%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU429+3 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:27:55 AM UTC 2025
% Result : Theorem 214.39s 214.66s
% Output : Proof 216.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU429+3 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 07:16:36 EDT 2025
% 0.12/0.34 % CPUTime :
% 214.39/214.66 % SZS status Theorem
% 214.39/214.66 % SZS output start Proof
% 214.39/214.66 tff(m1_subset_1_type, type, (
% 214.39/214.66 m1_subset_1: ( $i * $i ) > $o)).
% 214.39/214.66 tff(k1_zfmisc_1_type, type, (
% 214.39/214.66 k1_zfmisc_1: $i > $i)).
% 214.39/214.66 tff(tptp_fun_B_6304_type, type, (
% 214.39/214.66 tptp_fun_B_6304: $i)).
% 214.39/214.66 tff(a_4_1_relset_2_type, type, (
% 214.39/214.66 a_4_1_relset_2: ( $i * $i * $i * $i ) > $i)).
% 214.39/214.66 tff(tptp_fun_D_6305_type, type, (
% 214.39/214.66 tptp_fun_D_6305: $i)).
% 214.39/214.66 tff(tptp_fun_C_6303_type, type, (
% 214.39/214.66 tptp_fun_C_6303: $i)).
% 214.39/214.66 tff(tptp_fun_A_6302_type, type, (
% 214.39/214.66 tptp_fun_A_6302: $i)).
% 214.39/214.66 tff(m2_relset_1_type, type, (
% 214.39/214.66 m2_relset_1: ( $i * $i * $i ) > $o)).
% 214.39/214.66 tff(v1_xboole_0_type, type, (
% 214.39/214.66 v1_xboole_0: $i > $o)).
% 214.39/214.66 tff(1,plain,
% 214.39/214.66 (((~v1_xboole_0(A!6302)) & (m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302))) & (~((~m2_relset_1(D!6305, A!6302, B!6304)) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304))))))) <=> ((~v1_xboole_0(A!6302)) & m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302))) & (~((~m2_relset_1(D!6305, A!6302, B!6304)) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304))))))),
% 214.39/214.66 inference(rewrite,[status(thm)],[])).
% 214.39/214.66 tff(2,plain,
% 214.39/214.66 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))))),
% 214.39/214.66 inference(rewrite,[status(thm)],[])).
% 214.39/214.66 tff(3,plain,
% 214.39/214.66 ((~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : (m2_relset_1(D, A, B) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))))),
% 214.39/214.66 inference(rewrite,[status(thm)],[])).
% 214.39/214.66 tff(4,axiom,(~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : (m2_relset_1(D, A, B) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_relset_2')).
% 214.39/214.66 tff(5,plain,
% 214.39/214.66 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 214.39/214.66 inference(modus_ponens,[status(thm)],[4, 3])).
% 214.39/214.66 tff(6,plain,
% 214.39/214.66 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 214.39/214.66 inference(modus_ponens,[status(thm)],[5, 2])).
% 214.39/214.66 tff(7,plain,
% 214.39/214.66 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 214.39/214.66 inference(modus_ponens,[status(thm)],[6, 2])).
% 214.39/214.66 tff(8,plain,
% 214.39/214.66 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 214.39/214.66 inference(modus_ponens,[status(thm)],[7, 2])).
% 214.39/214.66 tff(9,plain,
% 214.39/214.66 ((~v1_xboole_0(A!6302)) & m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302))) & (~((~m2_relset_1(D!6305, A!6302, B!6304)) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304)))))),
% 214.39/214.66 inference(modus_ponens,[status(thm)],[8, 1])).
% 214.39/214.66 tff(10,plain,
% 214.39/214.66 (~((~m2_relset_1(D!6305, A!6302, B!6304)) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304))))),
% 214.39/214.66 inference(and_elim,[status(thm)],[9])).
% 214.39/214.66 tff(11,plain,
% 214.39/214.66 (~m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304)))),
% 214.39/214.66 inference(or_elim,[status(thm)],[10])).
% 214.39/214.66 tff(12,plain,
% 214.39/214.66 (m2_relset_1(D!6305, A!6302, B!6304)),
% 214.39/214.66 inference(or_elim,[status(thm)],[10])).
% 214.39/214.66 tff(13,plain,
% 214.39/214.66 (m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302)))),
% 214.39/214.66 inference(and_elim,[status(thm)],[9])).
% 214.39/214.66 tff(14,plain,
% 214.39/214.66 (~v1_xboole_0(A!6302)),
% 214.39/214.66 inference(and_elim,[status(thm)],[9])).
% 214.39/214.66 tff(15,plain,
% 214.39/214.66 (^[A: $i, B: $i, C: $i, D: $i] : refl((v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))) <=> (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))))),
% 214.39/214.66 inference(bind,[status(th)],[])).
% 214.39/214.66 tff(16,plain,
% 214.39/214.66 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 214.39/214.66 inference(quant_intro,[status(thm)],[15])).
% 214.39/214.66 tff(17,plain,
% 214.39/214.66 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) <=> (~(v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))))), ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) <=> (~(~(v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))))))), rewrite((~(~(v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))))) <=> (v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) <=> (v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))))), (((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))), rewrite(((v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))), (((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))))),
% 214.39/214.66 inference(bind,[status(th)],[])).
% 214.39/214.66 tff(18,plain,
% 214.39/214.66 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 214.39/214.66 inference(quant_intro,[status(thm)],[17])).
% 214.39/214.66 tff(19,plain,
% 214.39/214.66 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 214.39/214.66 inference(rewrite,[status(thm)],[])).
% 214.47/214.66 tff(20,plain,
% 214.47/214.66 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) & m2_relset_1(D, A, B)) <=> ((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))), (((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))), (((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 214.47/214.66 inference(bind,[status(th)],[])).
% 214.47/214.66 tff(21,plain,
% 214.47/214.66 (![A: $i, B: $i, C: $i, D: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 214.47/214.66 inference(quant_intro,[status(thm)],[20])).
% 214.47/214.66 tff(22,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s8_domain_1__e1_38__relset_2')).
% 214.47/214.66 tff(23,plain,
% 214.47/214.66 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 214.47/214.66 inference(modus_ponens,[status(thm)],[22, 21])).
% 214.47/214.66 tff(24,plain,
% 214.47/214.66 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 214.47/214.66 inference(modus_ponens,[status(thm)],[23, 19])).
% 214.47/214.66 tff(25,plain,(
% 214.47/214.66 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 214.47/214.66 inference(skolemize,[status(sab)],[24])).
% 214.47/214.66 tff(26,plain,
% 214.47/214.66 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 214.47/214.66 inference(modus_ponens,[status(thm)],[25, 18])).
% 214.47/214.66 tff(27,plain,
% 214.47/214.66 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 214.47/214.66 inference(modus_ponens,[status(thm)],[26, 16])).
% 214.47/214.66 tff(28,plain,
% 214.47/214.66 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | (v1_xboole_0(A!6302) | (~m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302)))) | (~m2_relset_1(D!6305, A!6302, B!6304)) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | v1_xboole_0(A!6302) | (~m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302)))) | (~m2_relset_1(D!6305, A!6302, B!6304)) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304))))),
% 216.08/216.30 inference(rewrite,[status(thm)],[])).
% 216.08/216.30 tff(29,plain,
% 216.08/216.30 ((v1_xboole_0(A!6302) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304))) | (~m2_relset_1(D!6305, A!6302, B!6304)) | (~m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302))))) <=> (v1_xboole_0(A!6302) | (~m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302)))) | (~m2_relset_1(D!6305, A!6302, B!6304)) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304))))),
% 216.08/216.30 inference(rewrite,[status(thm)],[])).
% 216.08/216.30 tff(30,plain,
% 216.08/216.30 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | (v1_xboole_0(A!6302) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304))) | (~m2_relset_1(D!6305, A!6302, B!6304)) | (~m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | (v1_xboole_0(A!6302) | (~m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302)))) | (~m2_relset_1(D!6305, A!6302, B!6304)) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304)))))),
% 216.08/216.30 inference(monotonicity,[status(thm)],[29])).
% 216.08/216.30 tff(31,plain,
% 216.08/216.30 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | (v1_xboole_0(A!6302) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304))) | (~m2_relset_1(D!6305, A!6302, B!6304)) | (~m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | v1_xboole_0(A!6302) | (~m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302)))) | (~m2_relset_1(D!6305, A!6302, B!6304)) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304))))),
% 216.08/216.30 inference(transitivity,[status(thm)],[30, 28])).
% 216.08/216.30 tff(32,plain,
% 216.08/216.30 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | (v1_xboole_0(A!6302) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304))) | (~m2_relset_1(D!6305, A!6302, B!6304)) | (~m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302)))))),
% 216.08/216.30 inference(quant_inst,[status(thm)],[])).
% 216.08/216.30 tff(33,plain,
% 216.08/216.30 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | v1_xboole_0(A!6302) | (~m1_subset_1(C!6303, k1_zfmisc_1(k1_zfmisc_1(A!6302)))) | (~m2_relset_1(D!6305, A!6302, B!6304)) | m1_subset_1(a_4_1_relset_2(A!6302, B!6304, C!6303, D!6305), k1_zfmisc_1(k1_zfmisc_1(B!6304)))),
% 216.08/216.30 inference(modus_ponens,[status(thm)],[32, 31])).
% 216.08/216.30 tff(34,plain,
% 216.08/216.30 ($false),
% 216.08/216.30 inference(unit_resolution,[status(thm)],[33, 27, 14, 13, 12, 11])).
% 216.08/216.30 % SZS output end Proof
% 216.65/216.83 % E exiting
%------------------------------------------------------------------------------