%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU424+1 : 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 05:27:53 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU424+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:14:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(m1_subset_1_type, type, (
% 0.19/0.37 m1_subset_1: ( $i * $i ) > $o)).
% 0.19/0.37 tff(k1_zfmisc_1_type, type, (
% 0.19/0.37 k1_zfmisc_1: $i > $i)).
% 0.19/0.37 tff(m2_relset_1_type, type, (
% 0.19/0.37 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.19/0.37 tff(v1_xboole_0_type, type, (
% 0.19/0.37 v1_xboole_0: $i > $o)).
% 0.19/0.37 tff(a_4_0_relset_2_type, type, (
% 0.19/0.37 a_4_0_relset_2: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_B_2_type, type, (
% 0.19/0.37 tptp_fun_B_2: $i)).
% 0.19/0.37 tff(tptp_fun_D_3_type, type, (
% 0.19/0.37 tptp_fun_D_3: $i)).
% 0.19/0.37 tff(tptp_fun_C_1_type, type, (
% 0.19/0.37 tptp_fun_C_1: $i)).
% 0.19/0.37 tff(tptp_fun_A_0_type, type, (
% 0.19/0.37 tptp_fun_A_0: $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i, D: $i] : refl((m1_subset_1(a_4_0_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(A)))) <=> (m1_subset_1(a_4_0_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(A)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(C, 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(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(C, 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(A)))))))), rewrite((~(~(v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(C, 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(A)))))), (((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_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(A)))) | m1_subset_1(a_4_0_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(A)))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (m1_subset_1(a_4_0_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(A))))), (((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (m1_subset_1(a_4_0_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(A))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_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(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) <=> ((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))), (((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_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(A)) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))), (((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i, D: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_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(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.38 tff(8,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s8_domain_1__e1_22__relset_2')).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.38 tff(11,plain,(
% 0.19/0.38 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (((~v1_xboole_0(A!0)) & (m1_subset_1(C!1, k1_zfmisc_1(A!0)) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))))) <=> ((~v1_xboole_0(A!0)) & m1_subset_1(C!1, k1_zfmisc_1(A!0)) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_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(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 ((~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m2_relset_1(D, A, B) => m1_subset_1(a_4_0_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(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(17,axiom,(~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m2_relset_1(D, A, B) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t18_relset_2')).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 ((~v1_xboole_0(A!0)) & m1_subset_1(C!1, k1_zfmisc_1(A!0)) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))),
% 0.19/0.38 inference(and_elim,[status(thm)],[22])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (~m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2)))),
% 0.19/0.38 inference(or_elim,[status(thm)],[23])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (m2_relset_1(D!3, A!0, B!2)),
% 0.19/0.38 inference(or_elim,[status(thm)],[23])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (m1_subset_1(C!1, k1_zfmisc_1(A!0))),
% 0.19/0.38 inference(and_elim,[status(thm)],[22])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (~v1_xboole_0(A!0)),
% 0.19/0.38 inference(and_elim,[status(thm)],[22])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A))))) | (v1_xboole_0(A!0) | (~m1_subset_1(C!1, k1_zfmisc_1(A!0))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A))))) | v1_xboole_0(A!0) | (~m1_subset_1(C!1, k1_zfmisc_1(A!0))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 ((m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0) | (~m2_relset_1(D!3, A!0, B!2)) | (~m1_subset_1(C!1, k1_zfmisc_1(A!0)))) <=> (v1_xboole_0(A!0) | (~m1_subset_1(C!1, k1_zfmisc_1(A!0))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A))))) | (m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0) | (~m2_relset_1(D!3, A!0, B!2)) | (~m1_subset_1(C!1, k1_zfmisc_1(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A))))) | (v1_xboole_0(A!0) | (~m1_subset_1(C!1, k1_zfmisc_1(A!0))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2)))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[29])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A))))) | (m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0) | (~m2_relset_1(D!3, A!0, B!2)) | (~m1_subset_1(C!1, k1_zfmisc_1(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A))))) | v1_xboole_0(A!0) | (~m1_subset_1(C!1, k1_zfmisc_1(A!0))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_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(A))))) | (m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0) | (~m2_relset_1(D!3, A!0, B!2)) | (~m1_subset_1(C!1, k1_zfmisc_1(A!0))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(A!0) | (~m1_subset_1(C!1, k1_zfmisc_1(A!0))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_0_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[33, 27, 26, 25, 24, 13])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------