%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU413+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:27:51 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU413+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 07:07:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(r2_hidden_type, type, (
% 0.19/0.39 r2_hidden: ( $i * $i ) > $o)).
% 0.19/0.39 tff(u1_orders_2_type, type, (
% 0.19/0.39 u1_orders_2: $i > $i)).
% 0.19/0.39 tff(k1_latsum_1_type, type, (
% 0.19/0.39 k1_latsum_1: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_B_1_type, type, (
% 0.19/0.39 tptp_fun_B_1: $i)).
% 0.19/0.39 tff(tptp_fun_A_0_type, type, (
% 0.19/0.39 tptp_fun_A_0: $i)).
% 0.19/0.39 tff(k4_tarski_type, type, (
% 0.19/0.39 k4_tarski: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_D_3_type, type, (
% 0.19/0.39 tptp_fun_D_3: $i)).
% 0.19/0.39 tff(tptp_fun_C_2_type, type, (
% 0.19/0.39 tptp_fun_C_2: $i)).
% 0.19/0.39 tff(r1_orders_2_type, type, (
% 0.19/0.39 r1_orders_2: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(m1_subset_1_type, type, (
% 0.19/0.39 m1_subset_1: ( $i * $i ) > $o)).
% 0.19/0.39 tff(u1_struct_0_type, type, (
% 0.19/0.39 u1_struct_0: $i > $i)).
% 0.19/0.39 tff(l1_orders_2_type, type, (
% 0.19/0.39 l1_orders_2: $i > $o)).
% 0.19/0.39 tff(v1_orders_2_type, type, (
% 0.19/0.39 v1_orders_2: $i > $o)).
% 0.19/0.39 tff(k1_zfmisc_1_type, type, (
% 0.19/0.39 k1_zfmisc_1: $i > $i)).
% 0.19/0.39 tff(k3_xboole_0_type, type, (
% 0.19/0.39 k3_xboole_0: ( $i * $i ) > $i)).
% 0.19/0.39 tff(v12_waybel_0_type, type, (
% 0.19/0.39 v12_waybel_0: ( $i * $i ) > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl(((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))) <=> ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))) <=> ![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_orders_2(A) & l1_orders_2(B)) <=> (~((~l1_orders_2(B)) | (~l1_orders_2(A))))), ((~(l1_orders_2(A) & l1_orders_2(B))) <=> (~(~((~l1_orders_2(B)) | (~l1_orders_2(A))))))), rewrite((~(~((~l1_orders_2(B)) | (~l1_orders_2(A))))) <=> ((~l1_orders_2(B)) | (~l1_orders_2(A)))), ((~(l1_orders_2(A) & l1_orders_2(B))) <=> ((~l1_orders_2(B)) | (~l1_orders_2(A))))), rewrite((v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))) <=> (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))), (((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> (((~l1_orders_2(B)) | (~l1_orders_2(A))) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))))), rewrite((((~l1_orders_2(B)) | (~l1_orders_2(A))) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))) <=> ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))), (((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> ![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> ![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (^[A: $i, B: $i] : rewrite(((l1_orders_2(A) & l1_orders_2(B)) => (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((l1_orders_2(A) & l1_orders_2(B)) => (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> ![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.40 tff(8,axiom,(![A: $i, B: $i] : ((l1_orders_2(A) & l1_orders_2(B)) => (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_latsum_1')).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.40 tff(11,plain,(
% 0.19/0.40 ![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 ((l1_orders_2(A!0) & (l1_orders_2(B!1) & m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))))))) <=> (l1_orders_2(A!0) & l1_orders_2(B!1) & m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 ((l1_orders_2(B!1) & (m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))))))) <=> (l1_orders_2(B!1) & m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 ((~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))))) <=> (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 ((m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1))))))) <=> (m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 ((l1_orders_2(B!1) & (m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))))))) <=> (l1_orders_2(B!1) & (m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 ((l1_orders_2(B!1) & (m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))))))) <=> (l1_orders_2(B!1) & m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[18, 15])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 ((l1_orders_2(A!0) & (l1_orders_2(B!1) & (m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1))))))))) <=> (l1_orders_2(A!0) & (l1_orders_2(B!1) & m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[19])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 ((l1_orders_2(A!0) & (l1_orders_2(B!1) & (m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1))))))))) <=> (l1_orders_2(A!0) & l1_orders_2(B!1) & m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[20, 14])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B)))) | ![D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r1_orders_2(k1_latsum_1(A, B), C, D) & r2_hidden(D, u1_struct_0(A)))) | (~m1_subset_1(D, u1_struct_0(k1_latsum_1(A, B))))))))) <=> (~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B)))) | ![D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r1_orders_2(k1_latsum_1(A, B), C, D) & r2_hidden(D, u1_struct_0(A)))) | (~m1_subset_1(D, u1_struct_0(k1_latsum_1(A, B)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 ((~![A: $i] : (l1_orders_2(A) => ![B: $i] : (l1_orders_2(B) => ![C: $i] : (m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B))) => ![D: $i] : (m1_subset_1(D, u1_struct_0(k1_latsum_1(A, B))) => ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r1_orders_2(k1_latsum_1(A, B), C, D)) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A)))))))) <=> (~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B)))) | ![D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r1_orders_2(k1_latsum_1(A, B), C, D) & r2_hidden(D, u1_struct_0(A)))) | (~m1_subset_1(D, u1_struct_0(k1_latsum_1(A, B)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(24,axiom,(~![A: $i] : (l1_orders_2(A) => ![B: $i] : (l1_orders_2(B) => ![C: $i] : (m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B))) => ![D: $i] : (m1_subset_1(D, u1_struct_0(k1_latsum_1(A, B))) => ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r1_orders_2(k1_latsum_1(A, B), C, D)) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_latsum_1')).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B)))) | ![D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r1_orders_2(k1_latsum_1(A, B), C, D) & r2_hidden(D, u1_struct_0(A)))) | (~m1_subset_1(D, u1_struct_0(k1_latsum_1(A, B))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B)))) | ![D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r1_orders_2(k1_latsum_1(A, B), C, D) & r2_hidden(D, u1_struct_0(A)))) | (~m1_subset_1(D, u1_struct_0(k1_latsum_1(A, B))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B)))) | ![D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r1_orders_2(k1_latsum_1(A, B), C, D) & r2_hidden(D, u1_struct_0(A)))) | (~m1_subset_1(D, u1_struct_0(k1_latsum_1(A, B))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B)))) | ![D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r1_orders_2(k1_latsum_1(A, B), C, D) & r2_hidden(D, u1_struct_0(A)))) | (~m1_subset_1(D, u1_struct_0(k1_latsum_1(A, B))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (l1_orders_2(A!0) & l1_orders_2(B!1) & m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) & (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (l1_orders_2(B!1)),
% 0.19/0.40 inference(and_elim,[status(thm)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (l1_orders_2(A!0)),
% 0.19/0.40 inference(and_elim,[status(thm)],[29])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | ((~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | (~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))))) <=> ((~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 ((~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))))) <=> (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1)))))) <=> ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1)))))) <=> ((~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | ((~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | (~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[37, 32])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | (~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[40, 31, 30, 13])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))) | l1_orders_2(k1_latsum_1(A!0, B!1))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (l1_orders_2(k1_latsum_1(A!0, B!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (^[A: $i] : refl(((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))), ((l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))) <=> (l1_orders_2(A) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))))), rewrite((l1_orders_2(A) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))), ((l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![A: $i] : (l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.41 tff(52,axiom,(![A: $i] : (l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_orders_2')).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.19/0.41 tff(55,plain,(
% 0.19/0.41 ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[54])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))) | ((~l1_orders_2(k1_latsum_1(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(k1_latsum_1(A!0, B!1)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(k1_latsum_1(A!0, B!1)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))) | ((~l1_orders_2(k1_latsum_1(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(k1_latsum_1(A!0, B!1)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))))))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 ((~l1_orders_2(k1_latsum_1(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[60, 43])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.19/0.41 inference(and_elim,[status(thm)],[29])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(k1_latsum_1(A!0, B!1))))))) | ((~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, C) <=> r2_hidden(k4_tarski(C!2, C), u1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(k1_latsum_1(A!0, B!1))))))) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, C) <=> r2_hidden(k4_tarski(C!2, C), u1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(k1_latsum_1(A!0, B!1))))))) | ((~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, C) <=> r2_hidden(k4_tarski(C!2, C), u1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(k1_latsum_1(A!0, B!1))))))) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, C) <=> r2_hidden(k4_tarski(C!2, C), u1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, C) <=> r2_hidden(k4_tarski(C!2, C), u1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[65, 62, 61])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (~(r2_hidden(C!2, u1_struct_0(A!0)) | (~(v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0)))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))))),
% 0.19/0.41 inference(and_elim,[status(thm)],[29])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.19/0.41 inference(or_elim,[status(thm)],[67])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, C) <=> r2_hidden(k4_tarski(C!2, C), u1_orders_2(k1_latsum_1(A!0, B!1)))))) | ((~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) <=> r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, C) <=> r2_hidden(k4_tarski(C!2, C), u1_orders_2(k1_latsum_1(A!0, B!1)))))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) <=> r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, C) <=> r2_hidden(k4_tarski(C!2, C), u1_orders_2(k1_latsum_1(A!0, B!1)))))) | ((~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) <=> r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, C) <=> r2_hidden(k4_tarski(C!2, C), u1_orders_2(k1_latsum_1(A!0, B!1)))))) | (~m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))) | (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) <=> r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) <=> r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[71, 68, 66])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) & r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) & r2_hidden(D!3, u1_struct_0(A!0))),
% 0.19/0.42 inference(or_elim,[status(thm)],[67])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3)),
% 0.19/0.42 inference(and_elim,[status(thm)],[73])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 ((~(r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) <=> r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3)) | r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 ((~(r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3) <=> r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1))))) | r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[76, 72])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (^[A: $i] : refl(((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A)))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A)))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[81, 79])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) <=> (v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))))), ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) <=> ((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))))), rewrite(((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) <=> (v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))), ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) <=> (v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A))))), (((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A))) <=> ((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A))))), rewrite(((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A))) <=> ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))), (((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A))) <=> ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))))), (![C: $i, D: $i] : ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A))) <=> ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A))))), ((l1_orders_2(B) => ![C: $i, D: $i] : ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A)))) <=> (l1_orders_2(B) => ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))))), rewrite((l1_orders_2(B) => ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))) <=> ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A))))), ((l1_orders_2(B) => ![C: $i, D: $i] : ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A)))) <=> ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A))))))), (![B: $i] : (l1_orders_2(B) => ![C: $i, D: $i] : ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A)))) <=> ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))))), ((l1_orders_2(A) => ![B: $i] : (l1_orders_2(B) => ![C: $i, D: $i] : ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A))))) <=> (l1_orders_2(A) => ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A))))))), rewrite((l1_orders_2(A) => ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))))), ((l1_orders_2(A) => ![B: $i] : (l1_orders_2(B) => ![C: $i, D: $i] : ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (![A: $i] : (l1_orders_2(A) => ![B: $i] : (l1_orders_2(B) => ![C: $i, D: $i] : ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.42 tff(88,axiom,(![A: $i] : (l1_orders_2(A) => ![B: $i] : (l1_orders_2(B) => ![C: $i, D: $i] : ((((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) & r2_hidden(D, u1_struct_0(A))) => r2_hidden(C, u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_latsum_1')).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.42 tff(91,plain,(
% 0.19/0.42 ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : ((~(v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B))) & r2_hidden(D, u1_struct_0(A)))) | r2_hidden(C, u1_struct_0(A)))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[90])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))) | ((~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))) | (~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (((~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B)))) | (~r2_hidden(D, u1_struct_0(A!0)))))) <=> ((~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))) | ((~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B)))) | (~r2_hidden(D, u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))) | ((~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 (((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))) | ((~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B)))) | (~r2_hidden(D, u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))) | (~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))) | ((~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B)))) | (~r2_hidden(D, u1_struct_0(A!0))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A, B)))) | (~r2_hidden(D, u1_struct_0(A))))))) | (~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[99, 31, 93])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B))))))) | ((~l1_orders_2(B!1)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B))))))) | (~l1_orders_2(B!1)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (((~l1_orders_2(B!1)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))))) <=> ((~l1_orders_2(B!1)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B))))))) | ((~l1_orders_2(B!1)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B))))))) | ((~l1_orders_2(B!1)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[102])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B))))))) | ((~l1_orders_2(B!1)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B))))))) | (~l1_orders_2(B!1)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[103, 101])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 ((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B))))))) | ((~l1_orders_2(B!1)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 ((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), B)) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) | (~r2_hidden(D, u1_struct_0(A!0))) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B))))))) | (~l1_orders_2(B!1)) | ![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[106, 30, 100])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (r2_hidden(D!3, u1_struct_0(A!0))),
% 0.19/0.43 inference(and_elim,[status(thm)],[73])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.19/0.43 inference(and_elim,[status(thm)],[73])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)),
% 0.19/0.43 inference(and_elim,[status(thm)],[73])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (~r2_hidden(C!2, u1_struct_0(A!0))),
% 0.19/0.43 inference(or_elim,[status(thm)],[67])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (((~![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))))) | (r2_hidden(C!2, u1_struct_0(A!0)) | (~r2_hidden(D!3, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1)))))) <=> ((~![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~r2_hidden(D!3, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(113,plain,
% 0.19/0.44 ((~![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))))) | (r2_hidden(C!2, u1_struct_0(A!0)) | (~r2_hidden(D!3, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(114,plain,
% 0.19/0.44 ((~![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~r2_hidden(D!3, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[114, 111, 110, 109, 108, 107, 77])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------