TSTP Solution File: SEU413+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU413+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Tue Sep 20 07:29:26 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18 % Problem : SEU413+1 : TPTP v8.1.0. Released v3.4.0.
% 0.12/0.19 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.40 % Computer : n018.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8042.1875MB
% 0.12/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 3 13:40:44 EDT 2022
% 0.12/0.40 % CPUTime :
% 0.12/0.41 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.41 Usage: tptp [options] [-file:]file
% 0.12/0.41 -h, -? prints this message.
% 0.12/0.41 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.41 -m, -model generate model.
% 0.12/0.41 -p, -proof generate proof.
% 0.12/0.41 -c, -core generate unsat core of named formulas.
% 0.12/0.41 -st, -statistics display statistics.
% 0.12/0.41 -t:timeout set timeout (in second).
% 0.12/0.41 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.41 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.41 -<param>:<value> configuration parameter and value.
% 0.12/0.41 -o:<output-file> file to place output in.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(r2_hidden_type, type, (
% 0.20/0.47 r2_hidden: ( $i * $i ) > $o)).
% 0.20/0.47 tff(u1_orders_2_type, type, (
% 0.20/0.47 u1_orders_2: $i > $i)).
% 0.20/0.47 tff(k1_latsum_1_type, type, (
% 0.20/0.47 k1_latsum_1: ( $i * $i ) > $i)).
% 0.20/0.47 tff(tptp_fun_B_1_type, type, (
% 0.20/0.47 tptp_fun_B_1: $i)).
% 0.20/0.47 tff(tptp_fun_A_0_type, type, (
% 0.20/0.47 tptp_fun_A_0: $i)).
% 0.20/0.47 tff(k4_tarski_type, type, (
% 0.20/0.47 k4_tarski: ( $i * $i ) > $i)).
% 0.20/0.47 tff(tptp_fun_D_3_type, type, (
% 0.20/0.47 tptp_fun_D_3: $i)).
% 0.20/0.47 tff(tptp_fun_C_2_type, type, (
% 0.20/0.47 tptp_fun_C_2: $i)).
% 0.20/0.47 tff(r1_orders_2_type, type, (
% 0.20/0.47 r1_orders_2: ( $i * $i * $i ) > $o)).
% 0.20/0.47 tff(m1_subset_1_type, type, (
% 0.20/0.47 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.47 tff(u1_struct_0_type, type, (
% 0.20/0.47 u1_struct_0: $i > $i)).
% 0.20/0.47 tff(l1_orders_2_type, type, (
% 0.20/0.47 l1_orders_2: $i > $o)).
% 0.20/0.47 tff(v1_orders_2_type, type, (
% 0.20/0.47 v1_orders_2: $i > $o)).
% 0.20/0.47 tff(k1_zfmisc_1_type, type, (
% 0.20/0.47 k1_zfmisc_1: $i > $i)).
% 0.20/0.47 tff(k3_xboole_0_type, type, (
% 0.20/0.47 k3_xboole_0: ( $i * $i ) > $i)).
% 0.20/0.47 tff(v12_waybel_0_type, type, (
% 0.20/0.47 v12_waybel_0: ( $i * $i ) > $o)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 (^[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)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (^[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))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(4,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.47 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')).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.47 tff(11,plain,(
% 0.20/0.47 ![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))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[10])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 ((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)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(15,plain,
% 0.20/0.47 ((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)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (((~(~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)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 ((~(~l1_orders_2(B!1))) <=> l1_orders_2(B!1)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (((~(~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))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[17, 16])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (((~(~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)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[18, 15])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 ((~(~l1_orders_2(A!0))) <=> l1_orders_2(A!0)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (((~(~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))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[20, 19])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (((~(~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)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[21, 14])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 ((~![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)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 ((~![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)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(25,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')).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (~![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))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (~![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))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (~![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))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (~![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))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (~![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))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (~![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))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (~![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))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[31, 23])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (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))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (l1_orders_2(B!1)),
% 0.20/0.48 inference(and_elim,[status(thm)],[33])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (l1_orders_2(A!0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[33])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (((~![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))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (((~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))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 ((~((~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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (((~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))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (((~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))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[39, 37])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (((~![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)))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (((~![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))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[41, 36])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 ((~![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))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 ((~![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)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[44, 35, 34, 13])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (((~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))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (l1_orders_2(k1_latsum_1(A!0, B!1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (^[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)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (![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))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (^[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)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (![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))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (![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))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[51, 49])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (![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))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (^[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))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.49 tff(56,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')).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.49 tff(59,plain,(
% 0.20/0.49 ![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))))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[58])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 (((~![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)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(62,plain,
% 0.20/0.49 ((~![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)))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 ((~![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))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 ((~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))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[64, 47])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.20/0.49 inference(and_elim,[status(thm)],[33])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (((~![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))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 ((~![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))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 ((~![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)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (![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)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[69, 66, 65])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 (~(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)))))),
% 0.20/0.49 inference(and_elim,[status(thm)],[33])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (m1_subset_1(D!3, u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.20/0.49 inference(or_elim,[status(thm)],[71])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (((~![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)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 ((~![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)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 ((~![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))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (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)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[75, 72, 70])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (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))),
% 0.20/0.49 inference(or_elim,[status(thm)],[71])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (r1_orders_2(k1_latsum_1(A!0, B!1), C!2, D!3)),
% 0.20/0.49 inference(and_elim,[status(thm)],[77])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 ((~(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)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 ((~(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)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[80, 76])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (^[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)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (^[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)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[85, 83])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (^[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)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(90,plain,
% 0.20/0.50 (^[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)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.50 tff(92,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')).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.50 tff(94,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.20/0.50 tff(95,plain,(
% 0.20/0.50 ![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)))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[94])).
% 0.20/0.50 tff(96,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.20/0.50 tff(97,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.20/0.50 tff(98,plain,
% 0.20/0.50 (((~![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(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B)))) | (~r2_hidden(D, u1_struct_0(A!0))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 ((~![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))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 ((~![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[100, 35, 97])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 (((~![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(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(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B)))) | (~r2_hidden(D, u1_struct_0(A!0)))))) | (~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))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 (((~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(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~r2_hidden(D, u1_struct_0(A!0))))) <=> ((~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))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(104,plain,
% 0.20/0.50 (((~![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(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(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~r2_hidden(D, u1_struct_0(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(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)))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.51 tff(105,plain,
% 0.20/0.51 (((~![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(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(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~r2_hidden(D, u1_struct_0(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(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))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[104, 102])).
% 0.20/0.51 tff(106,plain,
% 0.20/0.51 ((~![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(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(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~r2_hidden(D, u1_struct_0(A!0)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(107,plain,
% 0.20/0.51 ((~![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(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)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.51 tff(108,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[107, 34, 101])).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 (r2_hidden(D!3, u1_struct_0(A!0))),
% 0.20/0.51 inference(and_elim,[status(thm)],[77])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 (m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.20/0.51 inference(and_elim,[status(thm)],[77])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 (v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)),
% 0.20/0.51 inference(and_elim,[status(thm)],[77])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (~r2_hidden(C!2, u1_struct_0(A!0))),
% 0.20/0.51 inference(or_elim,[status(thm)],[71])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 (((~![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)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 ((~![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)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(115,plain,
% 0.20/0.51 ((~![C: $i, D: $i] : (r2_hidden(C, u1_struct_0(A!0)) | (~r2_hidden(D, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C, D), u1_orders_2(k1_latsum_1(A!0, B!1)))))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~r2_hidden(D!3, u1_struct_0(A!0))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)) | (~r2_hidden(k4_tarski(C!2, D!3), u1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[115, 112, 111, 110, 109, 108, 81])).
% 0.20/0.51 % SZS output end Proof
%------------------------------------------------------------------------------