%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU437+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:57 AM UTC 2025
% Result : Theorem 39.81s 40.07s
% Output : Proof 39.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU437+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 07:19:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 39.81/40.07 % SZS status Theorem
% 39.81/40.07 % SZS output start Proof
% 39.81/40.07 tff(r2_hidden_type, type, (
% 39.81/40.07 r2_hidden: ( $i * $i ) > $o)).
% 39.81/40.07 tff(tptp_fun_D_3_type, type, (
% 39.81/40.07 tptp_fun_D_3: $i)).
% 39.81/40.07 tff(k4_tarski_type, type, (
% 39.81/40.07 k4_tarski: ( $i * $i ) > $i)).
% 39.81/40.07 tff(tptp_fun_C_5_type, type, (
% 39.81/40.07 tptp_fun_C_5: ( $i * $i ) > $i)).
% 39.81/40.07 tff(k8_relset_2_type, type, (
% 39.81/40.07 k8_relset_2: ( $i * $i * $i * $i ) > $i)).
% 39.81/40.07 tff(tptp_fun_C_0_type, type, (
% 39.81/40.07 tptp_fun_C_0: $i)).
% 39.81/40.07 tff(tptp_fun_B_1_type, type, (
% 39.81/40.07 tptp_fun_B_1: $i)).
% 39.81/40.07 tff(tptp_fun_A_2_type, type, (
% 39.81/40.07 tptp_fun_A_2: $i)).
% 39.81/40.07 tff(tptp_fun_E_4_type, type, (
% 39.81/40.07 tptp_fun_E_4: $i)).
% 39.81/40.07 tff(tptp_fun_F_16_type, type, (
% 39.81/40.07 tptp_fun_F_16: ( $i * $i * $i ) > $i)).
% 39.81/40.07 tff(k9_relat_1_type, type, (
% 39.81/40.07 k9_relat_1: ( $i * $i ) > $i)).
% 39.81/40.07 tff(k1_tarski_type, type, (
% 39.81/40.07 k1_tarski: $i > $i)).
% 39.81/40.07 tff(v1_relat_1_type, type, (
% 39.81/40.07 v1_relat_1: $i > $o)).
% 39.81/40.07 tff(m1_subset_1_type, type, (
% 39.81/40.07 m1_subset_1: ( $i * $i ) > $o)).
% 39.81/40.07 tff(k1_zfmisc_1_type, type, (
% 39.81/40.07 k1_zfmisc_1: $i > $i)).
% 39.81/40.07 tff(k2_zfmisc_1_type, type, (
% 39.81/40.07 k2_zfmisc_1: ( $i * $i ) > $i)).
% 39.81/40.07 tff(r1_tarski_type, type, (
% 39.81/40.07 r1_tarski: ( $i * $i ) > $o)).
% 39.81/40.07 tff(v1_xboole_0_type, type, (
% 39.81/40.07 v1_xboole_0: $i > $o)).
% 39.81/40.07 tff(k7_relset_2_type, type, (
% 39.81/40.07 k7_relset_2: ( $i * $i * $i * $i ) > $i)).
% 39.81/40.07 tff(1,plain,
% 39.81/40.07 (^[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))))))),
% 39.81/40.07 inference(bind,[status(th)],[])).
% 39.81/40.07 tff(2,plain,
% 39.81/40.07 (![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)))))),
% 39.81/40.07 inference(quant_intro,[status(thm)],[1])).
% 39.81/40.07 tff(3,plain,
% 39.81/40.07 (![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)))))),
% 39.81/40.07 inference(rewrite,[status(thm)],[])).
% 39.81/40.07 tff(4,plain,
% 39.81/40.07 (^[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))))))),
% 39.81/40.07 inference(bind,[status(th)],[])).
% 39.81/40.07 tff(5,plain,
% 39.81/40.07 (![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)))))),
% 39.81/40.07 inference(quant_intro,[status(thm)],[4])).
% 39.81/40.07 tff(6,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/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 39.81/40.07 tff(7,plain,
% 39.81/40.07 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[6, 5])).
% 39.81/40.07 tff(8,plain,
% 39.81/40.07 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[7, 3])).
% 39.81/40.07 tff(9,plain,(
% 39.81/40.07 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 39.81/40.07 inference(skolemize,[status(sab)],[8])).
% 39.81/40.07 tff(10,plain,
% 39.81/40.07 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[9, 2])).
% 39.81/40.07 tff(11,plain,
% 39.81/40.07 ((m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))),
% 39.81/40.07 inference(rewrite,[status(thm)],[])).
% 39.81/40.07 tff(12,plain,
% 39.81/40.07 ((~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))) <=> (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))))),
% 39.81/40.07 inference(rewrite,[status(thm)],[])).
% 39.81/40.07 tff(13,plain,
% 39.81/40.07 ((m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))))) <=> (m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))),
% 39.81/40.07 inference(monotonicity,[status(thm)],[12])).
% 39.81/40.07 tff(14,plain,
% 39.81/40.07 ((m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))))))),
% 39.81/40.07 inference(monotonicity,[status(thm)],[13])).
% 39.81/40.07 tff(15,plain,
% 39.81/40.07 ((m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))),
% 39.81/40.07 inference(transitivity,[status(thm)],[14, 11])).
% 39.81/40.07 tff(16,plain,
% 39.81/40.07 ((~![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)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))),
% 39.81/40.07 inference(rewrite,[status(thm)],[])).
% 39.81/40.07 tff(17,plain,
% 39.81/40.07 ((~![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))) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_tarski(D, E) => r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E))))))) <=> (~![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)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))),
% 39.81/40.07 inference(rewrite,[status(thm)],[])).
% 39.81/40.07 tff(18,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))) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_tarski(D, E) => r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t40_relset_2')).
% 39.81/40.07 tff(19,plain,
% 39.81/40.07 (~![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)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[18, 17])).
% 39.81/40.07 tff(20,plain,
% 39.81/40.07 (~![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)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[19, 16])).
% 39.81/40.07 tff(21,plain,
% 39.81/40.07 (~![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)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[20, 16])).
% 39.81/40.07 tff(22,plain,
% 39.81/40.07 (~![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)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[21, 16])).
% 39.81/40.07 tff(23,plain,
% 39.81/40.07 (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[22, 15])).
% 39.81/40.07 tff(24,plain,
% 39.81/40.07 (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 39.81/40.07 inference(and_elim,[status(thm)],[23])).
% 39.81/40.07 tff(25,plain,
% 39.81/40.07 (m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 39.81/40.07 inference(or_elim,[status(thm)],[24])).
% 39.81/40.07 tff(26,plain,
% 39.81/40.07 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 39.81/40.07 inference(rewrite,[status(thm)],[])).
% 39.81/40.07 tff(27,plain,
% 39.81/40.07 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 39.81/40.07 inference(quant_inst,[status(thm)],[])).
% 39.81/40.07 tff(28,plain,
% 39.81/40.07 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[27, 26])).
% 39.81/40.07 tff(29,plain,
% 39.81/40.07 (v1_relat_1(E!4)),
% 39.81/40.07 inference(unit_resolution,[status(thm)],[28, 25, 10])).
% 39.81/40.07 tff(30,plain,
% 39.81/40.07 (^[A: $i, B: $i, C: $i] : refl(((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))) <=> ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))))),
% 39.81/40.07 inference(bind,[status(th)],[])).
% 39.81/40.07 tff(31,plain,
% 39.81/40.07 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))) <=> ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 39.81/40.07 inference(quant_intro,[status(thm)],[30])).
% 39.81/40.07 tff(32,plain,
% 39.81/40.07 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))) <=> ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 39.81/40.07 inference(rewrite,[status(thm)],[])).
% 39.81/40.07 tff(33,plain,
% 39.81/40.07 (^[A: $i, B: $i, C: $i] : rewrite((v1_relat_1(C) => (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))) <=> ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))))),
% 39.81/40.07 inference(bind,[status(th)],[])).
% 39.81/40.07 tff(34,plain,
% 39.81/40.07 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))) <=> ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 39.81/40.07 inference(quant_intro,[status(thm)],[33])).
% 39.81/40.07 tff(35,axiom,(![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t9_relset_2')).
% 39.81/40.07 tff(36,plain,
% 39.81/40.07 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[35, 34])).
% 39.81/40.07 tff(37,plain,
% 39.81/40.07 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[36, 32])).
% 39.81/40.07 tff(38,plain,(
% 39.81/40.07 ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 39.81/40.07 inference(skolemize,[status(sab)],[37])).
% 39.81/40.07 tff(39,plain,
% 39.81/40.07 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[38, 31])).
% 39.81/40.07 tff(40,plain,
% 39.81/40.07 (((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | ((~v1_relat_1(E!4)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | (~v1_relat_1(E!4)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)))),
% 39.81/40.07 inference(rewrite,[status(thm)],[])).
% 39.81/40.07 tff(41,plain,
% 39.81/40.07 ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | ((~v1_relat_1(E!4)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)))),
% 39.81/40.07 inference(quant_inst,[status(thm)],[])).
% 39.81/40.07 tff(42,plain,
% 39.81/40.07 ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | (~v1_relat_1(E!4)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))),
% 39.81/40.07 inference(modus_ponens,[status(thm)],[41, 40])).
% 39.81/40.07 tff(43,plain,
% 39.81/40.07 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)),
% 39.81/40.07 inference(unit_resolution,[status(thm)],[42, 39, 29])).
% 39.81/40.07 tff(44,plain,
% 39.81/40.07 (^[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)))))),
% 39.91/40.08 inference(bind,[status(th)],[])).
% 39.91/40.08 tff(45,plain,
% 39.91/40.08 (![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))))),
% 39.91/40.08 inference(quant_intro,[status(thm)],[44])).
% 39.91/40.08 tff(46,plain,
% 39.91/40.08 (^[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))))))),
% 39.91/40.08 inference(bind,[status(th)],[])).
% 39.91/40.08 tff(47,plain,
% 39.91/40.08 (![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))))),
% 39.91/40.08 inference(quant_intro,[status(thm)],[46])).
% 39.91/40.08 tff(48,plain,
% 39.91/40.08 (![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)))),
% 39.91/40.08 inference(rewrite,[status(thm)],[])).
% 39.91/40.08 tff(49,plain,
% 39.91/40.08 (^[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))))),
% 39.91/40.08 inference(bind,[status(th)],[])).
% 39.91/40.08 tff(50,plain,
% 39.91/40.08 (![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)))),
% 39.91/40.08 inference(quant_intro,[status(thm)],[49])).
% 39.91/40.08 tff(51,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/sandbox/benchmark/theBenchmark.p','redefinition_k8_relset_2')).
% 39.91/40.08 tff(52,plain,
% 39.91/40.08 (![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)))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[51, 50])).
% 39.91/40.08 tff(53,plain,
% 39.91/40.08 (![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)))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[52, 48])).
% 39.91/40.08 tff(54,plain,(
% 39.91/40.08 ![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)))),
% 39.91/40.08 inference(skolemize,[status(sab)],[53])).
% 39.91/40.08 tff(55,plain,
% 39.91/40.08 (![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))))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[54, 47])).
% 39.91/40.08 tff(56,plain,
% 39.91/40.08 (![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))))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[55, 45])).
% 39.91/40.08 tff(57,plain,
% 39.91/40.08 (m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 39.91/40.08 inference(and_elim,[status(thm)],[23])).
% 39.91/40.08 tff(58,plain,
% 39.91/40.08 (m1_subset_1(C!0, k1_zfmisc_1(A!2))),
% 39.91/40.08 inference(and_elim,[status(thm)],[23])).
% 39.91/40.08 tff(59,plain,
% 39.91/40.08 (((~![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(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)))) <=> ((~![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(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)))),
% 39.91/40.08 inference(rewrite,[status(thm)],[])).
% 39.91/40.08 tff(60,plain,
% 39.91/40.08 (((k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) <=> ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)))),
% 39.91/40.08 inference(rewrite,[status(thm)],[])).
% 39.91/40.08 tff(61,plain,
% 39.91/40.08 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3))))),
% 39.91/40.08 inference(monotonicity,[status(thm)],[60])).
% 39.91/40.08 tff(62,plain,
% 39.91/40.08 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)))),
% 39.91/40.08 inference(transitivity,[status(thm)],[61, 59])).
% 39.91/40.08 tff(63,plain,
% 39.91/40.08 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))),
% 39.91/40.08 inference(quant_inst,[status(thm)],[])).
% 39.91/40.08 tff(64,plain,
% 39.91/40.08 ((~![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(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[63, 62])).
% 39.91/40.08 tff(65,plain,
% 39.91/40.08 (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)),
% 39.91/40.08 inference(unit_resolution,[status(thm)],[64, 58, 57, 56])).
% 39.91/40.08 tff(66,plain,
% 39.91/40.08 (k7_relset_2(A!2, B!1, C!0, D!3) = k8_relset_2(A!2, B!1, C!0, D!3)),
% 39.91/40.08 inference(symmetry,[status(thm)],[65])).
% 39.91/40.08 tff(67,plain,
% 39.91/40.08 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3)) <=> r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))),
% 39.91/40.08 inference(monotonicity,[status(thm)],[66])).
% 39.91/40.08 tff(68,plain,
% 39.91/40.08 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3)) <=> r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))),
% 39.91/40.08 inference(symmetry,[status(thm)],[67])).
% 39.91/40.08 tff(69,plain,
% 39.91/40.08 (^[A: $i, B: $i] : refl((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))))))),
% 39.91/40.08 inference(bind,[status(th)],[])).
% 39.91/40.08 tff(70,plain,
% 39.91/40.08 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 39.91/40.08 inference(quant_intro,[status(thm)],[69])).
% 39.91/40.08 tff(71,plain,
% 39.91/40.08 (^[A: $i, B: $i] : rewrite((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))))))),
% 39.91/40.08 inference(bind,[status(th)],[])).
% 39.91/40.08 tff(72,plain,
% 39.91/40.08 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 39.91/40.08 inference(quant_intro,[status(thm)],[71])).
% 39.91/40.08 tff(73,plain,
% 39.91/40.08 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 39.91/40.08 inference(transitivity,[status(thm)],[72, 70])).
% 39.91/40.08 tff(74,plain,
% 39.91/40.08 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))), rewrite((r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))) <=> (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))) <=> (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))))), rewrite((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))))),
% 39.91/40.08 inference(bind,[status(th)],[])).
% 39.91/40.08 tff(75,plain,
% 39.91/40.08 (![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 39.91/40.08 inference(quant_intro,[status(thm)],[74])).
% 39.91/40.08 tff(76,plain,
% 39.91/40.08 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 39.91/40.08 inference(rewrite,[status(thm)],[])).
% 39.91/40.08 tff(77,plain,
% 39.91/40.08 (^[A: $i, B: $i] : rewrite((r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))))),
% 39.91/40.08 inference(bind,[status(th)],[])).
% 39.91/40.08 tff(78,plain,
% 39.91/40.08 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 39.91/40.08 inference(quant_intro,[status(thm)],[77])).
% 39.91/40.08 tff(79,axiom,(![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 39.91/40.08 tff(80,plain,
% 39.91/40.08 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[79, 78])).
% 39.91/40.08 tff(81,plain,
% 39.91/40.08 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[80, 76])).
% 39.91/40.08 tff(82,plain,(
% 39.91/40.08 ![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))),
% 39.91/40.08 inference(skolemize,[status(sab)],[81])).
% 39.91/40.08 tff(83,plain,
% 39.91/40.08 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[82, 75])).
% 39.91/40.08 tff(84,plain,
% 39.91/40.08 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[83, 73])).
% 39.91/40.08 tff(85,plain,
% 39.91/40.08 ((~![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))) | (~((~((~r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4))) | ![C: $i] : ((~r2_hidden(C, k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, k8_relset_2(A!2, B!1, C!0, E!4))))) | (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))))))),
% 39.91/40.08 inference(quant_inst,[status(thm)],[])).
% 39.91/40.08 tff(86,plain,
% 39.91/40.08 (~((~((~r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4))) | ![C: $i] : ((~r2_hidden(C, k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, k8_relset_2(A!2, B!1, C!0, E!4))))) | (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))))),
% 39.91/40.08 inference(unit_resolution,[status(thm)],[85, 84])).
% 39.91/40.08 tff(87,plain,
% 39.91/40.08 (((~((~r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4))) | ![C: $i] : ((~r2_hidden(C, k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, k8_relset_2(A!2, B!1, C!0, E!4))))) | (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))))) | (r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))),
% 39.91/40.08 inference(tautology,[status(thm)],[])).
% 39.91/40.08 tff(88,plain,
% 39.91/40.08 (r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))),
% 39.91/40.08 inference(unit_resolution,[status(thm)],[87, 86])).
% 39.91/40.08 tff(89,plain,
% 39.91/40.08 (~r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4))),
% 39.91/40.08 inference(or_elim,[status(thm)],[24])).
% 39.91/40.08 tff(90,plain,
% 39.91/40.08 ((~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))) | r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))),
% 39.91/40.08 inference(tautology,[status(thm)],[])).
% 39.91/40.08 tff(91,plain,
% 39.91/40.08 ((~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))),
% 39.91/40.08 inference(unit_resolution,[status(thm)],[90, 89])).
% 39.91/40.08 tff(92,plain,
% 39.91/40.08 (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))),
% 39.91/40.08 inference(unit_resolution,[status(thm)],[91, 88])).
% 39.91/40.08 tff(93,plain,
% 39.91/40.08 (((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))),
% 39.91/40.08 inference(tautology,[status(thm)],[])).
% 39.91/40.08 tff(94,plain,
% 39.91/40.08 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))),
% 39.91/40.08 inference(unit_resolution,[status(thm)],[93, 92])).
% 39.91/40.08 tff(95,plain,
% 39.91/40.08 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[94, 68])).
% 39.91/40.08 tff(96,plain,
% 39.91/40.08 (m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) <=> m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))),
% 39.91/40.08 inference(monotonicity,[status(thm)],[66])).
% 39.91/40.08 tff(97,plain,
% 39.91/40.08 (m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) <=> m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))),
% 39.91/40.08 inference(symmetry,[status(thm)],[96])).
% 39.91/40.08 tff(98,plain,
% 39.91/40.08 (^[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)))))),
% 39.91/40.08 inference(bind,[status(th)],[])).
% 39.91/40.08 tff(99,plain,
% 39.91/40.08 (![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))))),
% 39.91/40.08 inference(quant_intro,[status(thm)],[98])).
% 39.91/40.08 tff(100,plain,
% 39.91/40.08 (^[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))))))),
% 39.91/40.08 inference(bind,[status(th)],[])).
% 39.91/40.08 tff(101,plain,
% 39.91/40.08 (![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))))),
% 39.91/40.08 inference(quant_intro,[status(thm)],[100])).
% 39.91/40.08 tff(102,plain,
% 39.91/40.08 (![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)))),
% 39.91/40.08 inference(rewrite,[status(thm)],[])).
% 39.91/40.08 tff(103,plain,
% 39.91/40.08 (^[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))))),
% 39.91/40.08 inference(bind,[status(th)],[])).
% 39.91/40.08 tff(104,plain,
% 39.91/40.08 (![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)))),
% 39.91/40.08 inference(quant_intro,[status(thm)],[103])).
% 39.91/40.08 tff(105,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/sandbox/benchmark/theBenchmark.p','dt_k8_relset_2')).
% 39.91/40.08 tff(106,plain,
% 39.91/40.08 (![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)))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[105, 104])).
% 39.91/40.08 tff(107,plain,
% 39.91/40.08 (![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)))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[106, 102])).
% 39.91/40.08 tff(108,plain,(
% 39.91/40.08 ![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)))),
% 39.91/40.08 inference(skolemize,[status(sab)],[107])).
% 39.91/40.08 tff(109,plain,
% 39.91/40.08 (![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))))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[108, 101])).
% 39.91/40.08 tff(110,plain,
% 39.91/40.08 (![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))))),
% 39.91/40.08 inference(modus_ponens,[status(thm)],[109, 99])).
% 39.91/40.08 tff(111,plain,
% 39.91/40.08 (((~![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(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)))) <=> ((~![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(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)))),
% 39.91/40.09 inference(rewrite,[status(thm)],[])).
% 39.91/40.09 tff(112,plain,
% 39.91/40.09 ((m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) <=> ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)))),
% 39.91/40.09 inference(rewrite,[status(thm)],[])).
% 39.91/40.09 tff(113,plain,
% 39.91/40.09 (((~![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(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!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(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))))),
% 39.91/40.09 inference(monotonicity,[status(thm)],[112])).
% 39.91/40.09 tff(114,plain,
% 39.91/40.09 (((~![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(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!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(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)))),
% 39.91/40.09 inference(transitivity,[status(thm)],[113, 111])).
% 39.91/40.09 tff(115,plain,
% 39.91/40.09 ((~![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(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))),
% 39.91/40.09 inference(quant_inst,[status(thm)],[])).
% 39.91/40.09 tff(116,plain,
% 39.91/40.09 ((~![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(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))),
% 39.91/40.09 inference(modus_ponens,[status(thm)],[115, 114])).
% 39.91/40.09 tff(117,plain,
% 39.91/40.09 (m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))),
% 39.91/40.09 inference(unit_resolution,[status(thm)],[116, 58, 57, 110])).
% 39.91/40.09 tff(118,plain,
% 39.91/40.09 (m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))),
% 39.91/40.09 inference(modus_ponens,[status(thm)],[117, 97])).
% 39.91/40.09 tff(119,plain,
% 39.91/40.09 (^[A: $i, B: $i, C: $i] : refl(((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))) <=> ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))))),
% 39.91/40.09 inference(bind,[status(th)],[])).
% 39.91/40.09 tff(120,plain,
% 39.91/40.09 (![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))),
% 39.91/40.09 inference(quant_intro,[status(thm)],[119])).
% 39.91/40.09 tff(121,plain,
% 39.91/40.09 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) <=> (~((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))))), ((~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C))) <=> (~(~((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))))))), rewrite((~(~((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))))) <=> ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))), ((~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C))) <=> ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))))),
% 39.91/40.09 inference(bind,[status(th)],[])).
% 39.91/40.09 tff(122,plain,
% 39.91/40.09 (![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C))) <=> ![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))),
% 39.91/40.09 inference(quant_intro,[status(thm)],[121])).
% 39.91/40.09 tff(123,plain,
% 39.91/40.09 (![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C))) <=> ![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)))),
% 39.91/40.09 inference(rewrite,[status(thm)],[])).
% 39.91/40.09 tff(124,plain,
% 39.91/40.09 (^[A: $i, B: $i, C: $i] : rewrite((~((r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C))) & v1_xboole_0(C))) <=> (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C))))),
% 39.91/40.09 inference(bind,[status(th)],[])).
% 39.91/40.09 tff(125,plain,
% 39.91/40.09 (![A: $i, B: $i, C: $i] : (~((r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C))) & v1_xboole_0(C))) <=> ![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)))),
% 39.91/40.09 inference(quant_intro,[status(thm)],[124])).
% 39.91/40.09 tff(126,axiom,(![A: $i, B: $i, C: $i] : (~((r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C))) & v1_xboole_0(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 39.91/40.09 tff(127,plain,
% 39.91/40.09 (![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)))),
% 39.91/40.09 inference(modus_ponens,[status(thm)],[126, 125])).
% 39.91/40.09 tff(128,plain,
% 39.91/40.09 (![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)))),
% 39.91/40.09 inference(modus_ponens,[status(thm)],[127, 123])).
% 39.91/40.09 tff(129,plain,(
% 39.91/40.09 ![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)))),
% 39.91/40.09 inference(skolemize,[status(sab)],[128])).
% 39.91/40.09 tff(130,plain,
% 39.91/40.09 (![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))),
% 39.91/40.09 inference(modus_ponens,[status(thm)],[129, 122])).
% 39.91/40.09 tff(131,plain,
% 39.91/40.09 (![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))),
% 39.91/40.09 inference(modus_ponens,[status(thm)],[130, 120])).
% 39.91/40.09 tff(132,plain,
% 39.91/40.09 (((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | ((~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))))),
% 39.91/40.09 inference(rewrite,[status(thm)],[])).
% 39.91/40.09 tff(133,plain,
% 39.91/40.09 (((~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)))) <=> ((~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))))),
% 39.91/40.09 inference(rewrite,[status(thm)],[])).
% 39.91/40.09 tff(134,plain,
% 39.91/40.09 (((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | ((~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | ((~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3)))))),
% 39.91/40.09 inference(monotonicity,[status(thm)],[133])).
% 39.91/40.09 tff(135,plain,
% 39.91/40.09 (((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | ((~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))))),
% 39.91/40.09 inference(transitivity,[status(thm)],[134, 132])).
% 39.91/40.09 tff(136,plain,
% 39.91/40.09 ((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | ((~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))))),
% 39.91/40.09 inference(quant_inst,[status(thm)],[])).
% 39.91/40.09 tff(137,plain,
% 39.91/40.09 ((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3)))),
% 39.91/40.09 inference(modus_ponens,[status(thm)],[136, 135])).
% 39.91/40.09 tff(138,plain,
% 39.91/40.09 ((~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3)))),
% 39.91/40.09 inference(unit_resolution,[status(thm)],[137, 131])).
% 39.91/40.09 tff(139,plain,
% 39.91/40.09 (~v1_xboole_0(B!1)),
% 39.91/40.09 inference(unit_resolution,[status(thm)],[138, 118, 95])).
% 39.91/40.09 tff(140,plain,
% 39.91/40.09 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))))),
% 39.91/40.09 inference(bind,[status(th)],[])).
% 39.91/40.09 tff(141,plain,
% 39.91/40.09 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 39.92/40.09 inference(quant_intro,[status(thm)],[140])).
% 39.92/40.09 tff(142,plain,
% 39.92/40.09 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))))),
% 39.92/40.09 inference(bind,[status(th)],[])).
% 39.92/40.09 tff(143,plain,
% 39.92/40.09 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 39.92/40.09 inference(quant_intro,[status(thm)],[142])).
% 39.92/40.09 tff(144,plain,
% 39.92/40.09 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 39.92/40.09 inference(transitivity,[status(thm)],[143, 141])).
% 39.92/40.09 tff(145,plain,
% 39.92/40.09 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))) & (r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))) <=> (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))))),
% 39.92/40.09 inference(bind,[status(th)],[])).
% 39.92/40.09 tff(146,plain,
% 39.92/40.09 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))) & (r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 39.92/40.09 inference(quant_intro,[status(thm)],[145])).
% 39.92/40.09 tff(147,plain,
% 39.92/40.09 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))),
% 39.92/40.09 inference(rewrite,[status(thm)],[])).
% 39.92/40.09 tff(148,plain,
% 39.92/40.09 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))) <=> (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))), ((m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) <=> (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))), rewrite((m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) <=> ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))), ((m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) <=> ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))), (![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) <=> ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))), ((m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))) <=> (m1_subset_1(D, A) => ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))), rewrite((m1_subset_1(D, A) => ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))) <=> ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))), ((m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))) <=> ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))), (![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))) <=> ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))), ((m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))) <=> (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))), ((m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))))), (![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))) <=> ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))), (((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))) <=> ((~v1_xboole_0(A)) => ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))) <=> (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))), (((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))) <=> (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))))),
% 39.92/40.09 inference(bind,[status(th)],[])).
% 39.92/40.09 tff(149,plain,
% 39.92/40.09 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))),
% 39.92/40.09 inference(quant_intro,[status(thm)],[148])).
% 39.92/40.09 tff(150,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_relset_2')).
% 39.92/40.09 tff(151,plain,
% 39.92/40.09 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))),
% 39.92/40.09 inference(modus_ponens,[status(thm)],[150, 149])).
% 39.92/40.09 tff(152,plain,
% 39.92/40.09 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))),
% 39.92/40.09 inference(modus_ponens,[status(thm)],[151, 147])).
% 39.92/40.09 tff(153,plain,(
% 39.92/40.09 ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))) & (r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))),
% 39.92/40.09 inference(skolemize,[status(sab)],[152])).
% 39.92/40.09 tff(154,plain,
% 39.92/40.09 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 39.92/40.09 inference(modus_ponens,[status(thm)],[153, 146])).
% 39.92/40.09 tff(155,plain,
% 39.92/40.09 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 39.92/40.09 inference(modus_ponens,[status(thm)],[154, 144])).
% 39.92/40.09 tff(156,plain,
% 39.92/40.09 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E))))))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E))))))))))),
% 39.92/40.09 inference(rewrite,[status(thm)],[])).
% 39.92/40.09 tff(157,plain,
% 39.92/40.09 ((v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, B!1, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E))))))))))),
% 39.92/40.09 inference(rewrite,[status(thm)],[])).
% 39.92/40.09 tff(158,plain,
% 39.92/40.09 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, B!1, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))))),
% 39.92/40.09 inference(monotonicity,[status(thm)],[157])).
% 39.92/40.09 tff(159,plain,
% 39.92/40.09 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, B!1, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E))))))))))),
% 39.92/40.09 inference(transitivity,[status(thm)],[158, 156])).
% 39.92/40.09 tff(160,plain,
% 39.92/40.09 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, B!1, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 39.92/40.09 inference(quant_inst,[status(thm)],[])).
% 39.92/40.09 tff(161,plain,
% 39.92/40.09 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))),
% 39.92/40.09 inference(modus_ponens,[status(thm)],[160, 159])).
% 39.92/40.09 tff(162,plain,
% 39.92/40.09 (![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))),
% 39.92/40.09 inference(unit_resolution,[status(thm)],[161, 155, 139])).
% 39.92/40.09 tff(163,plain,
% 39.92/40.09 (((~![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E)))))))))) <=> ((~![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E)))))))))),
% 39.92/40.09 inference(rewrite,[status(thm)],[])).
% 39.92/40.09 tff(164,plain,
% 39.92/40.09 ((~![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E)))))))))),
% 39.92/40.10 inference(quant_inst,[status(thm)],[])).
% 39.92/40.10 tff(165,plain,
% 39.92/40.10 ((~![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))),
% 39.92/40.10 inference(modus_ponens,[status(thm)],[164, 163])).
% 39.92/40.10 tff(166,plain,
% 39.92/40.10 (![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))),
% 39.92/40.10 inference(unit_resolution,[status(thm)],[165, 58, 162])).
% 39.92/40.10 tff(167,plain,
% 39.92/40.10 ((~![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))) | (~((~((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1)))) | (~(r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1) | (~((~r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), B!1)))))))),
% 39.92/40.10 inference(quant_inst,[status(thm)],[])).
% 39.92/40.10 tff(168,plain,
% 39.92/40.10 (~((~((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1)))) | (~(r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1) | (~((~r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), B!1))))))),
% 39.92/40.10 inference(unit_resolution,[status(thm)],[167, 84])).
% 39.92/40.10 tff(169,plain,
% 39.92/40.10 (((~((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1)))) | (~(r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1) | (~((~r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), B!1)))))) | ((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1)))),
% 39.92/40.10 inference(tautology,[status(thm)],[])).
% 39.92/40.10 tff(170,plain,
% 39.92/40.10 ((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))),
% 39.92/40.10 inference(unit_resolution,[status(thm)],[169, 168])).
% 39.92/40.10 tff(171,plain,
% 39.92/40.10 (^[A: $i, B: $i] : refl((m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)))),
% 39.92/40.10 inference(bind,[status(th)],[])).
% 39.92/40.10 tff(172,plain,
% 39.92/40.10 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 39.92/40.10 inference(quant_intro,[status(thm)],[171])).
% 39.92/40.10 tff(173,plain,
% 39.92/40.10 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 39.92/40.10 inference(rewrite,[status(thm)],[])).
% 39.92/40.10 tff(174,axiom,(![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 39.92/40.10 tff(175,plain,
% 39.92/40.10 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 39.92/40.10 inference(modus_ponens,[status(thm)],[174, 173])).
% 39.92/40.10 tff(176,plain,(
% 39.92/40.10 ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 39.92/40.10 inference(skolemize,[status(sab)],[175])).
% 39.92/40.10 tff(177,plain,
% 39.92/40.10 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 39.92/40.10 inference(modus_ponens,[status(thm)],[176, 172])).
% 39.92/40.10 tff(178,plain,
% 39.92/40.10 ((~![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))) | (m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) <=> r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1))),
% 39.92/40.10 inference(quant_inst,[status(thm)],[])).
% 39.92/40.10 tff(179,plain,
% 39.92/40.10 (m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) <=> r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)),
% 39.92/40.10 inference(unit_resolution,[status(thm)],[178, 177])).
% 39.92/40.10 tff(180,plain,
% 39.92/40.10 ((~(m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) <=> r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)),
% 39.92/40.10 inference(tautology,[status(thm)],[])).
% 39.92/40.10 tff(181,plain,
% 39.92/40.10 (r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)),
% 39.92/40.10 inference(unit_resolution,[status(thm)],[180, 118, 179])).
% 39.92/40.10 tff(182,plain,
% 39.92/40.10 ((~((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1)))) | (~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))),
% 39.92/40.10 inference(tautology,[status(thm)],[])).
% 39.92/40.10 tff(183,plain,
% 39.92/40.10 (![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))),
% 39.92/40.10 inference(unit_resolution,[status(thm)],[182, 181, 170])).
% 39.92/40.10 tff(184,plain,
% 39.92/40.10 (((~![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))) | ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))) <=> ((~![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))),
% 39.92/40.10 inference(rewrite,[status(thm)],[])).
% 39.92/40.10 tff(185,plain,
% 39.92/40.10 ((~![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))) | ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))),
% 39.92/40.10 inference(quant_inst,[status(thm)],[])).
% 39.92/40.10 tff(186,plain,
% 39.92/40.10 ((~![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)),
% 39.92/40.10 inference(modus_ponens,[status(thm)],[185, 184])).
% 39.92/40.10 tff(187,plain,
% 39.92/40.10 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)),
% 39.92/40.10 inference(unit_resolution,[status(thm)],[186, 95, 183])).
% 39.92/40.10 tff(188,plain,
% 39.92/40.10 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 39.92/40.10 inference(bind,[status(th)],[])).
% 39.92/40.10 tff(189,plain,
% 39.92/40.10 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 39.92/40.10 inference(quant_intro,[status(thm)],[188])).
% 39.92/40.10 tff(190,plain,
% 39.92/40.10 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 39.92/40.10 inference(rewrite,[status(thm)],[])).
% 39.92/40.10 tff(191,plain,
% 39.92/40.10 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 39.92/40.10 inference(bind,[status(th)],[])).
% 39.92/40.10 tff(192,plain,
% 39.92/40.10 (![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 39.92/40.10 inference(quant_intro,[status(thm)],[191])).
% 39.92/40.10 tff(193,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 39.92/40.10 tff(194,plain,
% 39.92/40.10 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 39.92/40.10 inference(modus_ponens,[status(thm)],[193, 192])).
% 39.92/40.10 tff(195,plain,
% 39.92/40.10 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 39.92/40.10 inference(modus_ponens,[status(thm)],[194, 190])).
% 39.92/40.10 tff(196,plain,(
% 39.92/40.10 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 39.92/40.10 inference(skolemize,[status(sab)],[195])).
% 39.92/40.10 tff(197,plain,
% 39.92/40.10 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 39.92/40.10 inference(modus_ponens,[status(thm)],[196, 189])).
% 39.92/40.10 tff(198,plain,
% 39.92/40.10 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))),
% 39.92/40.10 inference(rewrite,[status(thm)],[])).
% 39.92/40.10 tff(199,plain,
% 39.92/40.10 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))),
% 39.92/40.10 inference(quant_inst,[status(thm)],[])).
% 39.92/40.10 tff(200,plain,
% 39.92/40.10 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)),
% 39.92/40.10 inference(modus_ponens,[status(thm)],[199, 198])).
% 39.92/40.10 tff(201,plain,
% 39.92/40.10 (m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)),
% 39.92/40.10 inference(unit_resolution,[status(thm)],[200, 197, 187])).
% 39.92/40.10 tff(202,plain,
% 39.92/40.10 (((~![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))) | ((~m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))) | (~m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))))))))),
% 39.92/40.10 inference(rewrite,[status(thm)],[])).
% 39.92/40.10 tff(203,plain,
% 39.92/40.10 ((~![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))) | ((~m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))))))))),
% 39.92/40.10 inference(quant_inst,[status(thm)],[])).
% 39.92/40.10 tff(204,plain,
% 39.92/40.10 ((~![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))) | (~m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))),
% 39.92/40.10 inference(modus_ponens,[status(thm)],[203, 202])).
% 39.92/40.10 tff(205,plain,
% 39.92/40.10 (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))),
% 39.92/40.10 inference(unit_resolution,[status(thm)],[204, 201, 166])).
% 39.92/40.10 tff(206,plain,
% 39.92/40.10 (((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))))) <=> ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))))),
% 39.92/40.11 inference(rewrite,[status(thm)],[])).
% 39.92/40.11 tff(207,plain,
% 39.92/40.11 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))))),
% 39.92/40.11 inference(quant_inst,[status(thm)],[])).
% 39.92/40.11 tff(208,plain,
% 39.92/40.11 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))))),
% 39.92/40.11 inference(modus_ponens,[status(thm)],[207, 206])).
% 39.92/40.11 tff(209,plain,
% 39.92/40.11 (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))),
% 39.92/40.11 inference(unit_resolution,[status(thm)],[208, 25, 205])).
% 39.92/40.11 tff(210,plain,
% 39.92/40.11 (((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))) | ((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))),
% 39.92/40.11 inference(tautology,[status(thm)],[])).
% 39.92/40.11 tff(211,plain,
% 39.92/40.11 ((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))),
% 39.92/40.11 inference(unit_resolution,[status(thm)],[210, 209])).
% 39.92/40.11 tff(212,plain,
% 39.92/40.11 (((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))),
% 39.92/40.11 inference(tautology,[status(thm)],[])).
% 39.92/40.11 tff(213,plain,
% 39.92/40.11 (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))),
% 39.92/40.11 inference(unit_resolution,[status(thm)],[212, 92])).
% 39.92/40.11 tff(214,plain,
% 39.92/40.11 ((~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))) | (~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))),
% 39.94/40.11 inference(tautology,[status(thm)],[])).
% 39.94/40.11 tff(215,plain,
% 39.94/40.11 ((~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))) | (~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))))),
% 39.94/40.11 inference(unit_resolution,[status(thm)],[214, 213])).
% 39.94/40.11 tff(216,plain,
% 39.94/40.11 (~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))),
% 39.94/40.11 inference(unit_resolution,[status(thm)],[215, 211])).
% 39.94/40.11 tff(217,plain,
% 39.94/40.11 (((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))),
% 39.94/40.11 inference(tautology,[status(thm)],[])).
% 39.94/40.11 tff(218,plain,
% 39.94/40.11 (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))),
% 39.94/40.11 inference(unit_resolution,[status(thm)],[217, 216])).
% 39.94/40.11 tff(219,plain,
% 39.94/40.11 ((~(r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) | (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))),
% 39.94/40.11 inference(tautology,[status(thm)],[])).
% 39.94/40.11 tff(220,plain,
% 39.94/40.11 ((~(r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))) | (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))),
% 39.94/40.11 inference(unit_resolution,[status(thm)],[219, 218])).
% 39.94/40.11 tff(221,plain,
% 39.94/40.11 (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)),
% 39.94/40.11 inference(unit_resolution,[status(thm)],[220, 43])).
% 39.94/40.11 tff(222,plain,
% 39.94/40.11 ((~![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))) | (~((~((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))) | (~(r1_tarski(D!3, E!4) | (~((~r2_hidden(tptp_fun_C_5(E!4, D!3), D!3)) | r2_hidden(tptp_fun_C_5(E!4, D!3), E!4)))))))),
% 39.94/40.11 inference(quant_inst,[status(thm)],[])).
% 39.94/40.11 tff(223,plain,
% 39.94/40.11 (~((~((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))) | (~(r1_tarski(D!3, E!4) | (~((~r2_hidden(tptp_fun_C_5(E!4, D!3), D!3)) | r2_hidden(tptp_fun_C_5(E!4, D!3), E!4))))))),
% 39.94/40.11 inference(unit_resolution,[status(thm)],[222, 84])).
% 39.94/40.11 tff(224,plain,
% 39.94/40.11 (((~((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))) | (~(r1_tarski(D!3, E!4) | (~((~r2_hidden(tptp_fun_C_5(E!4, D!3), D!3)) | r2_hidden(tptp_fun_C_5(E!4, D!3), E!4)))))) | ((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))),
% 39.94/40.11 inference(tautology,[status(thm)],[])).
% 39.94/40.11 tff(225,plain,
% 39.94/40.11 ((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))),
% 39.94/40.11 inference(unit_resolution,[status(thm)],[224, 223])).
% 39.94/40.11 tff(226,plain,
% 39.94/40.11 (r1_tarski(D!3, E!4)),
% 39.94/40.11 inference(or_elim,[status(thm)],[24])).
% 39.94/40.11 tff(227,plain,
% 39.94/40.11 ((~((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))) | (~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))),
% 39.94/40.11 inference(tautology,[status(thm)],[])).
% 39.94/40.11 tff(228,plain,
% 39.94/40.11 ((~((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))),
% 39.94/40.11 inference(unit_resolution,[status(thm)],[227, 226])).
% 39.94/40.11 tff(229,plain,
% 39.94/40.11 (![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))),
% 39.94/40.11 inference(unit_resolution,[status(thm)],[228, 225])).
% 39.94/40.11 tff(230,plain,
% 39.94/40.11 (((~![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))) | ((~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)) | r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))) <=> ((~![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))) | (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)) | r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))),
% 39.94/40.11 inference(rewrite,[status(thm)],[])).
% 39.94/40.11 tff(231,plain,
% 39.94/40.11 ((~![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))) | ((~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)) | r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))),
% 39.94/40.11 inference(quant_inst,[status(thm)],[])).
% 39.94/40.11 tff(232,plain,
% 39.94/40.11 ((~![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))) | (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)) | r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)),
% 39.94/40.11 inference(modus_ponens,[status(thm)],[231, 230])).
% 39.94/40.11 tff(233,plain,
% 39.94/40.11 (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)),
% 39.94/40.11 inference(unit_resolution,[status(thm)],[232, 229, 221])).
% 39.94/40.11 tff(234,plain,
% 39.94/40.11 (((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))) | r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)),
% 39.94/40.11 inference(tautology,[status(thm)],[])).
% 39.94/40.11 tff(235,plain,
% 39.94/40.11 (r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)),
% 39.94/40.11 inference(unit_resolution,[status(thm)],[234, 216])).
% 39.94/40.11 tff(236,plain,
% 39.94/40.11 (((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3)))))))) <=> ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3)))))))),
% 39.94/40.12 inference(rewrite,[status(thm)],[])).
% 39.94/40.12 tff(237,plain,
% 39.94/40.12 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3)))))))),
% 39.94/40.12 inference(quant_inst,[status(thm)],[])).
% 39.94/40.12 tff(238,plain,
% 39.94/40.12 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))))))),
% 39.94/40.12 inference(modus_ponens,[status(thm)],[237, 236])).
% 39.94/40.12 tff(239,plain,
% 39.94/40.12 (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3)))))),
% 39.94/40.12 inference(unit_resolution,[status(thm)],[238, 57, 205])).
% 39.94/40.12 tff(240,plain,
% 39.94/40.12 (((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))))) | ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))),
% 39.94/40.12 inference(tautology,[status(thm)],[])).
% 39.94/40.12 tff(241,plain,
% 39.94/40.12 ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))),
% 39.94/40.12 inference(unit_resolution,[status(thm)],[240, 239])).
% 39.94/40.12 tff(242,plain,
% 39.94/40.12 ((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))),
% 39.94/40.12 inference(tautology,[status(thm)],[])).
% 39.94/40.12 tff(243,plain,
% 39.94/40.12 ((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))),
% 39.94/40.12 inference(unit_resolution,[status(thm)],[242, 94])).
% 39.94/40.12 tff(244,plain,
% 39.94/40.12 (![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))),
% 39.94/40.12 inference(unit_resolution,[status(thm)],[243, 241])).
% 39.94/40.12 tff(245,plain,
% 39.94/40.12 (((~![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))) | ((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) <=> ((~![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))) | (~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))),
% 39.94/40.12 inference(rewrite,[status(thm)],[])).
% 39.94/40.12 tff(246,plain,
% 39.94/40.12 ((~![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))) | ((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))),
% 39.94/40.12 inference(quant_inst,[status(thm)],[])).
% 39.94/40.12 tff(247,plain,
% 39.94/40.12 ((~![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))) | (~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))),
% 39.94/40.12 inference(modus_ponens,[status(thm)],[246, 245])).
% 39.94/40.12 tff(248,plain,
% 39.94/40.12 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))),
% 39.94/40.12 inference(unit_resolution,[status(thm)],[247, 244, 235])).
% 39.94/40.12 tff(249,plain,
% 39.94/40.12 ((~(r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))) | r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)),
% 39.94/40.12 inference(tautology,[status(thm)],[])).
% 39.94/40.12 tff(250,plain,
% 39.94/40.12 (~(r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3))),
% 39.94/40.12 inference(unit_resolution,[status(thm)],[249, 248, 233])).
% 39.94/40.12 tff(251,plain,
% 39.94/40.12 (((~![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(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 39.94/40.12 inference(rewrite,[status(thm)],[])).
% 39.94/40.12 tff(252,plain,
% 39.94/40.12 ((~![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(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 39.94/40.12 inference(quant_inst,[status(thm)],[])).
% 39.94/40.12 tff(253,plain,
% 39.94/40.12 ((~![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(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 39.94/40.12 inference(modus_ponens,[status(thm)],[252, 251])).
% 39.94/40.12 tff(254,plain,
% 39.94/40.12 (v1_relat_1(D!3)),
% 39.94/40.12 inference(unit_resolution,[status(thm)],[253, 57, 10])).
% 39.94/40.12 tff(255,plain,
% 39.94/40.12 (((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | ((~v1_relat_1(D!3)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | (~v1_relat_1(D!3)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)))),
% 39.94/40.12 inference(rewrite,[status(thm)],[])).
% 39.94/40.12 tff(256,plain,
% 39.94/40.12 ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | ((~v1_relat_1(D!3)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)))),
% 39.94/40.12 inference(quant_inst,[status(thm)],[])).
% 39.94/40.12 tff(257,plain,
% 39.94/40.12 ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | (~v1_relat_1(D!3)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3))),
% 39.94/40.12 inference(modus_ponens,[status(thm)],[256, 255])).
% 39.94/40.12 tff(258,plain,
% 39.94/40.12 ($false),
% 39.96/40.19 inference(unit_resolution,[status(thm)],[257, 39, 254, 250])).
% 39.96/40.19 % SZS output end Proof
% 39.96/40.20 % E exiting
%------------------------------------------------------------------------------