%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU447+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 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU447+1 : TPTP v9.0.0. Released v3.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 07:25:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(k8_relset_2_type, type, (
% 0.21/0.41 k8_relset_2: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.41 tff(k3_subset_1_type, type, (
% 0.21/0.41 k3_subset_1: ( $i * $i ) > $i)).
% 0.21/0.41 tff(k9_relset_2_type, type, (
% 0.21/0.41 k9_relset_2: ( $i * $i * $i * $i * $i ) > $i)).
% 0.21/0.41 tff(tptp_fun_F_5_type, type, (
% 0.21/0.41 tptp_fun_F_5: $i)).
% 0.21/0.41 tff(k2_zfmisc_1_type, type, (
% 0.21/0.41 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.21/0.41 tff(tptp_fun_C_1_type, type, (
% 0.21/0.41 tptp_fun_C_1: $i)).
% 0.21/0.41 tff(tptp_fun_B_2_type, type, (
% 0.21/0.41 tptp_fun_B_2: $i)).
% 0.21/0.41 tff(tptp_fun_E_4_type, type, (
% 0.21/0.41 tptp_fun_E_4: $i)).
% 0.21/0.41 tff(tptp_fun_A_3_type, type, (
% 0.21/0.41 tptp_fun_A_3: $i)).
% 0.21/0.41 tff(tptp_fun_D_0_type, type, (
% 0.21/0.41 tptp_fun_D_0: $i)).
% 0.21/0.41 tff(k10_relset_1_type, type, (
% 0.21/0.41 k10_relset_1: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.41 tff(k5_relat_1_type, type, (
% 0.21/0.41 k5_relat_1: ( $i * $i ) > $i)).
% 0.21/0.41 tff(m1_subset_1_type, type, (
% 0.21/0.41 m1_subset_1: ( $i * $i ) > $o)).
% 0.21/0.41 tff(k1_zfmisc_1_type, type, (
% 0.21/0.41 k1_zfmisc_1: $i > $i)).
% 0.21/0.41 tff(m2_relset_1_type, type, (
% 0.21/0.41 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.21/0.41 tff(k7_relset_2_type, type, (
% 0.21/0.41 k7_relset_2: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.41 tff(k9_relat_1_type, type, (
% 0.21/0.41 k9_relat_1: ( $i * $i ) > $i)).
% 0.21/0.41 tff(m1_relset_1_type, type, (
% 0.21/0.41 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.21/0.41 tff(v1_relat_1_type, type, (
% 0.21/0.41 v1_relat_1: $i > $o)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.41 tff(6,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.41 tff(9,plain,(
% 0.21/0.41 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[8])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 ((m1_subset_1(D!0, k1_zfmisc_1(A!3)) & (m2_relset_1(E!4, A!3, B!2) & (~((~m2_relset_1(F!5, B!2, C!1)) | (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))))))) <=> (m1_subset_1(D!0, k1_zfmisc_1(A!3)) & m2_relset_1(E!4, A!3, B!2) & (~((~m2_relset_1(F!5, B!2, C!1)) | (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | ![F: $i] : ((~m2_relset_1(F, B, C)) | (k8_relset_2(B, C, k10_relset_1(A, B, E, D), F) = k8_relset_2(A, C, D, k3_subset_1(k2_zfmisc_1(A, C), k9_relset_2(A, B, C, E, k3_subset_1(k2_zfmisc_1(B, C), F))))))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | ![F: $i] : ((~m2_relset_1(F, B, C)) | (k8_relset_2(B, C, k10_relset_1(A, B, E, D), F) = k8_relset_2(A, C, D, k3_subset_1(k2_zfmisc_1(A, C), k9_relset_2(A, B, C, E, k3_subset_1(k2_zfmisc_1(B, C), F)))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(D, k1_zfmisc_1(A)) => ![E: $i] : (m2_relset_1(E, A, B) => ![F: $i] : (m2_relset_1(F, B, C) => (k8_relset_2(B, C, k10_relset_1(A, B, E, D), F) = k8_relset_2(A, C, D, k3_subset_1(k2_zfmisc_1(A, C), k9_relset_2(A, B, C, E, k3_subset_1(k2_zfmisc_1(B, C), F))))))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | ![F: $i] : ((~m2_relset_1(F, B, C)) | (k8_relset_2(B, C, k10_relset_1(A, B, E, D), F) = k8_relset_2(A, C, D, k3_subset_1(k2_zfmisc_1(A, C), k9_relset_2(A, B, C, E, k3_subset_1(k2_zfmisc_1(B, C), F)))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(14,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(D, k1_zfmisc_1(A)) => ![E: $i] : (m2_relset_1(E, A, B) => ![F: $i] : (m2_relset_1(F, B, C) => (k8_relset_2(B, C, k10_relset_1(A, B, E, D), F) = k8_relset_2(A, C, D, k3_subset_1(k2_zfmisc_1(A, C), k9_relset_2(A, B, C, E, k3_subset_1(k2_zfmisc_1(B, C), F))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t59_relset_2')).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | ![F: $i] : ((~m2_relset_1(F, B, C)) | (k8_relset_2(B, C, k10_relset_1(A, B, E, D), F) = k8_relset_2(A, C, D, k3_subset_1(k2_zfmisc_1(A, C), k9_relset_2(A, B, C, E, k3_subset_1(k2_zfmisc_1(B, C), F))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | ![F: $i] : ((~m2_relset_1(F, B, C)) | (k8_relset_2(B, C, k10_relset_1(A, B, E, D), F) = k8_relset_2(A, C, D, k3_subset_1(k2_zfmisc_1(A, C), k9_relset_2(A, B, C, E, k3_subset_1(k2_zfmisc_1(B, C), F))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | ![F: $i] : ((~m2_relset_1(F, B, C)) | (k8_relset_2(B, C, k10_relset_1(A, B, E, D), F) = k8_relset_2(A, C, D, k3_subset_1(k2_zfmisc_1(A, C), k9_relset_2(A, B, C, E, k3_subset_1(k2_zfmisc_1(B, C), F))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i, D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(A))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | ![F: $i] : ((~m2_relset_1(F, B, C)) | (k8_relset_2(B, C, k10_relset_1(A, B, E, D), F) = k8_relset_2(A, C, D, k3_subset_1(k2_zfmisc_1(A, C), k9_relset_2(A, B, C, E, k3_subset_1(k2_zfmisc_1(B, C), F))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (m1_subset_1(D!0, k1_zfmisc_1(A!3)) & m2_relset_1(E!4, A!3, B!2) & (~((~m2_relset_1(F!5, B!2, C!1)) | (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (m2_relset_1(E!4, A!3, B!2)),
% 0.21/0.41 inference(and_elim,[status(thm)],[19])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (((~![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!3, B!2)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2))))) <=> ((~![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!3, B!2)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 ((~![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!3, B!2)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 ((~![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!3, B!2)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (~((~m2_relset_1(F!5, B!2, C!1)) | (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))))),
% 0.21/0.42 inference(and_elim,[status(thm)],[19])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (m2_relset_1(F!5, B!2, C!1)),
% 0.21/0.42 inference(or_elim,[status(thm)],[25])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (((~![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(F!5, B!2, C!1)) | m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!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(F!5, B!2, C!1)) | m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 ((~![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(F!5, B!2, C!1)) | m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 ((~![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(F!5, B!2, C!1)) | m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[29, 26, 10])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.42 tff(36,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')).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.42 tff(39,plain,(
% 0.21/0.42 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[38])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (((~![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(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1))))) <=> ((~![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(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 ((~![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(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 ((~![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(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 ((~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[44, 30])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl(((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) <=> (~((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> (~(~((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))), rewrite((~(~((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))) <=> ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))), ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), (((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite((((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))), (((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : rewrite(((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.42 tff(53,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k9_relset_2')).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.21/0.42 tff(56,plain,(
% 0.21/0.42 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[55])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | ((~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))) | (k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))) | (k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (((k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2))))) <=> ((~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))) | (k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | ((k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | ((~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))) | (k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[60])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | ((k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))) | (k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[61, 59])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | ((k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))) | (k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 ((~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))) | (k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[64, 58])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[65, 45, 24])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) = k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))),
% 0.21/0.43 inference(symmetry,[status(thm)],[66])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (k3_subset_1(k2_zfmisc_1(A!3, C!1), k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))) = k3_subset_1(k2_zfmisc_1(A!3, C!1), k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (k3_subset_1(k2_zfmisc_1(A!3, C!1), k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))) = k3_subset_1(k2_zfmisc_1(A!3, C!1), k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)))),
% 0.21/0.43 inference(symmetry,[status(thm)],[68])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)))) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 (k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)))) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))),
% 0.21/0.43 inference(symmetry,[status(thm)],[70])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1) <=> m2_relset_1(k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (m2_relset_1(k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1) <=> m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[72])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) <=> (~((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> (~(~((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))), rewrite((~(~((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))) <=> ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))), ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), (((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C)) <=> (((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C)))), rewrite((((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C)) <=> (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))), (((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C)) <=> (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : rewrite(((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => m2_relset_1(k9_relset_2(A, B, C, D, E), A, C)) <=> ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => m2_relset_1(k9_relset_2(A, B, C, D, E), A, C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[79])).
% 0.21/0.43 tff(81,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => m2_relset_1(k9_relset_2(A, B, C, D, E), A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k9_relset_2')).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.21/0.43 tff(84,plain,(
% 0.21/0.43 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | m2_relset_1(k9_relset_2(A, B, C, D, E), A, C))),
% 0.21/0.43 inference(skolemize,[status(sab)],[83])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (m2_relset_1(k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | m2_relset_1(k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (m2_relset_1(k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (m2_relset_1(k9_relset_2(A, B, C, D, E), A, C) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | m2_relset_1(k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (m2_relset_1(k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 (m2_relset_1(k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[90, 45, 24])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 (m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[91, 73])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (^[A: $i, B: $i, C: $i] : refl(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[96, 94])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (^[A: $i, B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite((m2_relset_1(D, A, B) => (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))) <=> ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))), (![D: $i] : (m2_relset_1(D, A, B) => (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))) <=> ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m2_relset_1(D, A, B) => (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))) <=> (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m2_relset_1(D, A, B) => (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m2_relset_1(D, A, B) => (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[99])).
% 0.21/0.44 tff(101,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m2_relset_1(D, A, B) => (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t50_relset_2')).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.21/0.44 tff(104,plain,(
% 0.21/0.44 ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[103])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (m1_subset_1(D!0, k1_zfmisc_1(A!3))),
% 0.21/0.44 inference(and_elim,[status(thm)],[19])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))) | ((~m1_subset_1(D!0, k1_zfmisc_1(A!3))) | ![D: $i] : ((~m2_relset_1(D, A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, D, D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), D)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))) | (~m1_subset_1(D!0, k1_zfmisc_1(A!3))) | ![D: $i] : ((~m2_relset_1(D, A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, D, D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), D)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))) | ((~m1_subset_1(D!0, k1_zfmisc_1(A!3))) | ![D: $i] : ((~m2_relset_1(D, A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, D, D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), D)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | (k3_subset_1(B, k10_relset_1(A, B, D, C)) = k8_relset_2(A, B, C, k3_subset_1(k2_zfmisc_1(A, B), D)))))) | (~m1_subset_1(D!0, k1_zfmisc_1(A!3))) | ![D: $i] : ((~m2_relset_1(D, A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, D, D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), D))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (![D: $i] : ((~m2_relset_1(D, A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, D, D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), D))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[109, 106, 105])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (((~![D: $i] : ((~m2_relset_1(D, A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, D, D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), D))))) | ((~m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))))) <=> ((~![D: $i] : ((~m2_relset_1(D, A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, D, D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), D))))) | (~m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 ((~![D: $i] : ((~m2_relset_1(D, A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, D, D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), D))))) | ((~m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 ((~![D: $i] : ((~m2_relset_1(D, A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, D, D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), D))))) | (~m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 ((~m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)) | (k3_subset_1(C!1, k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[113, 110])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (k3_subset_1(C!1, k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0)) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[114, 92])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (^[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)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (![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))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (![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))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(119,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')).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.44 tff(121,plain,(
% 0.21/0.44 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.21/0.44 inference(skolemize,[status(sab)],[120])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(E!4, A!3, B!2) <=> m1_relset_1(E!4, A!3, B!2))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (m2_relset_1(E!4, A!3, B!2) <=> m1_relset_1(E!4, A!3, B!2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 ((~(m2_relset_1(E!4, A!3, B!2) <=> m1_relset_1(E!4, A!3, B!2))) | (~m2_relset_1(E!4, A!3, B!2)) | m1_relset_1(E!4, A!3, B!2)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 ((~(m2_relset_1(E!4, A!3, B!2) <=> m1_relset_1(E!4, A!3, B!2))) | m1_relset_1(E!4, A!3, B!2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[125, 20])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (m1_relset_1(E!4, A!3, B!2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[126, 124])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.44 tff(133,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')).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.21/0.44 tff(136,plain,(
% 0.21/0.44 ![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)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[135])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 (((~![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!3, B!2)) | (k10_relset_1(A!3, B!2, E!4, D!0) = k9_relat_1(E!4, D!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!3, B!2)) | (k10_relset_1(A!3, B!2, E!4, D!0) = k9_relat_1(E!4, D!0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 ((~![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!3, B!2)) | (k10_relset_1(A!3, B!2, E!4, D!0) = k9_relat_1(E!4, D!0)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(140,plain,
% 0.21/0.45 ((~![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!3, B!2)) | (k10_relset_1(A!3, B!2, E!4, D!0) = k9_relat_1(E!4, D!0))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.45 tff(141,plain,
% 0.21/0.45 ((~m1_relset_1(E!4, A!3, B!2)) | (k10_relset_1(A!3, B!2, E!4, D!0) = k9_relat_1(E!4, D!0))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[140, 137])).
% 0.21/0.45 tff(142,plain,
% 0.21/0.45 (k10_relset_1(A!3, B!2, E!4, D!0) = k9_relat_1(E!4, D!0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[141, 127])).
% 0.21/0.45 tff(143,plain,
% 0.21/0.45 (k9_relat_1(E!4, D!0) = k10_relset_1(A!3, B!2, E!4, D!0)),
% 0.21/0.45 inference(symmetry,[status(thm)],[142])).
% 0.21/0.45 tff(144,plain,
% 0.21/0.45 (k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), F!5) = k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[143])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), F!5)),
% 0.21/0.45 inference(symmetry,[status(thm)],[144])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 (^[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))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[146])).
% 0.21/0.45 tff(148,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 (^[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))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(150,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[149])).
% 0.21/0.45 tff(151,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')).
% 0.21/0.45 tff(152,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.21/0.45 tff(153,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.21/0.45 tff(154,plain,(
% 0.21/0.45 ![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)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[153])).
% 0.21/0.45 tff(155,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.21/0.45 tff(156,plain,
% 0.21/0.45 (((~![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!3, B!2)) | m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!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(E!4, A!3, B!2)) | m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(157,plain,
% 0.21/0.45 ((~![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!3, B!2)) | m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(158,plain,
% 0.21/0.45 ((~![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!3, B!2)) | m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.45 tff(159,plain,
% 0.21/0.45 ((~m1_relset_1(E!4, A!3, B!2)) | m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[158, 155])).
% 0.21/0.45 tff(160,plain,
% 0.21/0.45 (m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[159, 127])).
% 0.21/0.45 tff(161,plain,
% 0.21/0.45 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(162,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[161])).
% 0.21/0.45 tff(163,plain,
% 0.21/0.45 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> (~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))), rewrite((~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> (((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))))), rewrite((((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(164,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[163])).
% 0.21/0.45 tff(165,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(166,plain,
% 0.21/0.45 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(167,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[166])).
% 0.21/0.45 tff(168,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k8_relset_2')).
% 0.21/0.45 tff(169,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.21/0.45 tff(170,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.21/0.45 tff(171,plain,(
% 0.21/0.45 ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[170])).
% 0.21/0.45 tff(172,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.21/0.45 tff(173,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[172, 162])).
% 0.21/0.45 tff(174,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))) | (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))) | (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(175,plain,
% 0.21/0.45 (((k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2)))) <=> ((~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))) | (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(176,plain,
% 0.21/0.46 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))) | (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[175])).
% 0.21/0.46 tff(177,plain,
% 0.21/0.46 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))) | (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[176, 174])).
% 0.21/0.46 tff(178,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(179,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))) | (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.46 tff(180,plain,
% 0.21/0.46 ((~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))) | (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[179, 173])).
% 0.21/0.46 tff(181,plain,
% 0.21/0.46 (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[180, 160, 30])).
% 0.21/0.46 tff(182,plain,
% 0.21/0.46 (k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)),
% 0.21/0.46 inference(symmetry,[status(thm)],[181])).
% 0.21/0.46 tff(183,plain,
% 0.21/0.46 (k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), F!5)),
% 0.21/0.46 inference(transitivity,[status(thm)],[182, 145])).
% 0.21/0.46 tff(184,plain,
% 0.21/0.46 (k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)) = k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), F!5))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[183])).
% 0.21/0.46 tff(185,plain,
% 0.21/0.46 (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), F!5)) = k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))),
% 0.21/0.46 inference(symmetry,[status(thm)],[184])).
% 0.21/0.46 tff(186,plain,
% 0.21/0.46 (m1_subset_1(k9_relat_1(E!4, D!0), k1_zfmisc_1(B!2)) <=> m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[143])).
% 0.21/0.46 tff(187,plain,
% 0.21/0.46 (m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2)) <=> m1_subset_1(k9_relat_1(E!4, D!0), k1_zfmisc_1(B!2))),
% 0.21/0.46 inference(symmetry,[status(thm)],[186])).
% 0.21/0.46 tff(188,plain,
% 0.21/0.46 (m1_subset_1(k9_relat_1(E!4, D!0), k1_zfmisc_1(B!2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[160, 187])).
% 0.21/0.46 tff(189,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : refl(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(190,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), 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(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[189])).
% 0.21/0.46 tff(191,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(192,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), 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(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[191])).
% 0.21/0.46 tff(193,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), 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(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[192, 190])).
% 0.21/0.46 tff(194,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), 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(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(195,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))) <=> ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))) <=> ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C)))) <=> (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C)))))), rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(196,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), 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(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[195])).
% 0.21/0.46 tff(197,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t49_relset_2')).
% 0.21/0.46 tff(198,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.21/0.46 tff(199,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.21/0.46 tff(200,plain,(
% 0.21/0.46 ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[199])).
% 0.21/0.46 tff(201,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[200, 193])).
% 0.21/0.46 tff(202,plain,
% 0.21/0.46 (((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))) | ((~m1_subset_1(k9_relat_1(E!4, D!0), k1_zfmisc_1(B!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), D), k9_relat_1(E!4, D!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))) | (~m1_subset_1(k9_relat_1(E!4, D!0), k1_zfmisc_1(B!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), D), k9_relat_1(E!4, D!0)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(203,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))) | ((~m1_subset_1(k9_relat_1(E!4, D!0), k1_zfmisc_1(B!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), D), k9_relat_1(E!4, D!0)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(204,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (k3_subset_1(B, k8_relset_2(A, B, C, D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(A, B), D), C))))) | (~m1_subset_1(k9_relat_1(E!4, D!0), k1_zfmisc_1(B!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), D), k9_relat_1(E!4, D!0))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.21/0.46 tff(205,plain,
% 0.21/0.46 ((~m1_subset_1(k9_relat_1(E!4, D!0), k1_zfmisc_1(B!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), D), k9_relat_1(E!4, D!0))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[204, 201])).
% 0.21/0.46 tff(206,plain,
% 0.21/0.46 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), D), k9_relat_1(E!4, D!0))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[205, 188])).
% 0.21/0.46 tff(207,plain,
% 0.21/0.46 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), D), k9_relat_1(E!4, D!0))))) | ((~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), F!5)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k9_relat_1(E!4, D!0))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), D), k9_relat_1(E!4, D!0))))) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), F!5)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k9_relat_1(E!4, D!0))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(208,plain,
% 0.21/0.46 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), D), k9_relat_1(E!4, D!0))))) | ((~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), F!5)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k9_relat_1(E!4, D!0))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(209,plain,
% 0.21/0.46 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), D)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), D), k9_relat_1(E!4, D!0))))) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), F!5)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k9_relat_1(E!4, D!0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.21/0.47 tff(210,plain,
% 0.21/0.47 (k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), F!5)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k9_relat_1(E!4, D!0))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[209, 30, 206])).
% 0.21/0.47 tff(211,plain,
% 0.21/0.47 (k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k9_relat_1(E!4, D!0)) = k3_subset_1(C!1, k8_relset_2(B!2, C!1, k9_relat_1(E!4, D!0), F!5))),
% 0.21/0.47 inference(symmetry,[status(thm)],[210])).
% 0.21/0.47 tff(212,plain,
% 0.21/0.47 (^[A: $i, B: $i, C: $i] : refl((v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(213,plain,
% 0.21/0.47 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[212])).
% 0.21/0.47 tff(214,plain,
% 0.21/0.47 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(215,plain,
% 0.21/0.47 (^[A: $i, B: $i, C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(216,plain,
% 0.21/0.47 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[215])).
% 0.21/0.47 tff(217,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_relset_1')).
% 0.21/0.47 tff(218,plain,
% 0.21/0.47 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.21/0.47 tff(219,plain,
% 0.21/0.47 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.21/0.47 tff(220,plain,(
% 0.21/0.47 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[219])).
% 0.21/0.47 tff(221,plain,
% 0.21/0.47 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.21/0.47 tff(222,plain,
% 0.21/0.47 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(223,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(224,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!3, B!2))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.21/0.47 tff(225,plain,
% 0.21/0.47 (v1_relat_1(E!4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[224, 221, 24])).
% 0.21/0.47 tff(226,plain,
% 0.21/0.47 (^[A: $i, B: $i] : refl(((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(227,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[226])).
% 0.21/0.47 tff(228,plain,
% 0.21/0.47 (^[A: $i, B: $i] : rewrite(((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(229,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[228])).
% 0.21/0.47 tff(230,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[229, 227])).
% 0.21/0.47 tff(231,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(232,plain,
% 0.21/0.47 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((v1_relat_1(C) => (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))) <=> ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))), (![C: $i] : (v1_relat_1(C) => (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))) <=> ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))), ((v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))) <=> (v1_relat_1(B) => ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))))), rewrite((v1_relat_1(B) => ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))), ((v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(233,plain,
% 0.21/0.47 (![A: $i, B: $i] : (v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[232])).
% 0.21/0.47 tff(234,axiom,(![A: $i, B: $i] : (v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t159_relat_1')).
% 0.21/0.47 tff(235,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.21/0.47 tff(236,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[235, 231])).
% 0.21/0.47 tff(237,plain,(
% 0.21/0.47 ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[236])).
% 0.21/0.47 tff(238,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.21/0.47 tff(239,plain,
% 0.21/0.47 (((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))) | ((~v1_relat_1(E!4)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(E!4, C), D!0) = k9_relat_1(C, k9_relat_1(E!4, D!0)))))) <=> ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))) | (~v1_relat_1(E!4)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(E!4, C), D!0) = k9_relat_1(C, k9_relat_1(E!4, D!0)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(240,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))) | ((~v1_relat_1(E!4)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(E!4, C), D!0) = k9_relat_1(C, k9_relat_1(E!4, D!0)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(241,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(B, C), A) = k9_relat_1(C, k9_relat_1(B, A)))))) | (~v1_relat_1(E!4)) | ![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(E!4, C), D!0) = k9_relat_1(C, k9_relat_1(E!4, D!0))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.21/0.47 tff(242,plain,
% 0.21/0.47 (![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(E!4, C), D!0) = k9_relat_1(C, k9_relat_1(E!4, D!0))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[241, 238, 225])).
% 0.21/0.47 tff(243,plain,
% 0.21/0.47 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(244,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(245,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)) | (~m1_subset_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k1_zfmisc_1(k2_zfmisc_1(B!2, C!1))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.21/0.47 tff(246,plain,
% 0.21/0.47 (v1_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[245, 221, 45])).
% 0.21/0.47 tff(247,plain,
% 0.21/0.47 (((~![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(E!4, C), D!0) = k9_relat_1(C, k9_relat_1(E!4, D!0))))) | ((~v1_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))) | (k9_relat_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k9_relat_1(E!4, D!0))))) <=> ((~![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(E!4, C), D!0) = k9_relat_1(C, k9_relat_1(E!4, D!0))))) | (~v1_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))) | (k9_relat_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k9_relat_1(E!4, D!0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(248,plain,
% 0.21/0.47 ((~![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(E!4, C), D!0) = k9_relat_1(C, k9_relat_1(E!4, D!0))))) | ((~v1_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))) | (k9_relat_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k9_relat_1(E!4, D!0))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(249,plain,
% 0.21/0.47 ((~![C: $i] : ((~v1_relat_1(C)) | (k9_relat_1(k5_relat_1(E!4, C), D!0) = k9_relat_1(C, k9_relat_1(E!4, D!0))))) | (~v1_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))) | (k9_relat_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k9_relat_1(E!4, D!0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.21/0.47 tff(250,plain,
% 0.21/0.47 (k9_relat_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0) = k9_relat_1(k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5), k9_relat_1(E!4, D!0))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[249, 246, 242])).
% 0.21/0.47 tff(251,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1) <=> m1_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(252,plain,
% 0.21/0.47 (m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1) <=> m1_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[251, 122])).
% 0.21/0.47 tff(253,plain,
% 0.21/0.47 ((~(m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1) <=> m1_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1))) | (~m2_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)) | m1_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(254,plain,
% 0.21/0.47 (m1_relset_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[253, 92, 252])).
% 0.21/0.47 tff(255,plain,
% 0.21/0.47 (((~![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(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)) | (k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0) = k9_relat_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!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(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)) | (k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0) = k9_relat_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(256,plain,
% 0.21/0.47 ((~![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(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)) | (k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0) = k9_relat_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(257,plain,
% 0.21/0.47 ((~![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(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), A!3, C!1)) | (k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0) = k9_relat_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.21/0.47 tff(258,plain,
% 0.21/0.47 (k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0) = k9_relat_1(k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[257, 137, 254])).
% 0.21/0.47 tff(259,plain,
% 0.21/0.47 (k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0) = k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))),
% 0.21/0.47 inference(transitivity,[status(thm)],[258, 250, 211, 185])).
% 0.21/0.47 tff(260,plain,
% 0.21/0.47 (k3_subset_1(C!1, k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0)) = k3_subset_1(C!1, k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[259])).
% 0.21/0.48 tff(261,plain,
% 0.21/0.48 (k3_subset_1(C!1, k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))) = k3_subset_1(C!1, k10_relset_1(A!3, C!1, k5_relat_1(E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)), D!0))),
% 0.21/0.48 inference(symmetry,[status(thm)],[260])).
% 0.21/0.48 tff(262,plain,
% 0.21/0.48 (m1_subset_1(k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) <=> m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[182])).
% 0.21/0.48 tff(263,plain,
% 0.21/0.48 (m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) <=> m1_subset_1(k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1))),
% 0.21/0.48 inference(symmetry,[status(thm)],[262])).
% 0.21/0.48 tff(264,plain,
% 0.21/0.48 (^[A: $i, B: $i, C: $i, D: $i] : refl((m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(265,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[264])).
% 0.21/0.48 tff(266,plain,
% 0.21/0.48 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> (~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))), rewrite((~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> (((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))))), rewrite((((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(267,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[266])).
% 0.21/0.48 tff(268,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(269,plain,
% 0.21/0.48 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(270,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[269])).
% 0.21/0.48 tff(271,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k8_relset_2')).
% 0.21/0.48 tff(272,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.21/0.48 tff(273,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[272, 268])).
% 0.21/0.48 tff(274,plain,(
% 0.21/0.48 ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[273])).
% 0.21/0.48 tff(275,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[274, 267])).
% 0.21/0.48 tff(276,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[275, 265])).
% 0.21/0.48 tff(277,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(278,plain,
% 0.21/0.48 ((m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2)))) <=> ((~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(279,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[278])).
% 0.21/0.48 tff(280,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[279, 277])).
% 0.21/0.48 tff(281,plain,
% 0.21/0.48 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(282,plain,
% 0.21/0.48 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.21/0.48 tff(283,plain,
% 0.21/0.48 ((~m1_subset_1(F!5, k1_zfmisc_1(k2_zfmisc_1(B!2, C!1)))) | m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1)) | (~m1_subset_1(k10_relset_1(A!3, B!2, E!4, D!0), k1_zfmisc_1(B!2)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[282, 276])).
% 0.21/0.48 tff(284,plain,
% 0.21/0.48 (m1_subset_1(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[283, 160, 30])).
% 0.21/0.48 tff(285,plain,
% 0.21/0.48 (m1_subset_1(k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[284, 263])).
% 0.21/0.48 tff(286,plain,
% 0.21/0.48 (^[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)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(287,plain,
% 0.21/0.48 (![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))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[286])).
% 0.21/0.48 tff(288,plain,
% 0.21/0.48 (![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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(289,plain,
% 0.21/0.48 (^[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)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(290,plain,
% 0.21/0.48 (![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))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[289])).
% 0.21/0.48 tff(291,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')).
% 0.21/0.48 tff(292,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.21/0.48 tff(293,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.21/0.48 tff(294,plain,(
% 0.21/0.48 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 0.21/0.48 inference(skolemize,[status(sab)],[293])).
% 0.21/0.48 tff(295,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[294, 287])).
% 0.21/0.48 tff(296,plain,
% 0.21/0.48 (((~![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(k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1))) | (k3_subset_1(C!1, k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)))) <=> ((~![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(k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1))) | (k3_subset_1(C!1, k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(297,plain,
% 0.21/0.48 ((~![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(k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1))) | (k3_subset_1(C!1, k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(298,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))) | (~m1_subset_1(k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1))) | (k3_subset_1(C!1, k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.21/0.48 tff(299,plain,
% 0.21/0.48 ((~m1_subset_1(k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5), k1_zfmisc_1(C!1))) | (k3_subset_1(C!1, k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[298, 295])).
% 0.21/0.48 tff(300,plain,
% 0.21/0.48 (k3_subset_1(C!1, k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5))) = k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[299, 285])).
% 0.21/0.48 tff(301,plain,
% 0.21/0.48 (k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k3_subset_1(C!1, k3_subset_1(C!1, k7_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5)))),
% 0.21/0.48 inference(symmetry,[status(thm)],[300])).
% 0.21/0.48 tff(302,plain,
% 0.21/0.48 (k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[181, 301, 261, 115, 71])).
% 0.21/0.49 tff(303,plain,
% 0.21/0.49 (~(k8_relset_2(B!2, C!1, k10_relset_1(A!3, B!2, E!4, D!0), F!5) = k8_relset_2(A!3, C!1, D!0, k3_subset_1(k2_zfmisc_1(A!3, C!1), k9_relset_2(A!3, B!2, C!1, E!4, k3_subset_1(k2_zfmisc_1(B!2, C!1), F!5)))))),
% 0.21/0.49 inference(or_elim,[status(thm)],[25])).
% 0.21/0.49 tff(304,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[303, 302])).
% 0.21/0.49 % SZS output end Proof
% 0.21/0.49 % E exiting
%------------------------------------------------------------------------------