],[79, 324])).
% 4.26/4.48 tff(326,plain,
% 4.26/4.48 (k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))) = 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(D!3)))),
% 4.26/4.48 inference(monotonicity,[status(thm)],[325])).
% 4.26/4.48 tff(327,plain,
% 4.26/4.48 (k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))) = k8_relset_2(A!2, B!1, D!3, E!4)),
% 4.26/4.48 inference(transitivity,[status(thm)],[326, 322, 313])).
% 4.26/4.48 tff(328,plain,
% 4.26/4.48 (k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, D!3, E!4), k8_relset_2(A!2, B!1, C!0, E!4))),
% 4.26/4.48 inference(monotonicity,[status(thm)],[327, 305])).
% 4.26/4.48 tff(329,plain,
% 4.26/4.48 (k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4))),
% 4.26/4.48 inference(transitivity,[status(thm)],[328, 257])).
% 4.26/4.48 tff(330,plain,
% 4.26/4.48 (^[A: $i, B: $i, C: $i] : refl((m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))),
% 4.26/4.48 inference(bind,[status(th)],[])).
% 4.26/4.48 tff(331,plain,
% 4.26/4.48 (![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.48 inference(quant_intro,[status(thm)],[330])).
% 4.26/4.48 tff(332,plain,
% 4.26/4.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))))), rewrite((((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))))),
% 4.26/4.48 inference(bind,[status(th)],[])).
% 4.26/4.48 tff(333,plain,
% 4.26/4.48 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.48 inference(quant_intro,[status(thm)],[332])).
% 4.26/4.48 tff(334,plain,
% 4.26/4.48 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 4.26/4.48 inference(rewrite,[status(thm)],[])).
% 4.26/4.48 tff(335,plain,
% 4.26/4.48 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))))),
% 4.26/4.48 inference(bind,[status(th)],[])).
% 4.26/4.48 tff(336,plain,
% 4.26/4.48 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 4.26/4.48 inference(quant_intro,[status(thm)],[335])).
% 4.26/4.48 tff(337,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_subset_1')).
% 4.26/4.48 tff(338,plain,
% 4.26/4.48 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 4.26/4.48 inference(modus_ponens,[status(thm)],[337, 336])).
% 4.26/4.48 tff(339,plain,
% 4.26/4.48 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 4.26/4.48 inference(modus_ponens,[status(thm)],[338, 334])).
% 4.26/4.48 tff(340,plain,(
% 4.26/4.48 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 4.26/4.48 inference(skolemize,[status(sab)],[339])).
% 4.26/4.48 tff(341,plain,
% 4.26/4.48 (![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.48 inference(modus_ponens,[status(thm)],[340, 333])).
% 4.26/4.48 tff(342,plain,
% 4.26/4.48 (![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 4.26/4.48 inference(modus_ponens,[status(thm)],[341, 331])).
% 4.26/4.48 tff(343,plain,
% 4.26/4.48 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2)))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2)))),
% 4.26/4.48 inference(rewrite,[status(thm)],[])).
% 4.26/4.48 tff(344,plain,
% 4.26/4.48 ((m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2)) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) <=> ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2)))),
% 4.26/4.48 inference(rewrite,[status(thm)],[])).
% 4.26/4.48 tff(345,plain,
% 4.26/4.48 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2)) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))))),
% 4.26/4.48 inference(monotonicity,[status(thm)],[344])).
% 4.26/4.48 tff(346,plain,
% 4.26/4.48 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2)) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2)))),
% 4.26/4.48 inference(transitivity,[status(thm)],[345, 343])).
% 4.26/4.48 tff(347,plain,
% 4.26/4.48 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2)) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))),
% 4.26/4.48 inference(quant_inst,[status(thm)],[])).
% 4.26/4.48 tff(348,plain,
% 4.26/4.48 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))),
% 4.26/4.48 inference(modus_ponens,[status(thm)],[347, 346])).
% 4.26/4.48 tff(349,plain,
% 4.26/4.48 (m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))),
% 4.26/4.48 inference(unit_resolution,[status(thm)],[348, 220, 228, 342])).
% 4.26/4.48 tff(350,plain,
% 4.26/4.48 (((~![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(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))) | (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), 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(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))) | (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)))),
% 4.26/4.48 inference(rewrite,[status(thm)],[])).
% 4.26/4.48 tff(351,plain,
% 4.26/4.48 (((k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2)))) <=> ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))) | (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)))),
% 4.26/4.49 inference(rewrite,[status(thm)],[])).
% 4.26/4.49 tff(352,plain,
% 4.26/4.49 (((~![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, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k4_subset_1(A!2, C!0, D!3), 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(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))) | (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4))))),
% 4.26/4.49 inference(monotonicity,[status(thm)],[351])).
% 4.26/4.49 tff(353,plain,
% 4.26/4.49 (((~![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, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k4_subset_1(A!2, C!0, D!3), 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(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))) | (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)))),
% 4.26/4.49 inference(transitivity,[status(thm)],[352, 350])).
% 4.26/4.49 tff(354,plain,
% 4.26/4.49 ((~![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, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))))),
% 4.26/4.49 inference(quant_inst,[status(thm)],[])).
% 4.26/4.49 tff(355,plain,
% 4.26/4.49 ((~![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(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))) | (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4))),
% 4.26/4.49 inference(modus_ponens,[status(thm)],[354, 353])).
% 4.26/4.49 tff(356,plain,
% 4.26/4.49 (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)),
% 4.26/4.49 inference(unit_resolution,[status(thm)],[355, 21, 270, 349])).
% 4.26/4.49 tff(357,plain,
% 4.26/4.49 (k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)),
% 4.26/4.49 inference(symmetry,[status(thm)],[356])).
% 4.26/4.49 tff(358,plain,
% 4.26/4.49 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3)))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3)))),
% 4.26/4.49 inference(rewrite,[status(thm)],[])).
% 4.26/4.49 tff(359,plain,
% 4.26/4.49 (((k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) <=> ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3)))),
% 4.26/4.49 inference(rewrite,[status(thm)],[])).
% 4.26/4.49 tff(360,plain,
% 4.26/4.49 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3))))),
% 4.26/4.49 inference(monotonicity,[status(thm)],[359])).
% 4.26/4.49 tff(361,plain,
% 4.26/4.49 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3)))),
% 4.26/4.49 inference(transitivity,[status(thm)],[360, 358])).
% 4.26/4.49 tff(362,plain,
% 4.26/4.49 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | ((k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))),
% 4.26/4.49 inference(quant_inst,[status(thm)],[])).
% 4.26/4.49 tff(363,plain,
% 4.26/4.49 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(A!2))) | (k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3))),
% 4.26/4.49 inference(modus_ponens,[status(thm)],[362, 361])).
% 4.26/4.49 tff(364,plain,
% 4.26/4.49 (k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3)),
% 4.26/4.49 inference(unit_resolution,[status(thm)],[363, 220, 228, 124])).
% 4.26/4.49 tff(365,plain,
% 4.26/4.49 (k2_xboole_0(C!0, D!3) = k4_subset_1(A!2, C!0, D!3)),
% 4.26/4.49 inference(symmetry,[status(thm)],[364])).
% 4.26/4.49 tff(366,plain,
% 4.26/4.49 (k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)),
% 4.26/4.49 inference(monotonicity,[status(thm)],[365])).
% 4.26/4.49 tff(367,plain,
% 4.26/4.49 (m1_subset_1(k2_xboole_0(C!0, D!3), k1_zfmisc_1(A!2)) <=> m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))),
% 4.26/4.49 inference(monotonicity,[status(thm)],[365])).
% 4.26/4.49 tff(368,plain,
% 4.26/4.49 (m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2)) <=> m1_subset_1(k2_xboole_0(C!0, D!3), k1_zfmisc_1(A!2))),
% 4.26/4.49 inference(symmetry,[status(thm)],[367])).
% 4.26/4.49 tff(369,plain,
% 4.26/4.49 (m1_subset_1(k2_xboole_0(C!0, D!3), k1_zfmisc_1(A!2))),
% 4.26/4.49 inference(modus_ponens,[status(thm)],[349, 368])).
% 4.26/4.49 tff(370,plain,
% 4.26/4.49 (((~![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(k2_xboole_0(C!0, D!3), 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, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3)))))))) <=> ((~![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(k2_xboole_0(C!0, D!3), 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, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3)))))))),
% 4.26/4.49 inference(rewrite,[status(thm)],[])).
% 4.26/4.49 tff(371,plain,
% 4.26/4.49 ((~![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(k2_xboole_0(C!0, D!3), 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, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3)))))))),
% 4.26/4.49 inference(quant_inst,[status(thm)],[])).
% 4.26/4.49 tff(372,plain,
% 4.26/4.49 ((~![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(k2_xboole_0(C!0, D!3), 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, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3))))))),
% 4.26/4.49 inference(modus_ponens,[status(thm)],[371, 370])).
% 4.26/4.49 tff(373,plain,
% 4.26/4.49 ((~m1_subset_1(k2_xboole_0(C!0, D!3), 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, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3))))))),
% 4.26/4.49 inference(unit_resolution,[status(thm)],[372, 291])).
% 4.26/4.49 tff(374,plain,
% 4.26/4.49 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3))))))),
% 4.26/4.49 inference(unit_resolution,[status(thm)],[373, 369])).
% 4.26/4.49 tff(375,plain,
% 4.26/4.49 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3))))))),
% 4.26/4.49 inference(rewrite,[status(thm)],[])).
% 4.26/4.49 tff(376,plain,
% 4.26/4.49 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3))))))),
% 4.26/4.49 inference(quant_inst,[status(thm)],[])).
% 4.26/4.49 tff(377,plain,
% 4.26/4.49 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3)))))),
% 4.26/4.49 inference(modus_ponens,[status(thm)],[376, 375])).
% 4.26/4.49 tff(378,plain,
% 4.26/4.49 (k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), 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(k2_xboole_0(C!0, D!3))))),
% 4.26/4.49 inference(unit_resolution,[status(thm)],[377, 21, 374])).
% 4.26/4.49 tff(379,plain,
% 4.26/4.49 (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(k2_xboole_0(C!0, D!3)))) = k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), E!4)),
% 4.26/4.49 inference(symmetry,[status(thm)],[378])).
% 4.26/4.49 tff(380,plain,
% 4.26/4.49 (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(k2_xboole_0(C!0, D!3)))) = k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)),
% 4.26/4.49 inference(transitivity,[status(thm)],[379, 366, 357])).
% 4.26/4.49 tff(381,plain,
% 4.26/4.49 ((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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))) <=> (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)))),
% 4.26/4.49 inference(monotonicity,[status(thm)],[380, 329])).
% 4.26/4.49 tff(382,plain,
% 4.26/4.49 ((k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, 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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))))),
% 4.26/4.49 inference(symmetry,[status(thm)],[381])).
% 4.26/4.49 tff(383,plain,
% 4.26/4.49 ((~(k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, 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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))))),
% 4.26/4.49 inference(monotonicity,[status(thm)],[382])).
% 4.26/4.49 tff(384,plain,
% 4.26/4.49 (~(k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k5_subset_1(B!1, k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, D!3, E!4)))),
% 4.26/4.49 inference(or_elim,[status(thm)],[20])).
% 4.26/4.49 tff(385,plain,
% 4.26/4.49 (~(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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))))),
% 4.26/4.49 inference(modus_ponens,[status(thm)],[384, 383])).
% 4.26/4.49 tff(386,plain,
% 4.26/4.49 (m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1))) <=> m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.49 inference(monotonicity,[status(thm)],[205])).
% 4.26/4.49 tff(387,plain,
% 4.26/4.49 (m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1))) <=> m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.49 inference(symmetry,[status(thm)],[386])).
% 4.26/4.49 tff(388,plain,
% 4.26/4.49 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1))))),
% 4.26/4.49 inference(rewrite,[status(thm)],[])).
% 4.26/4.49 tff(389,plain,
% 4.26/4.49 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | ((~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1))))),
% 4.26/4.49 inference(quant_inst,[status(thm)],[])).
% 4.26/4.49 tff(390,plain,
% 4.26/4.49 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_zfmisc_1(B))))) | m1_subset_1(k4_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))) | (~m1_subset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))) | m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.49 inference(modus_ponens,[status(thm)],[389, 388])).
% 4.26/4.49 tff(391,plain,
% 4.26/4.49 (m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.49 inference(unit_resolution,[status(thm)],[390, 91, 63])).
% 4.26/4.49 tff(392,plain,
% 4.26/4.49 (m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))),
% 4.26/4.49 inference(modus_ponens,[status(thm)],[391, 387])).
% 4.26/4.49 tff(393,plain,
% 4.26/4.49 (^[A: $i, B: $i] : refl(((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))))),
% 4.26/4.49 inference(bind,[status(th)],[])).
% 4.26/4.49 tff(394,plain,
% 4.26/4.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))),
% 4.26/4.49 inference(quant_intro,[status(thm)],[393])).
% 4.26/4.49 tff(395,plain,
% 4.26/4.49 (^[A: $i, B: $i] : rewrite(((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))))),
% 4.26/4.49 inference(bind,[status(th)],[])).
% 4.26/4.49 tff(396,plain,
% 4.26/4.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))),
% 4.26/4.49 inference(quant_intro,[status(thm)],[395])).
% 4.26/4.49 tff(397,plain,
% 4.26/4.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))),
% 4.26/4.49 inference(transitivity,[status(thm)],[396, 394])).
% 4.26/4.49 tff(398,plain,
% 4.26/4.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))),
% 4.26/4.49 inference(rewrite,[status(thm)],[])).
% 4.26/4.49 tff(399,plain,
% 4.26/4.49 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((B = k4_subset_1(k1_zfmisc_1(A), C, D)) => (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D)))) <=> ((~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))))), ((m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((B = k4_subset_1(k1_zfmisc_1(A), C, D)) => (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))))) <=> (m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))))))), rewrite((m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))))) <=> ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))), ((m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((B = k4_subset_1(k1_zfmisc_1(A), C, D)) => (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))))) <=> ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((B = k4_subset_1(k1_zfmisc_1(A), C, D)) => (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))))) <=> ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))), ((m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((B = k4_subset_1(k1_zfmisc_1(A), C, D)) => (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D)))))) <=> (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))), ((m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((B = k4_subset_1(k1_zfmisc_1(A), C, D)) => (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((B = k4_subset_1(k1_zfmisc_1(A), C, D)) => (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D)))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))), ((m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((B = k4_subset_1(k1_zfmisc_1(A), C, D)) => (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))))))) <=> (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))), ((m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((B = k4_subset_1(k1_zfmisc_1(A), C, D)) => (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))))),
% 4.26/4.49 inference(bind,[status(th)],[])).
% 4.26/4.49 tff(400,plain,
% 4.26/4.49 (![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((B = k4_subset_1(k1_zfmisc_1(A), C, D)) => (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))),
% 4.34/4.49 inference(quant_intro,[status(thm)],[399])).
% 4.34/4.49 tff(401,axiom,(![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))) => ((B = k4_subset_1(k1_zfmisc_1(A), C, D)) => (k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_mssubfam')).
% 4.34/4.49 tff(402,plain,
% 4.34/4.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))),
% 4.34/4.49 inference(modus_ponens,[status(thm)],[401, 400])).
% 4.34/4.49 tff(403,plain,
% 4.34/4.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))),
% 4.34/4.49 inference(modus_ponens,[status(thm)],[402, 398])).
% 4.34/4.49 tff(404,plain,(
% 4.34/4.49 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))),
% 4.34/4.49 inference(skolemize,[status(sab)],[403])).
% 4.34/4.49 tff(405,plain,
% 4.34/4.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))),
% 4.34/4.49 inference(modus_ponens,[status(thm)],[404, 397])).
% 4.34/4.49 tff(406,plain,
% 4.34/4.49 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))) | ((~m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D))))))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))) | (~m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D))))))),
% 4.34/4.50 inference(rewrite,[status(thm)],[])).
% 4.34/4.50 tff(407,plain,
% 4.34/4.50 (((~m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!1))))))) <=> ((~m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D))))))),
% 4.34/4.50 inference(rewrite,[status(thm)],[])).
% 4.34/4.50 tff(408,plain,
% 4.34/4.50 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))) | ((~m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!1)))))))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))) | ((~m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D)))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[407])).
% 4.34/4.50 tff(409,plain,
% 4.34/4.50 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))) | ((~m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!1)))))))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))) | (~m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D))))))),
% 4.34/4.50 inference(transitivity,[status(thm)],[408, 406])).
% 4.34/4.50 tff(410,plain,
% 4.34/4.50 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))) | ((~m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!1)))))))),
% 4.34/4.50 inference(quant_inst,[status(thm)],[])).
% 4.34/4.50 tff(411,plain,
% 4.34/4.50 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((k8_setfam_1(A, B) = k5_subset_1(A, k8_setfam_1(A, C), k8_setfam_1(A, D))) | (~(B = k4_subset_1(k1_zfmisc_1(A), C, D))) | (~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A)))))))) | (~m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D)))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[410, 409])).
% 4.34/4.50 tff(412,plain,
% 4.34/4.50 ((~m1_subset_1(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D)))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[411, 405])).
% 4.34/4.50 tff(413,plain,
% 4.34/4.50 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D)))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[412, 392])).
% 4.34/4.50 tff(414,plain,
% 4.34/4.50 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D)))))) | ((~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), D)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D)))))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), D)))))),
% 4.34/4.50 inference(rewrite,[status(thm)],[])).
% 4.34/4.50 tff(415,plain,
% 4.34/4.50 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D)))))) | ((~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), D)))))),
% 4.34/4.50 inference(quant_inst,[status(thm)],[])).
% 4.34/4.50 tff(416,plain,
% 4.34/4.50 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, C), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), C, D)))))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_zfmisc_1(k1_zfmisc_1(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), D))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[415, 414])).
% 4.34/4.50 tff(417,plain,
% 4.34/4.50 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), D))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[416, 97, 413])).
% 4.34/4.50 tff(418,plain,
% 4.34/4.50 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), D))))) | ((~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), D))))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))))),
% 4.34/4.50 inference(rewrite,[status(thm)],[])).
% 4.34/4.50 tff(419,plain,
% 4.34/4.50 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), D))))) | ((~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))))),
% 4.34/4.52 inference(quant_inst,[status(thm)],[])).
% 4.34/4.52 tff(420,plain,
% 4.34/4.52 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, D))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), D))))) | (~m1_subset_1(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)), k1_zfmisc_1(k1_zfmisc_1(B!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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))))),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[419, 418])).
% 4.34/4.52 tff(421,plain,
% 4.34/4.52 ((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(k2_xboole_0(C!0, D!3)))) = k5_subset_1(B!1, k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))), k8_setfam_1(B!1, k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[420, 111, 417])).
% 4.34/4.52 tff(422,plain,
% 4.34/4.52 (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3))) = k4_subset_1(k1_zfmisc_1(B!1), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[421, 385])).
% 4.34/4.52 tff(423,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[422, 206])).
% 4.34/4.52 % SZS output end Proof
% 4.34/4.53 % E exiting
%------------------------------------------------------------------------------