%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU448+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:28:00 AM UTC 2025
% Result : Theorem 133.27s 133.47s
% Output : Proof 133.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU448+1 : TPTP v9.0.0. Released v3.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 07:26:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 133.27/133.47 % SZS status Theorem
% 133.27/133.47 % SZS output start Proof
% 133.27/133.47 tff(r1_xboole_0_type, type, (
% 133.27/133.47 r1_xboole_0: ( $i * $i ) > $o)).
% 133.27/133.47 tff(k9_relat_1_type, type, (
% 133.27/133.47 k9_relat_1: ( $i * $i ) > $i)).
% 133.27/133.47 tff(tptp_fun_D_3_type, type, (
% 133.27/133.47 tptp_fun_D_3: $i)).
% 133.27/133.47 tff(k4_relat_1_type, type, (
% 133.27/133.47 k4_relat_1: $i > $i)).
% 133.27/133.47 tff(tptp_fun_E_4_type, type, (
% 133.27/133.47 tptp_fun_E_4: $i)).
% 133.27/133.47 tff(k3_subset_1_type, type, (
% 133.27/133.47 k3_subset_1: ( $i * $i ) > $i)).
% 133.27/133.47 tff(tptp_fun_C_0_type, type, (
% 133.27/133.47 tptp_fun_C_0: $i)).
% 133.27/133.47 tff(tptp_fun_A_2_type, type, (
% 133.27/133.47 tptp_fun_A_2: $i)).
% 133.27/133.47 tff(k6_relset_1_type, type, (
% 133.27/133.47 k6_relset_1: ( $i * $i * $i ) > $i)).
% 133.27/133.47 tff(tptp_fun_B_1_type, type, (
% 133.27/133.47 tptp_fun_B_1: $i)).
% 133.27/133.47 tff(m1_relset_1_type, type, (
% 133.27/133.47 m1_relset_1: ( $i * $i * $i ) > $o)).
% 133.27/133.47 tff(m2_relset_1_type, type, (
% 133.27/133.47 m2_relset_1: ( $i * $i * $i ) > $o)).
% 133.27/133.47 tff(r1_tarski_type, type, (
% 133.27/133.47 r1_tarski: ( $i * $i ) > $o)).
% 133.27/133.47 tff(k10_relset_1_type, type, (
% 133.27/133.47 k10_relset_1: ( $i * $i * $i * $i ) > $i)).
% 133.27/133.47 tff(m1_subset_1_type, type, (
% 133.27/133.47 m1_subset_1: ( $i * $i ) > $o)).
% 133.27/133.47 tff(k1_zfmisc_1_type, type, (
% 133.27/133.47 k1_zfmisc_1: $i > $i)).
% 133.27/133.48 tff(k2_zfmisc_1_type, type, (
% 133.27/133.48 k2_zfmisc_1: ( $i * $i ) > $i)).
% 133.27/133.48 tff(1,plain,
% 133.27/133.48 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(2,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[1])).
% 133.27/133.48 tff(3,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(4,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 133.27/133.48 tff(5,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 133.27/133.48 tff(6,plain,(
% 133.27/133.48 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 133.27/133.48 inference(skolemize,[status(sab)],[5])).
% 133.27/133.48 tff(7,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[6, 2])).
% 133.27/133.48 tff(8,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1))),
% 133.27/133.48 inference(quant_inst,[status(thm)],[])).
% 133.27/133.48 tff(9,plain,
% 133.27/133.48 (m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1)),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[8, 7])).
% 133.27/133.48 tff(10,plain,
% 133.27/133.48 ((m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(11,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C))))))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(12,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C))))))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(13,axiom,(~![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t62_relset_2')).
% 133.27/133.48 tff(14,plain,
% 133.27/133.48 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[13, 12])).
% 133.27/133.48 tff(15,plain,
% 133.27/133.48 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[14, 11])).
% 133.27/133.48 tff(16,plain,
% 133.27/133.48 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[15, 11])).
% 133.27/133.48 tff(17,plain,
% 133.27/133.48 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[16, 11])).
% 133.27/133.48 tff(18,plain,
% 133.27/133.48 (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0))))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[17, 10])).
% 133.27/133.48 tff(19,plain,
% 133.27/133.48 (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))),
% 133.27/133.48 inference(and_elim,[status(thm)],[18])).
% 133.27/133.48 tff(20,plain,
% 133.27/133.48 (m2_relset_1(E!4, A!2, B!1)),
% 133.27/133.48 inference(or_elim,[status(thm)],[19])).
% 133.27/133.48 tff(21,plain,
% 133.27/133.48 ((~(m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1))) | (~m2_relset_1(E!4, A!2, B!1)) | m1_relset_1(E!4, A!2, B!1)),
% 133.27/133.48 inference(tautology,[status(thm)],[])).
% 133.27/133.48 tff(22,plain,
% 133.27/133.48 ((~(m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1))) | m1_relset_1(E!4, A!2, B!1)),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[21, 20])).
% 133.27/133.48 tff(23,plain,
% 133.27/133.48 (m1_relset_1(E!4, A!2, B!1)),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[22, 9])).
% 133.27/133.48 tff(24,plain,
% 133.27/133.48 (^[A: $i, B: $i, C: $i] : refl(((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(25,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[24])).
% 133.27/133.48 tff(26,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(27,plain,
% 133.27/133.48 (^[A: $i, B: $i, C: $i] : rewrite((m1_relset_1(C, A, B) => (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(28,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[27])).
% 133.27/133.48 tff(29,axiom,(![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => (k6_relset_1(A, B, C) = k4_relat_1(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k6_relset_1')).
% 133.27/133.48 tff(30,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[29, 28])).
% 133.27/133.48 tff(31,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[30, 26])).
% 133.27/133.48 tff(32,plain,(
% 133.27/133.48 ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 133.27/133.48 inference(skolemize,[status(sab)],[31])).
% 133.27/133.48 tff(33,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[32, 25])).
% 133.27/133.48 tff(34,plain,
% 133.27/133.48 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | ((~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | (~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(35,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | ((~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)))),
% 133.27/133.48 inference(quant_inst,[status(thm)],[])).
% 133.27/133.48 tff(36,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | (~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[35, 34])).
% 133.27/133.48 tff(37,plain,
% 133.27/133.48 ((~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4))),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[36, 33])).
% 133.27/133.48 tff(38,plain,
% 133.27/133.48 (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[37, 23])).
% 133.27/133.48 tff(39,plain,
% 133.27/133.48 (k4_relat_1(E!4) = k6_relset_1(A!2, B!1, E!4)),
% 133.27/133.48 inference(symmetry,[status(thm)],[38])).
% 133.27/133.48 tff(40,plain,
% 133.27/133.48 (k9_relat_1(k4_relat_1(E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)),
% 133.27/133.48 inference(monotonicity,[status(thm)],[39])).
% 133.27/133.48 tff(41,plain,
% 133.27/133.48 (k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k4_relat_1(E!4), D!3)),
% 133.27/133.48 inference(symmetry,[status(thm)],[40])).
% 133.27/133.48 tff(42,plain,
% 133.27/133.48 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)) <=> r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))),
% 133.27/133.48 inference(monotonicity,[status(thm)],[41])).
% 133.27/133.48 tff(43,plain,
% 133.27/133.48 (^[A: $i, B: $i] : refl(((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B)))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(44,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B)) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[43])).
% 133.27/133.48 tff(45,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B)) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(46,plain,
% 133.27/133.48 (^[A: $i, B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(A)) => (k3_subset_1(A, k3_subset_1(A, B)) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B)))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(47,plain,
% 133.27/133.48 (![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => (k3_subset_1(A, k3_subset_1(A, B)) = B)) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[46])).
% 133.27/133.48 tff(48,axiom,(![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => (k3_subset_1(A, k3_subset_1(A, B)) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','involutiveness_k3_subset_1')).
% 133.27/133.48 tff(49,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[48, 47])).
% 133.27/133.48 tff(50,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[49, 45])).
% 133.27/133.48 tff(51,plain,(
% 133.27/133.48 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 133.27/133.48 inference(skolemize,[status(sab)],[50])).
% 133.27/133.48 tff(52,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[51, 44])).
% 133.27/133.48 tff(53,plain,
% 133.27/133.48 (m1_subset_1(C!0, k1_zfmisc_1(A!2))),
% 133.27/133.48 inference(and_elim,[status(thm)],[18])).
% 133.27/133.48 tff(54,plain,
% 133.27/133.48 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (k3_subset_1(A!2, k3_subset_1(A!2, C!0)) = C!0))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (k3_subset_1(A!2, k3_subset_1(A!2, C!0)) = C!0))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(55,plain,
% 133.27/133.48 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (k3_subset_1(A!2, k3_subset_1(A!2, C!0)) = C!0))),
% 133.27/133.48 inference(quant_inst,[status(thm)],[])).
% 133.27/133.48 tff(56,plain,
% 133.27/133.48 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (k3_subset_1(A!2, k3_subset_1(A!2, C!0)) = C!0)),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[55, 54])).
% 133.27/133.48 tff(57,plain,
% 133.27/133.48 (k3_subset_1(A!2, k3_subset_1(A!2, C!0)) = C!0),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[56, 53, 52])).
% 133.27/133.48 tff(58,plain,
% 133.27/133.48 (m1_relset_1(k4_relat_1(E!4), B!1, A!2) <=> m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 133.27/133.48 inference(monotonicity,[status(thm)],[39])).
% 133.27/133.48 tff(59,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k4_relat_1(E!4), B!1, A!2) <=> m1_relset_1(k4_relat_1(E!4), B!1, A!2))),
% 133.27/133.48 inference(quant_inst,[status(thm)],[])).
% 133.27/133.48 tff(60,plain,
% 133.27/133.48 (m2_relset_1(k4_relat_1(E!4), B!1, A!2) <=> m1_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[59, 7])).
% 133.27/133.48 tff(61,plain,
% 133.27/133.48 (m2_relset_1(k4_relat_1(E!4), B!1, A!2) <=> m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 133.27/133.48 inference(monotonicity,[status(thm)],[39])).
% 133.27/133.48 tff(62,plain,
% 133.27/133.48 (m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2) <=> m2_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 133.27/133.48 inference(symmetry,[status(thm)],[61])).
% 133.27/133.48 tff(63,plain,
% 133.27/133.48 (^[A: $i, B: $i, C: $i] : refl(((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(64,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[63])).
% 133.27/133.48 tff(65,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(66,plain,
% 133.27/133.48 (^[A: $i, B: $i, C: $i] : rewrite((m1_relset_1(C, A, B) => m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(67,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[66])).
% 133.27/133.48 tff(68,axiom,(![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => m2_relset_1(k6_relset_1(A, B, C), B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_relset_1')).
% 133.27/133.48 tff(69,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[68, 67])).
% 133.27/133.48 tff(70,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[69, 65])).
% 133.27/133.48 tff(71,plain,(
% 133.27/133.48 ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 133.27/133.48 inference(skolemize,[status(sab)],[70])).
% 133.27/133.48 tff(72,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[71, 64])).
% 133.27/133.48 tff(73,plain,
% 133.27/133.48 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | ((~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | (~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(74,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | ((~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2))),
% 133.27/133.48 inference(quant_inst,[status(thm)],[])).
% 133.27/133.48 tff(75,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | (~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[74, 73])).
% 133.27/133.48 tff(76,plain,
% 133.27/133.48 ((~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[75, 72])).
% 133.27/133.48 tff(77,plain,
% 133.27/133.48 (m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[76, 23])).
% 133.27/133.48 tff(78,plain,
% 133.27/133.48 (m2_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[77, 62])).
% 133.27/133.48 tff(79,plain,
% 133.27/133.48 ((~(m2_relset_1(k4_relat_1(E!4), B!1, A!2) <=> m1_relset_1(k4_relat_1(E!4), B!1, A!2))) | (~m2_relset_1(k4_relat_1(E!4), B!1, A!2)) | m1_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 133.27/133.48 inference(tautology,[status(thm)],[])).
% 133.27/133.48 tff(80,plain,
% 133.27/133.48 (m1_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[79, 78, 60])).
% 133.27/133.48 tff(81,plain,
% 133.27/133.48 (m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[80, 58])).
% 133.27/133.48 tff(82,plain,
% 133.27/133.48 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))) <=> ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(83,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[82])).
% 133.27/133.48 tff(84,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(85,plain,
% 133.27/133.48 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((m1_relset_1(C, A, B) => (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))) <=> ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(86,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : (m1_relset_1(C, A, B) => (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[85])).
% 133.27/133.48 tff(87,axiom,(![A: $i, B: $i, C: $i, D: $i] : (m1_relset_1(C, A, B) => (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k10_relset_1')).
% 133.27/133.48 tff(88,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[87, 86])).
% 133.27/133.48 tff(89,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[88, 84])).
% 133.27/133.48 tff(90,plain,(
% 133.27/133.48 ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 133.27/133.48 inference(skolemize,[status(sab)],[89])).
% 133.27/133.48 tff(91,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[90, 83])).
% 133.27/133.48 tff(92,plain,
% 133.27/133.48 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(93,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))),
% 133.27/133.48 inference(quant_inst,[status(thm)],[])).
% 133.27/133.48 tff(94,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[93, 92])).
% 133.27/133.48 tff(95,plain,
% 133.27/133.48 ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[94, 91])).
% 133.27/133.48 tff(96,plain,
% 133.27/133.48 (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[95, 81])).
% 133.27/133.48 tff(97,plain,
% 133.27/133.48 (k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3) = k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3)),
% 133.27/133.48 inference(symmetry,[status(thm)],[96])).
% 133.27/133.48 tff(98,plain,
% 133.27/133.48 (r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)),
% 133.27/133.48 inference(monotonicity,[status(thm)],[97, 57])).
% 133.27/133.48 tff(99,plain,
% 133.27/133.48 (r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 133.27/133.48 inference(symmetry,[status(thm)],[98])).
% 133.27/133.48 tff(100,plain,
% 133.27/133.48 ((~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) <=> (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)))),
% 133.27/133.48 inference(monotonicity,[status(thm)],[42])).
% 133.27/133.48 tff(101,plain,
% 133.27/133.48 ((~r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)) <=> (~r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))),
% 133.27/133.48 inference(monotonicity,[status(thm)],[99])).
% 133.27/133.48 tff(102,assumption,(~r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)), introduced(assumption)).
% 133.27/133.48 tff(103,plain,
% 133.27/133.48 (~r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[102, 101])).
% 133.27/133.48 tff(104,plain,
% 133.27/133.48 (m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2)) <=> m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 133.27/133.48 inference(monotonicity,[status(thm)],[97])).
% 133.27/133.48 tff(105,plain,
% 133.27/133.48 (m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2)) <=> m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 133.27/133.48 inference(symmetry,[status(thm)],[104])).
% 133.27/133.48 tff(106,plain,
% 133.27/133.48 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))) <=> ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(107,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[106])).
% 133.27/133.48 tff(108,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(109,plain,
% 133.27/133.48 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((m1_relset_1(C, A, B) => m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))) <=> ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(110,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : (m1_relset_1(C, A, B) => m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[109])).
% 133.27/133.48 tff(111,axiom,(![A: $i, B: $i, C: $i, D: $i] : (m1_relset_1(C, A, B) => m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k10_relset_1')).
% 133.27/133.48 tff(112,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[111, 110])).
% 133.27/133.48 tff(113,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[112, 108])).
% 133.27/133.48 tff(114,plain,(
% 133.27/133.48 ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 133.27/133.48 inference(skolemize,[status(sab)],[113])).
% 133.27/133.48 tff(115,plain,
% 133.27/133.48 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[114, 107])).
% 133.27/133.48 tff(116,plain,
% 133.27/133.48 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | (~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2)))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(117,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2)))),
% 133.27/133.48 inference(quant_inst,[status(thm)],[])).
% 133.27/133.48 tff(118,plain,
% 133.27/133.48 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | (~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[117, 116])).
% 133.27/133.48 tff(119,plain,
% 133.27/133.48 ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[118, 115])).
% 133.27/133.48 tff(120,plain,
% 133.27/133.48 (m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 133.27/133.48 inference(unit_resolution,[status(thm)],[119, 81])).
% 133.27/133.48 tff(121,plain,
% 133.27/133.48 (m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[120, 105])).
% 133.27/133.48 tff(122,plain,
% 133.27/133.48 (^[A: $i, B: $i] : refl(((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(123,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[122])).
% 133.27/133.48 tff(124,plain,
% 133.27/133.48 (^[A: $i, B: $i] : rewrite(((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(125,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[124])).
% 133.27/133.48 tff(126,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 133.27/133.48 inference(transitivity,[status(thm)],[125, 123])).
% 133.27/133.48 tff(127,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(128,plain,
% 133.27/133.48 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))))),
% 133.27/133.48 inference(bind,[status(th)],[])).
% 133.27/133.48 tff(129,plain,
% 133.27/133.48 (![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 133.27/133.48 inference(quant_intro,[status(thm)],[128])).
% 133.27/133.48 tff(130,axiom,(![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t43_subset_1')).
% 133.27/133.48 tff(131,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 133.27/133.48 tff(132,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[131, 127])).
% 133.27/133.48 tff(133,plain,(
% 133.27/133.48 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 133.27/133.48 inference(skolemize,[status(sab)],[132])).
% 133.27/133.48 tff(134,plain,
% 133.27/133.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 133.27/133.48 inference(modus_ponens,[status(thm)],[133, 126])).
% 133.27/133.48 tff(135,plain,
% 133.27/133.48 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | ((~m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C)))))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | (~m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C)))))),
% 133.27/133.48 inference(rewrite,[status(thm)],[])).
% 133.27/133.48 tff(136,plain,
% 133.27/133.48 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | ((~m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C)))))),
% 133.27/133.48 inference(quant_inst,[status(thm)],[])).
% 133.27/133.48 tff(137,plain,
% 133.27/133.48 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | (~m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[136, 135])).
% 133.27/133.49 tff(138,plain,
% 133.27/133.49 ((~m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[137, 134])).
% 133.27/133.49 tff(139,plain,
% 133.27/133.49 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[138, 121])).
% 133.27/133.49 tff(140,plain,
% 133.27/133.49 (^[A: $i, B: $i] : refl(((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))))),
% 133.27/133.49 inference(bind,[status(th)],[])).
% 133.27/133.49 tff(141,plain,
% 133.27/133.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 133.27/133.49 inference(quant_intro,[status(thm)],[140])).
% 133.27/133.49 tff(142,plain,
% 133.27/133.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 133.27/133.49 inference(rewrite,[status(thm)],[])).
% 133.27/133.49 tff(143,plain,
% 133.27/133.49 (^[A: $i, B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))))),
% 133.27/133.49 inference(bind,[status(th)],[])).
% 133.27/133.49 tff(144,plain,
% 133.27/133.49 (![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 133.27/133.49 inference(quant_intro,[status(thm)],[143])).
% 133.27/133.49 tff(145,axiom,(![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_subset_1')).
% 133.27/133.49 tff(146,plain,
% 133.27/133.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[145, 144])).
% 133.27/133.49 tff(147,plain,
% 133.27/133.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[146, 142])).
% 133.27/133.49 tff(148,plain,(
% 133.27/133.49 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 133.27/133.49 inference(skolemize,[status(sab)],[147])).
% 133.27/133.49 tff(149,plain,
% 133.27/133.49 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[148, 141])).
% 133.27/133.49 tff(150,plain,
% 133.27/133.49 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2)))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2)))),
% 133.27/133.49 inference(rewrite,[status(thm)],[])).
% 133.27/133.49 tff(151,plain,
% 133.27/133.49 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2)))),
% 133.27/133.49 inference(quant_inst,[status(thm)],[])).
% 133.27/133.49 tff(152,plain,
% 133.27/133.49 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[151, 150])).
% 133.27/133.49 tff(153,plain,
% 133.27/133.49 (m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[152, 53, 149])).
% 133.27/133.49 tff(154,plain,
% 133.27/133.49 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))) | ((~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))) | (~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))))),
% 133.27/133.49 inference(rewrite,[status(thm)],[])).
% 133.27/133.49 tff(155,plain,
% 133.27/133.49 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))) | ((~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))))),
% 133.27/133.49 inference(quant_inst,[status(thm)],[])).
% 133.27/133.49 tff(156,plain,
% 133.27/133.49 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))) | (~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[155, 154])).
% 133.27/133.49 tff(157,plain,
% 133.27/133.49 (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[156, 153, 139])).
% 133.27/133.49 tff(158,plain,
% 133.27/133.49 ((~(r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))) | (~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 133.27/133.49 inference(tautology,[status(thm)],[])).
% 133.27/133.49 tff(159,plain,
% 133.27/133.49 ((~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[158, 157])).
% 133.27/133.49 tff(160,plain,
% 133.27/133.49 (~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[159, 103])).
% 133.27/133.49 tff(161,plain,
% 133.27/133.49 (^[A: $i, B: $i] : refl(((~r1_xboole_0(A, B)) | r1_xboole_0(B, A)) <=> ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A)))),
% 133.27/133.49 inference(bind,[status(th)],[])).
% 133.27/133.49 tff(162,plain,
% 133.27/133.49 (![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A)) <=> ![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 133.27/133.49 inference(quant_intro,[status(thm)],[161])).
% 133.27/133.49 tff(163,plain,
% 133.27/133.49 (![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A)) <=> ![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 133.27/133.49 inference(rewrite,[status(thm)],[])).
% 133.27/133.49 tff(164,plain,
% 133.27/133.49 (^[A: $i, B: $i] : rewrite((r1_xboole_0(A, B) => r1_xboole_0(B, A)) <=> ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A)))),
% 133.27/133.49 inference(bind,[status(th)],[])).
% 133.27/133.49 tff(165,plain,
% 133.27/133.49 (![A: $i, B: $i] : (r1_xboole_0(A, B) => r1_xboole_0(B, A)) <=> ![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 133.27/133.49 inference(quant_intro,[status(thm)],[164])).
% 133.27/133.49 tff(166,axiom,(![A: $i, B: $i] : (r1_xboole_0(A, B) => r1_xboole_0(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 133.27/133.49 tff(167,plain,
% 133.27/133.49 (![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[166, 165])).
% 133.27/133.49 tff(168,plain,
% 133.27/133.49 (![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[167, 163])).
% 133.27/133.49 tff(169,plain,(
% 133.27/133.49 ![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 133.27/133.49 inference(skolemize,[status(sab)],[168])).
% 133.27/133.49 tff(170,plain,
% 133.27/133.49 (![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[169, 162])).
% 133.27/133.49 tff(171,plain,
% 133.27/133.49 (((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)))) <=> ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)))),
% 133.27/133.49 inference(rewrite,[status(thm)],[])).
% 133.27/133.49 tff(172,plain,
% 133.27/133.49 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)))),
% 133.27/133.49 inference(quant_inst,[status(thm)],[])).
% 133.27/133.49 tff(173,plain,
% 133.27/133.49 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[172, 171])).
% 133.27/133.49 tff(174,plain,
% 133.27/133.49 ((~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[173, 170])).
% 133.27/133.49 tff(175,plain,
% 133.27/133.49 (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[174, 160])).
% 133.27/133.49 tff(176,plain,
% 133.27/133.49 (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[175, 100])).
% 133.27/133.49 tff(177,plain,
% 133.27/133.49 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_relset_1(E!4, A!2, B!1)) | (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_relset_1(E!4, A!2, B!1)) | (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 133.27/133.49 inference(rewrite,[status(thm)],[])).
% 133.27/133.49 tff(178,plain,
% 133.27/133.49 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_relset_1(E!4, A!2, B!1)) | (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 133.27/133.49 inference(quant_inst,[status(thm)],[])).
% 133.27/133.49 tff(179,plain,
% 133.27/133.49 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_relset_1(E!4, A!2, B!1)) | (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[178, 177])).
% 133.27/133.49 tff(180,plain,
% 133.27/133.49 ((~m1_relset_1(E!4, A!2, B!1)) | (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[179, 91])).
% 133.27/133.49 tff(181,plain,
% 133.27/133.49 (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[180, 23])).
% 133.27/133.49 tff(182,plain,
% 133.27/133.49 (k9_relat_1(E!4, k3_subset_1(A!2, C!0)) = k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0))),
% 133.27/133.49 inference(symmetry,[status(thm)],[181])).
% 133.27/133.49 tff(183,plain,
% 133.27/133.49 (r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 133.27/133.49 inference(monotonicity,[status(thm)],[182])).
% 133.27/133.49 tff(184,plain,
% 133.27/133.49 (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 133.27/133.49 inference(symmetry,[status(thm)],[183])).
% 133.27/133.49 tff(185,plain,
% 133.27/133.49 (~(r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0))),
% 133.27/133.49 inference(or_elim,[status(thm)],[19])).
% 133.27/133.49 tff(186,plain,
% 133.27/133.49 ((r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)) | r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) | r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)),
% 133.27/133.49 inference(tautology,[status(thm)],[])).
% 133.27/133.49 tff(187,plain,
% 133.27/133.49 (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) | r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[186, 185])).
% 133.27/133.49 tff(188,plain,
% 133.27/133.49 (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[187, 102])).
% 133.27/133.49 tff(189,plain,
% 133.27/133.49 (r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[188, 184])).
% 133.27/133.49 tff(190,plain,
% 133.27/133.49 (m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1)) <=> m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 133.27/133.49 inference(monotonicity,[status(thm)],[182])).
% 133.27/133.49 tff(191,plain,
% 133.27/133.49 (m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1)) <=> m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 133.27/133.49 inference(symmetry,[status(thm)],[190])).
% 133.27/133.49 tff(192,plain,
% 133.27/133.49 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | ((~m1_relset_1(E!4, A!2, B!1)) | m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | (~m1_relset_1(E!4, A!2, B!1)) | m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1)))),
% 133.27/133.49 inference(rewrite,[status(thm)],[])).
% 133.27/133.49 tff(193,plain,
% 133.27/133.49 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | ((~m1_relset_1(E!4, A!2, B!1)) | m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1)))),
% 133.27/133.49 inference(quant_inst,[status(thm)],[])).
% 133.27/133.49 tff(194,plain,
% 133.27/133.49 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | (~m1_relset_1(E!4, A!2, B!1)) | m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[193, 192])).
% 133.27/133.49 tff(195,plain,
% 133.27/133.49 ((~m1_relset_1(E!4, A!2, B!1)) | m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[194, 115])).
% 133.27/133.49 tff(196,plain,
% 133.27/133.49 (m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 133.27/133.49 inference(unit_resolution,[status(thm)],[195, 23])).
% 133.27/133.49 tff(197,plain,
% 133.27/133.49 (m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 133.27/133.49 inference(modus_ponens,[status(thm)],[196, 191])).
% 133.27/133.49 tff(198,plain,
% 133.27/133.49 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | ((~m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C)))))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | (~m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C)))))),
% 133.35/133.49 inference(rewrite,[status(thm)],[])).
% 133.35/133.49 tff(199,plain,
% 133.35/133.49 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | ((~m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C)))))),
% 133.35/133.49 inference(quant_inst,[status(thm)],[])).
% 133.35/133.49 tff(200,plain,
% 133.35/133.49 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | (~m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))),
% 133.35/133.49 inference(modus_ponens,[status(thm)],[199, 198])).
% 133.35/133.49 tff(201,plain,
% 133.35/133.49 ((~m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))),
% 133.35/133.49 inference(unit_resolution,[status(thm)],[200, 134])).
% 133.35/133.49 tff(202,plain,
% 133.35/133.49 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))),
% 133.35/133.49 inference(unit_resolution,[status(thm)],[201, 197])).
% 133.35/133.49 tff(203,plain,
% 133.35/133.49 (m1_subset_1(D!3, k1_zfmisc_1(B!1))),
% 133.35/133.49 inference(and_elim,[status(thm)],[18])).
% 133.35/133.49 tff(204,plain,
% 133.35/133.49 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))))),
% 133.35/133.49 inference(rewrite,[status(thm)],[])).
% 133.35/133.49 tff(205,plain,
% 133.35/133.49 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))))),
% 133.35/133.49 inference(quant_inst,[status(thm)],[])).
% 133.35/133.49 tff(206,plain,
% 133.35/133.49 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))),
% 133.35/133.49 inference(modus_ponens,[status(thm)],[205, 204])).
% 133.35/133.49 tff(207,plain,
% 133.35/133.49 (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 133.35/133.49 inference(unit_resolution,[status(thm)],[206, 203, 202])).
% 133.35/133.49 tff(208,plain,
% 133.35/133.49 ((~(r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) | (~r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))),
% 133.35/133.49 inference(tautology,[status(thm)],[])).
% 133.35/133.49 tff(209,plain,
% 133.35/133.49 (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) | (~r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))),
% 133.35/133.49 inference(unit_resolution,[status(thm)],[208, 207])).
% 133.35/133.49 tff(210,plain,
% 133.35/133.49 (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)),
% 133.35/133.49 inference(unit_resolution,[status(thm)],[209, 189])).
% 133.35/133.49 tff(211,plain,
% 133.35/133.49 (((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))) <=> ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 133.35/133.49 inference(rewrite,[status(thm)],[])).
% 133.35/133.49 tff(212,plain,
% 133.35/133.49 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 133.35/133.49 inference(quant_inst,[status(thm)],[])).
% 133.35/133.49 tff(213,plain,
% 133.35/133.49 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 133.35/133.49 inference(modus_ponens,[status(thm)],[212, 211])).
% 133.35/133.49 tff(214,plain,
% 133.35/133.49 ((~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 133.35/133.49 inference(unit_resolution,[status(thm)],[213, 170])).
% 133.35/133.49 tff(215,plain,
% 133.35/133.49 (r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 133.35/133.49 inference(unit_resolution,[status(thm)],[214, 210])).
% 133.35/133.49 tff(216,plain,
% 133.35/133.49 (^[A: $i, B: $i, C: $i] : refl(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))))),
% 133.35/133.49 inference(bind,[status(th)],[])).
% 133.35/133.49 tff(217,plain,
% 133.35/133.49 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 133.35/133.49 inference(quant_intro,[status(thm)],[216])).
% 133.35/133.49 tff(218,plain,
% 133.35/133.49 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))))),
% 133.35/133.49 inference(bind,[status(th)],[])).
% 133.35/133.49 tff(219,plain,
% 133.35/133.49 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 133.35/133.49 inference(quant_intro,[status(thm)],[218])).
% 133.35/133.49 tff(220,plain,
% 133.35/133.49 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 133.35/133.49 inference(transitivity,[status(thm)],[219, 217])).
% 133.35/133.49 tff(221,plain,
% 133.35/133.49 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 133.35/133.49 inference(rewrite,[status(thm)],[])).
% 133.35/133.49 tff(222,plain,
% 133.35/133.49 (^[A: $i, B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : rewrite((m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))) <=> ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))), (![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))) <=> ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))), ((m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))) <=> (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))), rewrite((m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))), ((m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))) <=> ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))))),
% 133.35/133.50 inference(bind,[status(th)],[])).
% 133.35/133.50 tff(223,plain,
% 133.35/133.50 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 133.35/133.50 inference(quant_intro,[status(thm)],[222])).
% 133.35/133.50 tff(224,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t46_relset_2')).
% 133.35/133.50 tff(225,plain,
% 133.35/133.50 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[224, 223])).
% 133.35/133.50 tff(226,plain,
% 133.35/133.50 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[225, 221])).
% 133.35/133.50 tff(227,plain,(
% 133.35/133.50 ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 133.35/133.50 inference(skolemize,[status(sab)],[226])).
% 133.35/133.50 tff(228,plain,
% 133.35/133.50 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[227, 220])).
% 133.35/133.50 tff(229,plain,
% 133.35/133.50 (((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))) | ((~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))) | (~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0)))))))),
% 133.35/133.50 inference(rewrite,[status(thm)],[])).
% 133.35/133.50 tff(230,plain,
% 133.35/133.50 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))) | ((~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0)))))))),
% 133.35/133.50 inference(quant_inst,[status(thm)],[])).
% 133.35/133.50 tff(231,plain,
% 133.35/133.50 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))) | (~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[230, 229])).
% 133.35/133.50 tff(232,plain,
% 133.35/133.50 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[231, 228, 153])).
% 133.35/133.50 tff(233,plain,
% 133.35/133.50 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0))))))),
% 133.35/133.50 inference(rewrite,[status(thm)],[])).
% 133.35/133.50 tff(234,plain,
% 133.35/133.50 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0))))))),
% 133.35/133.50 inference(quant_inst,[status(thm)],[])).
% 133.35/133.50 tff(235,plain,
% 133.35/133.50 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[234, 233])).
% 133.35/133.50 tff(236,plain,
% 133.35/133.50 (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[235, 203, 232])).
% 133.35/133.50 tff(237,plain,
% 133.35/133.50 (^[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)))))),
% 133.35/133.50 inference(bind,[status(th)],[])).
% 133.35/133.50 tff(238,plain,
% 133.35/133.50 (![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))))),
% 133.35/133.50 inference(quant_intro,[status(thm)],[237])).
% 133.35/133.50 tff(239,plain,
% 133.35/133.50 (![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))))),
% 133.35/133.50 inference(rewrite,[status(thm)],[])).
% 133.35/133.50 tff(240,plain,
% 133.35/133.50 (^[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)))))),
% 133.35/133.50 inference(bind,[status(th)],[])).
% 133.35/133.50 tff(241,plain,
% 133.35/133.50 (![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))))),
% 133.35/133.50 inference(quant_intro,[status(thm)],[240])).
% 133.35/133.50 tff(242,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')).
% 133.35/133.50 tff(243,plain,
% 133.35/133.50 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[242, 241])).
% 133.35/133.50 tff(244,plain,
% 133.35/133.50 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[243, 239])).
% 133.35/133.50 tff(245,plain,(
% 133.35/133.50 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 133.35/133.50 inference(skolemize,[status(sab)],[244])).
% 133.35/133.50 tff(246,plain,
% 133.35/133.50 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[245, 238])).
% 133.35/133.50 tff(247,plain,
% 133.35/133.50 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 133.35/133.50 inference(rewrite,[status(thm)],[])).
% 133.35/133.50 tff(248,plain,
% 133.35/133.50 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 133.35/133.50 inference(quant_inst,[status(thm)],[])).
% 133.35/133.50 tff(249,plain,
% 133.35/133.50 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[248, 247])).
% 133.35/133.50 tff(250,plain,
% 133.35/133.50 (m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[249, 20, 246])).
% 133.35/133.50 tff(251,plain,
% 133.35/133.50 (((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))))) <=> ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))))),
% 133.35/133.50 inference(rewrite,[status(thm)],[])).
% 133.35/133.50 tff(252,plain,
% 133.35/133.50 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))))),
% 133.35/133.50 inference(quant_inst,[status(thm)],[])).
% 133.35/133.50 tff(253,plain,
% 133.35/133.50 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[252, 251])).
% 133.35/133.50 tff(254,plain,
% 133.35/133.50 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[253, 250, 236])).
% 133.35/133.50 tff(255,plain,
% 133.35/133.50 ((~(r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) | (~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 133.35/133.50 inference(tautology,[status(thm)],[])).
% 133.35/133.50 tff(256,plain,
% 133.35/133.50 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) | (~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[255, 254])).
% 133.35/133.50 tff(257,plain,
% 133.35/133.50 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[256, 215])).
% 133.35/133.50 tff(258,plain,
% 133.35/133.50 ($false),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[257, 176])).
% 133.35/133.50 tff(259,plain,(r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)), inference(lemma,lemma(discharge,[]))).
% 133.35/133.50 tff(260,plain,
% 133.35/133.50 (r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[259, 99])).
% 133.35/133.50 tff(261,plain,
% 133.35/133.50 ((~(r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) | (~r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))),
% 133.35/133.50 inference(tautology,[status(thm)],[])).
% 133.35/133.50 tff(262,plain,
% 133.35/133.50 (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) | (~r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[261, 157])).
% 133.35/133.50 tff(263,plain,
% 133.35/133.50 (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[262, 260])).
% 133.35/133.50 tff(264,plain,
% 133.35/133.50 (((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))) <=> ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))),
% 133.35/133.50 inference(rewrite,[status(thm)],[])).
% 133.35/133.50 tff(265,plain,
% 133.35/133.50 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))),
% 133.35/133.50 inference(quant_inst,[status(thm)],[])).
% 133.35/133.50 tff(266,plain,
% 133.35/133.50 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[265, 264])).
% 133.35/133.50 tff(267,plain,
% 133.35/133.50 ((~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[266, 170])).
% 133.35/133.50 tff(268,plain,
% 133.35/133.50 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[267, 263])).
% 133.35/133.50 tff(269,plain,
% 133.35/133.50 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[268, 42])).
% 133.35/133.50 tff(270,plain,
% 133.35/133.50 ((~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))) <=> (~r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))),
% 133.35/133.50 inference(monotonicity,[status(thm)],[184])).
% 133.35/133.50 tff(271,plain,
% 133.35/133.50 ((r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)) | (~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))) | (~r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0))),
% 133.35/133.50 inference(tautology,[status(thm)],[])).
% 133.35/133.50 tff(272,plain,
% 133.35/133.50 ((~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))) | (~r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[271, 185])).
% 133.35/133.50 tff(273,plain,
% 133.35/133.50 (~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[272, 259])).
% 133.35/133.50 tff(274,plain,
% 133.35/133.50 (~r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[273, 270])).
% 133.35/133.50 tff(275,plain,
% 133.35/133.50 ((~(r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))) | (~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 133.35/133.50 inference(tautology,[status(thm)],[])).
% 133.35/133.50 tff(276,plain,
% 133.35/133.50 ((~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[275, 207])).
% 133.35/133.50 tff(277,plain,
% 133.35/133.50 (~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)),
% 133.35/133.50 inference(unit_resolution,[status(thm)],[276, 274])).
% 133.35/133.50 tff(278,plain,
% 133.35/133.50 (((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3))) <=> ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3))),
% 133.35/133.50 inference(rewrite,[status(thm)],[])).
% 133.35/133.50 tff(279,plain,
% 133.35/133.50 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3))),
% 133.35/133.50 inference(quant_inst,[status(thm)],[])).
% 133.35/133.50 tff(280,plain,
% 133.35/133.50 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)),
% 133.35/133.50 inference(modus_ponens,[status(thm)],[279, 278])).
% 133.35/133.50 tff(281,plain,
% 133.47/133.66 ((~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)),
% 133.47/133.66 inference(unit_resolution,[status(thm)],[280, 170])).
% 133.47/133.66 tff(282,plain,
% 133.47/133.66 (~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 133.47/133.66 inference(unit_resolution,[status(thm)],[281, 277])).
% 133.47/133.66 tff(283,plain,
% 133.47/133.66 ((~(r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))) | (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 133.47/133.66 inference(tautology,[status(thm)],[])).
% 133.47/133.66 tff(284,plain,
% 133.47/133.66 ((~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 133.47/133.66 inference(unit_resolution,[status(thm)],[283, 254])).
% 133.47/133.66 tff(285,plain,
% 133.47/133.66 (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))),
% 133.47/133.66 inference(unit_resolution,[status(thm)],[284, 282])).
% 133.47/133.66 tff(286,plain,
% 133.47/133.66 ($false),
% 133.47/133.66 inference(unit_resolution,[status(thm)],[285, 269])).
% 133.47/133.66 % SZS output end Proof
% 133.47/133.66 % E exiting
%------------------------------------------------------------------------------