%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU427+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU427+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 07:16:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(k8_relset_2_type, type, (
% 0.19/0.46 k8_relset_2: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.46 tff(tptp_fun_E_4_type, type, (
% 0.19/0.46 tptp_fun_E_4: $i)).
% 0.19/0.46 tff(tptp_fun_D_3_type, type, (
% 0.19/0.46 tptp_fun_D_3: $i)).
% 0.19/0.46 tff(tptp_fun_B_1_type, type, (
% 0.19/0.46 tptp_fun_B_1: $i)).
% 0.19/0.46 tff(tptp_fun_A_2_type, type, (
% 0.19/0.46 tptp_fun_A_2: $i)).
% 0.19/0.46 tff(k4_subset_1_type, type, (
% 0.19/0.46 k4_subset_1: ( $i * $i * $i ) > $i)).
% 0.19/0.46 tff(tptp_fun_C_0_type, type, (
% 0.19/0.46 tptp_fun_C_0: $i)).
% 0.19/0.46 tff(k7_relset_2_type, type, (
% 0.19/0.46 k7_relset_2: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.46 tff(m1_subset_1_type, type, (
% 0.19/0.46 m1_subset_1: ( $i * $i ) > $o)).
% 0.19/0.46 tff(k1_zfmisc_1_type, type, (
% 0.19/0.46 k1_zfmisc_1: $i > $i)).
% 0.19/0.46 tff(k2_zfmisc_1_type, type, (
% 0.19/0.46 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.19/0.46 tff(k1_xboole_0_type, type, (
% 0.19/0.46 k1_xboole_0: $i)).
% 0.19/0.46 tff(k4_relset_2_type, type, (
% 0.19/0.46 k4_relset_2: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.46 tff(k3_pua2mss1_type, type, (
% 0.19/0.46 k3_pua2mss1: $i > $i)).
% 0.19/0.46 tff(k6_relset_2_type, type, (
% 0.19/0.46 k6_relset_2: ( $i * $i * $i ) > $i)).
% 0.19/0.46 tff(k8_setfam_1_type, type, (
% 0.19/0.46 k8_setfam_1: ( $i * $i ) > $i)).
% 0.19/0.46 tff(k2_xboole_0_type, type, (
% 0.19/0.46 k2_xboole_0: ( $i * $i ) > $i)).
% 0.19/0.46 tff(k5_relset_2_type, type, (
% 0.19/0.46 k5_relset_2: ( $i * $i ) > $i)).
% 0.19/0.46 tff(k9_relat_1_type, type, (
% 0.19/0.46 k9_relat_1: ( $i * $i ) > $i)).
% 0.19/0.46 tff(m2_relset_1_type, type, (
% 0.19/0.46 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(v1_funct_2_type, type, (
% 0.19/0.46 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(v1_funct_1_type, type, (
% 0.19/0.46 v1_funct_1: $i > $o)).
% 0.19/0.46 tff(v1_relat_1_type, type, (
% 0.19/0.46 v1_relat_1: $i > $o)).
% 0.19/0.46 tff(1,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(2,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.46 tff(3,plain,
% 0.19/0.46 (^[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))))) | (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))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(4,plain,
% 0.19/0.46 (![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))))) | (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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.47 tff(5,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(6,plain,
% 0.19/0.47 (^[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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(7,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.47 tff(8,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')).
% 0.19/0.47 tff(9,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.47 tff(10,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.47 tff(11,plain,(
% 0.19/0.47 ![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)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[10])).
% 0.19/0.47 tff(12,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.47 tff(13,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.47 tff(14,plain,
% 0.19/0.47 ((m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(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) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~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(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) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(15,plain,
% 0.19/0.47 ((~((k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~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) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(16,plain,
% 0.19/0.47 ((m1_subset_1(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) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~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)) & (~((k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.47 tff(17,plain,
% 0.19/0.47 ((m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(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) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~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(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) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.47 tff(18,plain,
% 0.19/0.47 ((m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(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) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~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(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) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[17, 14])).
% 0.19/0.47 tff(19,plain,
% 0.19/0.47 ((~![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] : ((k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k8_relset_2(A, B, D, E)) | (~(k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, E), k3_pua2mss1(C)) = k1_xboole_0)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))) <=> (~![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] : ((k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k8_relset_2(A, B, D, E)) | (~(k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, E), k3_pua2mss1(C)) = k1_xboole_0)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(20,plain,
% 0.19/0.47 ((~![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))) => ((k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, E), k3_pua2mss1(C)) = k1_xboole_0) => (k8_relset_2(A, B, k4_subset_1(A, C, D), 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] : ((k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k8_relset_2(A, B, D, E)) | (~(k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, E), k3_pua2mss1(C)) = k1_xboole_0)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(21,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))) => ((k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, E), k3_pua2mss1(C)) = k1_xboole_0) => (k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k8_relset_2(A, B, D, E))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t26_relset_2')).
% 0.19/0.47 tff(22,plain,
% 0.19/0.47 (~![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] : ((k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k8_relset_2(A, B, D, E)) | (~(k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, E), k3_pua2mss1(C)) = k1_xboole_0)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.47 tff(23,plain,
% 0.19/0.47 (~![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] : ((k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k8_relset_2(A, B, D, E)) | (~(k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, E), k3_pua2mss1(C)) = k1_xboole_0)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.19/0.47 tff(24,plain,
% 0.19/0.47 (~![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] : ((k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k8_relset_2(A, B, D, E)) | (~(k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, E), k3_pua2mss1(C)) = k1_xboole_0)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.47 tff(25,plain,
% 0.19/0.47 (~![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] : ((k8_relset_2(A, B, k4_subset_1(A, C, D), E) = k8_relset_2(A, B, D, E)) | (~(k4_relset_2(k1_zfmisc_1(A), B, k6_relset_2(B, A, E), k3_pua2mss1(C)) = k1_xboole_0)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.19/0.47 tff(26,plain,
% 0.19/0.47 (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(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) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.47 tff(27,plain,
% 0.19/0.47 (~((k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k8_relset_2(A!2, B!1, D!3, E!4)) | (~(k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 0.19/0.47 inference(and_elim,[status(thm)],[26])).
% 0.19/0.47 tff(28,plain,
% 0.19/0.47 (m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 0.19/0.47 inference(or_elim,[status(thm)],[27])).
% 0.19/0.47 tff(29,plain,
% 0.19/0.47 (m1_subset_1(D!3, k1_zfmisc_1(A!2))),
% 0.19/0.47 inference(and_elim,[status(thm)],[26])).
% 0.19/0.47 tff(30,plain,
% 0.19/0.47 (((~![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(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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(31,plain,
% 0.19/0.47 (((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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 (((~![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, 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))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.47 tff(33,plain,
% 0.19/0.47 (((~![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, 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)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[32, 30])).
% 0.19/0.47 tff(34,plain,
% 0.19/0.47 ((~![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, 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))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 ((~![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(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))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.47 tff(36,plain,
% 0.19/0.47 (k8_relset_2(A!2, B!1, D!3, E!4) = k7_relset_2(A!2, B!1, D!3, E!4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[35, 29, 28, 13])).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 (k7_relset_2(A!2, B!1, D!3, E!4) = k8_relset_2(A!2, B!1, D!3, E!4)),
% 0.19/0.47 inference(symmetry,[status(thm)],[36])).
% 0.19/0.47 tff(38,plain,
% 0.19/0.47 (^[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)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 (^[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)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[41, 39])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (^[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))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.47 tff(46,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')).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.47 tff(48,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.47 tff(49,plain,(
% 0.19/0.47 ![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))))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[48])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 (((~![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(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))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(52,plain,
% 0.19/0.47 ((~![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(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))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 ((~![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(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)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.48 tff(54,plain,
% 0.19/0.48 (![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)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[53, 29, 50])).
% 0.19/0.48 tff(55,plain,
% 0.19/0.48 (((~![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)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(56,plain,
% 0.19/0.48 ((~![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)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(57,plain,
% 0.19/0.48 ((~![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.48 tff(58,plain,
% 0.19/0.48 (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)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[57, 28, 54])).
% 0.19/0.48 tff(59,plain,
% 0.19/0.48 (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)),
% 0.19/0.48 inference(symmetry,[status(thm)],[58])).
% 0.19/0.48 tff(60,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(61,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.48 tff(62,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(63,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')).
% 0.19/0.48 tff(64,plain,
% 0.19/0.48 (![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.48 tff(65,plain,(
% 0.19/0.48 ![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[64])).
% 0.19/0.48 tff(66,plain,
% 0.19/0.48 (![A: $i, B: $i] : (k3_pua2mss1(k2_xboole_0(A, B)) = k2_xboole_0(k3_pua2mss1(A), k3_pua2mss1(B)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.19/0.48 tff(67,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(68,plain,
% 0.19/0.48 (k3_pua2mss1(k2_xboole_0(C!0, D!3)) = k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.48 tff(69,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(70,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.48 tff(71,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(72,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(73,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.48 tff(74,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')).
% 0.19/0.48 tff(75,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.48 tff(76,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.19/0.48 tff(77,plain,(
% 0.19/0.48 ![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)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[76])).
% 0.19/0.48 tff(78,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.19/0.48 tff(79,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(80,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(81,plain,
% 0.19/0.48 ((~![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))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.48 tff(82,plain,
% 0.19/0.48 (k6_relset_2(B!1, A!2, E!4) = k5_relset_2(A!2, E!4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[81, 28, 78])).
% 0.19/0.48 tff(83,plain,
% 0.19/0.48 (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)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[82, 68])).
% 0.19/0.48 tff(84,plain,
% 0.19/0.48 (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))) = 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)))),
% 0.19/0.48 inference(symmetry,[status(thm)],[83])).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 (k5_relset_2(A!2, E!4) = k6_relset_2(B!1, A!2, E!4)),
% 0.19/0.48 inference(symmetry,[status(thm)],[82])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (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))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 (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))),
% 0.19/0.48 inference(symmetry,[status(thm)],[86])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 (^[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))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.48 tff(95,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')).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.48 tff(98,plain,(
% 0.19/0.48 ![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))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[97])).
% 0.19/0.48 tff(99,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 (((~![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))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 ((~![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))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 ((~![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)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 (~((~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))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[103, 28, 100])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 (((~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))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 (m2_relset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (m2_relset_1(k5_relset_2(A!2, E!4), k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[106, 87])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.48 tff(113,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')).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.19/0.48 tff(116,plain,(
% 0.19/0.48 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[115])).
% 0.19/0.48 tff(117,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 (((~![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)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 ((~![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)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 ((~![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 ((~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))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.19/0.48 tff(122,plain,
% 0.19/0.48 (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))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[121, 107])).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(124,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.48 tff(125,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(126,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.48 tff(128,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')).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.48 tff(130,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.19/0.48 tff(131,plain,(
% 0.19/0.48 ![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)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[130])).
% 0.19/0.48 tff(132,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.19/0.48 tff(133,plain,
% 0.19/0.48 (((~![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)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(134,plain,
% 0.19/0.48 ((~![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)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(135,plain,
% 0.19/0.48 ((~![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.48 tff(136,plain,
% 0.19/0.48 (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)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[135, 132, 122])).
% 0.19/0.48 tff(137,plain,
% 0.19/0.48 (k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(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)))),
% 0.19/0.48 inference(symmetry,[status(thm)],[136])).
% 0.19/0.48 tff(138,plain,
% 0.19/0.48 (^[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)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(139,plain,
% 0.19/0.48 (![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))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.48 tff(140,plain,
% 0.19/0.48 (![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))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(141,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')).
% 0.19/0.48 tff(142,plain,
% 0.19/0.48 (![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.48 tff(143,plain,(
% 0.19/0.48 ![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 0.19/0.48 inference(skolemize,[status(sab)],[142])).
% 0.19/0.48 tff(144,plain,
% 0.19/0.48 (![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.19/0.48 tff(145,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(146,plain,
% 0.19/0.48 (k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3)) = k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.19/0.48 tff(147,plain,
% 0.19/0.48 (k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0)) = k2_xboole_0(k3_pua2mss1(C!0), k3_pua2mss1(D!3))),
% 0.19/0.48 inference(symmetry,[status(thm)],[146])).
% 0.19/0.48 tff(148,plain,
% 0.19/0.48 (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)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[147])).
% 0.19/0.48 tff(149,plain,
% 0.19/0.48 (^[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))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(150,plain,
% 0.19/0.48 (![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)))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[149])).
% 0.19/0.48 tff(151,plain,
% 0.19/0.48 (![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)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(152,plain,
% 0.19/0.49 (^[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))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(153,plain,
% 0.19/0.49 (![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)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[152])).
% 0.19/0.49 tff(154,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')).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.49 tff(156,plain,
% 0.19/0.49 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.19/0.49 tff(157,plain,(
% 0.19/0.49 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[156])).
% 0.19/0.49 tff(158,plain,
% 0.19/0.49 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.19/0.49 tff(159,plain,
% 0.19/0.49 (((~![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)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(160,plain,
% 0.19/0.49 ((~![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)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(161,plain,
% 0.19/0.49 ((~![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.49 tff(162,plain,
% 0.19/0.49 (v1_relat_1(E!4)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[161, 28, 158])).
% 0.19/0.49 tff(163,plain,
% 0.19/0.49 (^[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)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(164,plain,
% 0.19/0.49 (![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))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[163])).
% 0.19/0.49 tff(165,plain,
% 0.19/0.49 (^[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)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(166,plain,
% 0.19/0.49 (![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))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[165])).
% 0.19/0.49 tff(167,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(168,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(169,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[168])).
% 0.19/0.49 tff(170,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')).
% 0.19/0.49 tff(171,plain,
% 0.19/0.49 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.19/0.49 tff(172,plain,
% 0.19/0.49 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.19/0.49 tff(173,plain,(
% 0.19/0.49 ![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[172])).
% 0.19/0.49 tff(174,plain,
% 0.19/0.49 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.19/0.49 tff(175,plain,
% 0.19/0.49 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[174, 164])).
% 0.19/0.49 tff(176,plain,
% 0.19/0.49 (((~![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))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(177,plain,
% 0.19/0.49 ((~![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))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(178,plain,
% 0.19/0.49 ((~![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)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.49 tff(179,plain,
% 0.19/0.49 (~((~v1_relat_1(k5_relset_2(A!2, E!4))) | (~v1_funct_1(k5_relset_2(A!2, E!4))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[178, 175, 162])).
% 0.19/0.49 tff(180,plain,
% 0.19/0.49 (((~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))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(181,plain,
% 0.19/0.49 (v1_relat_1(k5_relset_2(A!2, E!4))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.19/0.49 tff(182,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(183,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[182])).
% 0.19/0.49 tff(184,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(185,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(186,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[185])).
% 0.19/0.49 tff(187,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')).
% 0.19/0.49 tff(188,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.49 tff(189,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.19/0.49 tff(190,plain,(
% 0.19/0.49 ![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))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[189])).
% 0.19/0.49 tff(191,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[190, 183])).
% 0.19/0.49 tff(192,plain,
% 0.19/0.49 (((~![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)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(193,plain,
% 0.19/0.49 ((~![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)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(194,plain,
% 0.19/0.49 ((~![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.19/0.49 tff(195,plain,
% 0.19/0.49 (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)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[194, 191, 181])).
% 0.19/0.49 tff(196,plain,
% 0.19/0.49 (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))) = k9_relat_1(k5_relset_2(A!2, E!4), k2_xboole_0(k3_pua2mss1(D!3), k3_pua2mss1(C!0)))),
% 0.19/0.49 inference(symmetry,[status(thm)],[195])).
% 0.19/0.49 tff(197,plain,
% 0.19/0.49 (k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.49 tff(198,plain,
% 0.19/0.49 (k9_relat_1(k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))),
% 0.19/0.49 inference(symmetry,[status(thm)],[197])).
% 0.19/0.49 tff(199,plain,
% 0.19/0.49 (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(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.49 tff(200,plain,
% 0.19/0.49 (m1_subset_1(k6_relset_2(B!1, A!2, E!4), k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A!2), k1_zfmisc_1(B!1))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[122, 199])).
% 0.19/0.49 tff(201,plain,
% 0.19/0.49 (((~![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(k6_relset_2(B!1, 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, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k6_relset_2(B!1, 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(k6_relset_2(B!1, 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, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(202,plain,
% 0.19/0.49 ((~![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(k6_relset_2(B!1, 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, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(203,plain,
% 0.19/0.49 ((~![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(k6_relset_2(B!1, 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, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.19/0.49 tff(204,plain,
% 0.19/0.49 ((~m1_subset_1(k6_relset_2(B!1, 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, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[203, 132])).
% 0.19/0.49 tff(205,plain,
% 0.19/0.49 (k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k9_relat_1(k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[204, 200])).
% 0.19/0.49 tff(206,plain,
% 0.19/0.49 (k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0)) = k1_xboole_0),
% 0.19/0.49 inference(or_elim,[status(thm)],[27])).
% 0.19/0.49 tff(207,plain,
% 0.19/0.49 (k1_xboole_0 = k4_relset_2(k1_zfmisc_1(A!2), B!1, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(C!0))),
% 0.19/0.49 inference(symmetry,[status(thm)],[206])).
% 0.19/0.49 tff(208,plain,
% 0.19/0.49 (k1_xboole_0 = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(C!0))),
% 0.19/0.49 inference(transitivity,[status(thm)],[207, 205, 198])).
% 0.19/0.49 tff(209,plain,
% 0.19/0.49 (k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_xboole_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)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[208])).
% 0.19/0.49 tff(210,plain,
% 0.19/0.49 (^[A: $i] : refl((k2_xboole_0(A, k1_xboole_0) = A) <=> (k2_xboole_0(A, k1_xboole_0) = A))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(211,plain,
% 0.19/0.49 (![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A) <=> ![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)),
% 0.19/0.49 inference(quant_intro,[status(thm)],[210])).
% 0.19/0.49 tff(212,plain,
% 0.19/0.49 (![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A) <=> ![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(213,axiom,(![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_boole')).
% 0.19/0.49 tff(214,plain,
% 0.19/0.49 (![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.49 tff(215,plain,(
% 0.19/0.49 ![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)),
% 0.19/0.49 inference(skolemize,[status(sab)],[214])).
% 0.19/0.49 tff(216,plain,
% 0.19/0.49 (![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.19/0.49 tff(217,plain,
% 0.19/0.49 ((~![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)) | (k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_xboole_0) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(218,plain,
% 0.19/0.49 (k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_xboole_0) = k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.19/0.49 tff(219,plain,
% 0.19/0.49 (k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)) = k2_xboole_0(k9_relat_1(k5_relset_2(A!2, E!4), k3_pua2mss1(D!3)), k1_xboole_0)),
% 0.19/0.49 inference(symmetry,[status(thm)],[218])).
% 0.19/0.49 tff(220,plain,
% 0.19/0.49 (((~![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))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(221,plain,
% 0.19/0.49 ((~![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))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(222,plain,
% 0.19/0.49 ((~![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)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.19/0.49 tff(223,plain,
% 0.19/0.49 ((~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)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[222, 132])).
% 0.19/0.49 tff(224,plain,
% 0.19/0.49 (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))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[223, 122])).
% 0.19/0.49 tff(225,plain,
% 0.19/0.49 (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))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.49 tff(226,plain,
% 0.19/0.49 (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, k6_relset_2(B!1, A!2, E!4), k3_pua2mss1(k2_xboole_0(C!0, D!3)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[225, 224, 219, 209, 196, 148, 137, 84])).
% 0.19/0.49 tff(227,plain,
% 0.19/0.49 (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(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(k2_xboole_0(C!0, D!3))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[226])).
% 0.19/0.49 tff(228,plain,
% 0.19/0.49 (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_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)))),
% 0.19/0.49 inference(symmetry,[status(thm)],[227])).
% 0.19/0.49 tff(229,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(230,plain,
% 0.19/0.49 (![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)))) <=> ![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))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[229])).
% 0.19/0.49 tff(231,plain,
% 0.19/0.49 (^[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))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(232,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[231])).
% 0.19/0.49 tff(233,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(234,plain,
% 0.19/0.49 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(235,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[234])).
% 0.19/0.49 tff(236,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')).
% 0.19/0.49 tff(237,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.19/0.49 tff(238,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[237, 233])).
% 0.19/0.49 tff(239,plain,(
% 0.19/0.49 ![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)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[238])).
% 0.19/0.49 tff(240,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[239, 232])).
% 0.19/0.49 tff(241,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[240, 230])).
% 0.19/0.49 tff(242,plain,
% 0.19/0.49 (m1_subset_1(C!0, k1_zfmisc_1(A!2))),
% 0.19/0.49 inference(and_elim,[status(thm)],[26])).
% 0.19/0.49 tff(243,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(244,plain,
% 0.19/0.50 (((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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(245,plain,
% 0.19/0.50 (((~![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))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[244])).
% 0.19/0.50 tff(246,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[245, 243])).
% 0.19/0.50 tff(247,plain,
% 0.19/0.50 ((~![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))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(248,plain,
% 0.19/0.50 ((~![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))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.19/0.50 tff(249,plain,
% 0.19/0.50 (k4_subset_1(A!2, C!0, D!3) = k2_xboole_0(C!0, D!3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[248, 242, 29, 241])).
% 0.19/0.50 tff(250,plain,
% 0.19/0.50 (k2_xboole_0(C!0, D!3) = k4_subset_1(A!2, C!0, D!3)),
% 0.19/0.50 inference(symmetry,[status(thm)],[249])).
% 0.19/0.50 tff(251,plain,
% 0.19/0.50 (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))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.50 tff(252,plain,
% 0.19/0.50 (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))),
% 0.19/0.50 inference(symmetry,[status(thm)],[251])).
% 0.19/0.50 tff(253,plain,
% 0.19/0.50 (^[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)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(254,plain,
% 0.19/0.50 (![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))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[253])).
% 0.19/0.50 tff(255,plain,
% 0.19/0.50 (^[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))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(256,plain,
% 0.19/0.50 (![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))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[255])).
% 0.19/0.50 tff(257,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(258,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(259,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[258])).
% 0.19/0.50 tff(260,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')).
% 0.19/0.50 tff(261,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.19/0.50 tff(262,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[261, 257])).
% 0.19/0.50 tff(263,plain,(
% 0.19/0.50 ![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)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[262])).
% 0.19/0.50 tff(264,plain,
% 0.19/0.50 (![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))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[263, 256])).
% 0.19/0.50 tff(265,plain,
% 0.19/0.50 (![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))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[264, 254])).
% 0.19/0.50 tff(266,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(267,plain,
% 0.19/0.50 ((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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(268,plain,
% 0.19/0.50 (((~![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))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[267])).
% 0.19/0.50 tff(269,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[268, 266])).
% 0.19/0.50 tff(270,plain,
% 0.19/0.50 ((~![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))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(271,plain,
% 0.19/0.50 ((~![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))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.19/0.50 tff(272,plain,
% 0.19/0.50 (m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[271, 242, 29, 265])).
% 0.19/0.50 tff(273,plain,
% 0.19/0.50 (m1_subset_1(k2_xboole_0(C!0, D!3), k1_zfmisc_1(A!2))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[272, 252])).
% 0.19/0.50 tff(274,plain,
% 0.19/0.50 (((~![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)))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(275,plain,
% 0.19/0.50 ((~![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)))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(276,plain,
% 0.19/0.50 ((~![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))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.19/0.50 tff(277,plain,
% 0.19/0.50 ((~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))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[276, 50])).
% 0.19/0.50 tff(278,plain,
% 0.19/0.50 (![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))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[277, 273])).
% 0.19/0.50 tff(279,plain,
% 0.19/0.50 (((~![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))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(280,plain,
% 0.19/0.50 ((~![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))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(281,plain,
% 0.19/0.50 ((~![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)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.19/0.50 tff(282,plain,
% 0.19/0.50 (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))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[281, 28, 278])).
% 0.19/0.50 tff(283,plain,
% 0.19/0.50 (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)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.50 tff(284,plain,
% 0.19/0.50 (k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k2_xboole_0(C!0, D!3), E!4)),
% 0.19/0.50 inference(symmetry,[status(thm)],[283])).
% 0.19/0.50 tff(285,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(286,plain,
% 0.19/0.50 (((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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(287,plain,
% 0.19/0.50 (((~![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))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[286])).
% 0.19/0.51 tff(288,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[287, 285])).
% 0.19/0.51 tff(289,plain,
% 0.19/0.51 ((~![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))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(290,plain,
% 0.19/0.51 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k4_subset_1(A!2, C!0, D!3), k1_zfmisc_1(A!2))) | (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.19/0.51 tff(291,plain,
% 0.19/0.51 (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k7_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[290, 28, 13, 272])).
% 0.19/0.51 tff(292,plain,
% 0.19/0.51 (k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k8_relset_2(A!2, B!1, D!3, E!4)),
% 0.19/0.51 inference(transitivity,[status(thm)],[291, 284, 282, 228, 59, 37])).
% 0.19/0.51 tff(293,plain,
% 0.19/0.51 (~(k8_relset_2(A!2, B!1, k4_subset_1(A!2, C!0, D!3), E!4) = k8_relset_2(A!2, B!1, D!3, E!4))),
% 0.19/0.51 inference(or_elim,[status(thm)],[27])).
% 0.19/0.51 tff(294,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[293, 292])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------