TSTP Solution File: ALG215+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG215+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 6 16:09:15 EDT 2022
% Result : Theorem 0.76s 0.73s
% Output : Proof 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG215+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n026.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 : Mon Aug 29 14:10:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.76/0.73 % SZS status Theorem
% 0.76/0.73 % SZS output start Proof
% 0.76/0.73 tff(r1_tarski_type, type, (
% 0.76/0.73 r1_tarski: ( $i * $i ) > $o)).
% 0.76/0.73 tff(k1_xboole_0_type, type, (
% 0.76/0.73 k1_xboole_0: $i)).
% 0.76/0.73 tff(k2_rmod_4_type, type, (
% 0.76/0.73 k2_rmod_4: ( $i * $i * $i ) > $i)).
% 0.76/0.73 tff(tptp_fun_D_2_type, type, (
% 0.76/0.73 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.76/0.73 tff(tptp_fun_A_0_type, type, (
% 0.76/0.73 tptp_fun_A_0: $i)).
% 0.76/0.73 tff(tptp_fun_B_1_type, type, (
% 0.76/0.73 tptp_fun_B_1: $i)).
% 0.76/0.73 tff(m2_rmod_4_type, type, (
% 0.76/0.73 m2_rmod_4: ( $i * $i * $i * $i ) > $o)).
% 0.76/0.73 tff(m1_rmod_4_type, type, (
% 0.76/0.73 m1_rmod_4: ( $i * $i * $i ) > $o)).
% 0.76/0.73 tff(tptp_fun_B_22_type, type, (
% 0.76/0.73 tptp_fun_B_22: $i > $i)).
% 0.76/0.73 tff(u1_struct_0_type, type, (
% 0.76/0.73 u1_struct_0: $i > $i)).
% 0.76/0.73 tff(tptp_fun_A_24_type, type, (
% 0.76/0.73 tptp_fun_A_24: $i)).
% 0.76/0.73 tff(v1_xboole_0_type, type, (
% 0.76/0.73 v1_xboole_0: $i > $o)).
% 0.76/0.73 tff(m1_subset_1_type, type, (
% 0.76/0.73 m1_subset_1: ( $i * $i ) > $o)).
% 0.76/0.73 tff(k1_zfmisc_1_type, type, (
% 0.76/0.73 k1_zfmisc_1: $i > $i)).
% 0.76/0.73 tff(k1_rlvect_1_type, type, (
% 0.76/0.73 k1_rlvect_1: $i > $i)).
% 0.76/0.73 tff(k5_rmod_4_type, type, (
% 0.76/0.73 k5_rmod_4: ( $i * $i * $i ) > $i)).
% 0.76/0.73 tff(v1_rmod_5_type, type, (
% 0.76/0.73 v1_rmod_5: ( $i * $i * $i ) > $o)).
% 0.76/0.73 tff(k1_subset_1_type, type, (
% 0.76/0.73 k1_subset_1: $i > $i)).
% 0.76/0.73 tff(l1_vectsp_2_type, type, (
% 0.76/0.73 l1_vectsp_2: ( $i * $i ) > $o)).
% 0.76/0.73 tff(v5_vectsp_2_type, type, (
% 0.76/0.73 v5_vectsp_2: ( $i * $i ) > $o)).
% 0.76/0.73 tff(v6_rlvect_1_type, type, (
% 0.76/0.73 v6_rlvect_1: $i > $o)).
% 0.76/0.73 tff(v5_rlvect_1_type, type, (
% 0.76/0.73 v5_rlvect_1: $i > $o)).
% 0.76/0.73 tff(v4_rlvect_1_type, type, (
% 0.76/0.73 v4_rlvect_1: $i > $o)).
% 0.76/0.73 tff(v3_rlvect_1_type, type, (
% 0.76/0.73 v3_rlvect_1: $i > $o)).
% 0.76/0.73 tff(v3_struct_0_type, type, (
% 0.76/0.73 v3_struct_0: $i > $o)).
% 0.76/0.73 tff(l3_vectsp_1_type, type, (
% 0.76/0.73 l3_vectsp_1: $i > $o)).
% 0.76/0.73 tff(v8_vectsp_1_type, type, (
% 0.76/0.73 v8_vectsp_1: $i > $o)).
% 0.76/0.73 tff(v7_vectsp_1_type, type, (
% 0.76/0.73 v7_vectsp_1: $i > $o)).
% 0.76/0.73 tff(v6_vectsp_1_type, type, (
% 0.76/0.73 v6_vectsp_1: $i > $o)).
% 0.76/0.73 tff(v4_group_1_type, type, (
% 0.76/0.73 v4_group_1: $i > $o)).
% 0.76/0.73 tff(1,plain,
% 0.76/0.73 (^[A: $i] : refl((~((~m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_22(A))))) <=> (~((~m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_22(A))))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(2,plain,
% 0.76/0.73 (![A: $i] : (~((~m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_22(A))))) <=> ![A: $i] : (~((~m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_22(A)))))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[1])).
% 0.76/0.73 tff(3,plain,
% 0.76/0.73 (^[A: $i] : rewrite((m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A)) & v1_xboole_0(tptp_fun_B_22(A))) <=> (~((~m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_22(A))))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(4,plain,
% 0.76/0.73 (![A: $i] : (m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A)) & v1_xboole_0(tptp_fun_B_22(A))) <=> ![A: $i] : (~((~m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_22(A)))))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[3])).
% 0.76/0.73 tff(5,plain,
% 0.76/0.73 (![A: $i] : ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) <=> ![A: $i] : ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(6,axiom,(![A: $i] : ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rc2_subset_1')).
% 0.76/0.73 tff(7,plain,
% 0.76/0.73 (![A: $i] : ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.76/0.73 tff(8,plain,(
% 0.76/0.73 ![A: $i] : (m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A)) & v1_xboole_0(tptp_fun_B_22(A)))),
% 0.76/0.73 inference(skolemize,[status(sab)],[7])).
% 0.76/0.73 tff(9,plain,
% 0.76/0.73 (![A: $i] : (~((~m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_22(A)))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.76/0.73 tff(10,plain,
% 0.76/0.73 (![A: $i] : (~((~m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_22(A)))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.76/0.73 tff(11,plain,
% 0.76/0.73 ((~![A: $i] : (~((~m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_22(A)))))) | (~((~m1_subset_1(tptp_fun_B_22(u1_struct_0(A!24)), k1_zfmisc_1(u1_struct_0(A!24)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24))))))),
% 0.76/0.73 inference(quant_inst,[status(thm)],[])).
% 0.76/0.73 tff(12,plain,
% 0.76/0.73 (~((~m1_subset_1(tptp_fun_B_22(u1_struct_0(A!24)), k1_zfmisc_1(u1_struct_0(A!24)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))))),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.76/0.73 tff(13,plain,
% 0.76/0.73 (((~m1_subset_1(tptp_fun_B_22(u1_struct_0(A!24)), k1_zfmisc_1(u1_struct_0(A!24)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24))))) | v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))),
% 0.76/0.73 inference(tautology,[status(thm)],[])).
% 0.76/0.73 tff(14,plain,
% 0.76/0.73 (v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.76/0.73 tff(15,plain,
% 0.76/0.73 (^[A: $i, B: $i] : refl(((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)) <=> ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(16,plain,
% 0.76/0.73 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)) <=> ![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[15])).
% 0.76/0.73 tff(17,plain,
% 0.76/0.73 (^[A: $i, B: $i] : trans(monotonicity(rewrite((v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)) <=> (~((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))), ((~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> (~(~((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))))), rewrite((~(~((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))) <=> ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))), ((~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(18,plain,
% 0.76/0.73 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[17])).
% 0.76/0.73 tff(19,plain,
% 0.76/0.73 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(20,plain,
% 0.76/0.73 (^[A: $i, B: $i] : rewrite((~((v1_xboole_0(A) & (~(A = B))) & v1_xboole_0(B))) <=> (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(21,plain,
% 0.76/0.73 (![A: $i, B: $i] : (~((v1_xboole_0(A) & (~(A = B))) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[20])).
% 0.76/0.73 tff(22,axiom,(![A: $i, B: $i] : (~((v1_xboole_0(A) & (~(A = B))) & v1_xboole_0(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 0.76/0.73 tff(23,plain,
% 0.76/0.73 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.76/0.73 tff(24,plain,
% 0.76/0.73 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.76/0.73 tff(25,plain,(
% 0.76/0.73 ![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.76/0.73 inference(skolemize,[status(sab)],[24])).
% 0.76/0.73 tff(26,plain,
% 0.76/0.73 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.76/0.73 tff(27,plain,
% 0.76/0.73 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.76/0.73 tff(28,plain,
% 0.76/0.73 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(29,axiom,(v1_xboole_0(k1_xboole_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.76/0.73 tff(30,plain,
% 0.76/0.73 (v1_xboole_0(k1_xboole_0)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.76/0.73 tff(31,plain,
% 0.76/0.73 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = k1_xboole_0))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = k1_xboole_0))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(32,plain,
% 0.76/0.73 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = k1_xboole_0))),
% 0.76/0.73 inference(quant_inst,[status(thm)],[])).
% 0.76/0.73 tff(33,plain,
% 0.76/0.73 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = k1_xboole_0)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.76/0.73 tff(34,plain,
% 0.76/0.73 (tptp_fun_B_22(u1_struct_0(A!24)) = k1_xboole_0),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[33, 30, 27, 14])).
% 0.76/0.73 tff(35,plain,
% 0.76/0.73 ((~![A: $i] : (~((~m1_subset_1(tptp_fun_B_22(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_22(A)))))) | (~((~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1))))))),
% 0.76/0.73 inference(quant_inst,[status(thm)],[])).
% 0.76/0.73 tff(36,plain,
% 0.76/0.73 (~((~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))))),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[35, 10])).
% 0.76/0.73 tff(37,plain,
% 0.76/0.73 (((~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1))))) | v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))),
% 0.76/0.73 inference(tautology,[status(thm)],[])).
% 0.76/0.73 tff(38,plain,
% 0.76/0.73 (v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.76/0.73 tff(39,plain,
% 0.76/0.73 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = tptp_fun_B_22(u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = tptp_fun_B_22(u1_struct_0(B!1))))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(40,plain,
% 0.76/0.73 (((~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = tptp_fun_B_22(u1_struct_0(B!1)))) <=> ((~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = tptp_fun_B_22(u1_struct_0(B!1))))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(41,plain,
% 0.76/0.73 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = tptp_fun_B_22(u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = tptp_fun_B_22(u1_struct_0(B!1)))))),
% 0.76/0.73 inference(monotonicity,[status(thm)],[40])).
% 0.76/0.73 tff(42,plain,
% 0.76/0.73 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = tptp_fun_B_22(u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = tptp_fun_B_22(u1_struct_0(B!1))))),
% 0.76/0.73 inference(transitivity,[status(thm)],[41, 39])).
% 0.76/0.73 tff(43,plain,
% 0.76/0.73 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = tptp_fun_B_22(u1_struct_0(B!1))))),
% 0.76/0.73 inference(quant_inst,[status(thm)],[])).
% 0.76/0.73 tff(44,plain,
% 0.76/0.73 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(A!24)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1)))) | (tptp_fun_B_22(u1_struct_0(A!24)) = tptp_fun_B_22(u1_struct_0(B!1)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.76/0.73 tff(45,plain,
% 0.76/0.73 (tptp_fun_B_22(u1_struct_0(A!24)) = tptp_fun_B_22(u1_struct_0(B!1))),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[44, 27, 14, 38])).
% 0.76/0.73 tff(46,plain,
% 0.76/0.73 (tptp_fun_B_22(u1_struct_0(B!1)) = tptp_fun_B_22(u1_struct_0(A!24))),
% 0.76/0.73 inference(symmetry,[status(thm)],[45])).
% 0.76/0.73 tff(47,plain,
% 0.76/0.73 (tptp_fun_B_22(u1_struct_0(B!1)) = k1_xboole_0),
% 0.76/0.73 inference(transitivity,[status(thm)],[46, 34])).
% 0.76/0.73 tff(48,plain,
% 0.76/0.73 (m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1))) <=> m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0)),
% 0.76/0.73 inference(monotonicity,[status(thm)],[47])).
% 0.76/0.73 tff(49,plain,
% 0.76/0.73 (m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0) <=> m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))),
% 0.76/0.73 inference(symmetry,[status(thm)],[48])).
% 0.76/0.73 tff(50,plain,
% 0.76/0.73 (^[A: $i] : refl((~((~v1_xboole_0(k1_subset_1(A))) | (~m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A))))) <=> (~((~v1_xboole_0(k1_subset_1(A))) | (~m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A))))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(51,plain,
% 0.76/0.73 (![A: $i] : (~((~v1_xboole_0(k1_subset_1(A))) | (~m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A))))) <=> ![A: $i] : (~((~v1_xboole_0(k1_subset_1(A))) | (~m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A)))))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[50])).
% 0.76/0.73 tff(52,plain,
% 0.76/0.73 (^[A: $i] : rewrite((v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A))) <=> (~((~v1_xboole_0(k1_subset_1(A))) | (~m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A))))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(53,plain,
% 0.76/0.73 (![A: $i] : (v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A))) <=> ![A: $i] : (~((~v1_xboole_0(k1_subset_1(A))) | (~m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A)))))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[52])).
% 0.76/0.73 tff(54,plain,
% 0.76/0.73 (![A: $i] : (v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A))) <=> ![A: $i] : (v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(55,axiom,(![A: $i] : (v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_subset_1')).
% 0.76/0.73 tff(56,plain,
% 0.76/0.73 (![A: $i] : (v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.76/0.73 tff(57,plain,(
% 0.76/0.73 ![A: $i] : (v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A)))),
% 0.76/0.73 inference(skolemize,[status(sab)],[56])).
% 0.76/0.73 tff(58,plain,
% 0.76/0.73 (![A: $i] : (~((~v1_xboole_0(k1_subset_1(A))) | (~m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A)))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.76/0.73 tff(59,plain,
% 0.76/0.73 (![A: $i] : (~((~v1_xboole_0(k1_subset_1(A))) | (~m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A)))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.76/0.73 tff(60,plain,
% 0.76/0.73 ((~![A: $i] : (~((~v1_xboole_0(k1_subset_1(A))) | (~m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A)))))) | (~((~v1_xboole_0(k1_subset_1(u1_struct_0(B!1)))) | (~m1_subset_1(k1_subset_1(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))))),
% 0.76/0.73 inference(quant_inst,[status(thm)],[])).
% 0.76/0.73 tff(61,plain,
% 0.76/0.73 (~((~v1_xboole_0(k1_subset_1(u1_struct_0(B!1)))) | (~m1_subset_1(k1_subset_1(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.76/0.73 tff(62,plain,
% 0.76/0.73 (((~v1_xboole_0(k1_subset_1(u1_struct_0(B!1)))) | (~m1_subset_1(k1_subset_1(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | v1_xboole_0(k1_subset_1(u1_struct_0(B!1)))),
% 0.76/0.73 inference(tautology,[status(thm)],[])).
% 0.76/0.73 tff(63,plain,
% 0.76/0.73 (v1_xboole_0(k1_subset_1(u1_struct_0(B!1)))),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.76/0.73 tff(64,plain,
% 0.76/0.73 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(k1_subset_1(u1_struct_0(B!1)))) | (k1_subset_1(u1_struct_0(B!1)) = k1_xboole_0))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(k1_subset_1(u1_struct_0(B!1)))) | (k1_subset_1(u1_struct_0(B!1)) = k1_xboole_0))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(65,plain,
% 0.76/0.73 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(k1_subset_1(u1_struct_0(B!1)))) | (k1_subset_1(u1_struct_0(B!1)) = k1_xboole_0))),
% 0.76/0.73 inference(quant_inst,[status(thm)],[])).
% 0.76/0.73 tff(66,plain,
% 0.76/0.73 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(k1_subset_1(u1_struct_0(B!1)))) | (k1_subset_1(u1_struct_0(B!1)) = k1_xboole_0)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.76/0.73 tff(67,plain,
% 0.76/0.73 (k1_subset_1(u1_struct_0(B!1)) = k1_xboole_0),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[66, 30, 27, 63])).
% 0.76/0.73 tff(68,plain,
% 0.76/0.73 (k1_xboole_0 = k1_subset_1(u1_struct_0(B!1))),
% 0.76/0.73 inference(symmetry,[status(thm)],[67])).
% 0.76/0.73 tff(69,plain,
% 0.76/0.73 (v1_rmod_5(k1_xboole_0, A!0, B!1) <=> v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1)),
% 0.76/0.73 inference(monotonicity,[status(thm)],[68])).
% 0.76/0.73 tff(70,plain,
% 0.76/0.73 (v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1) <=> v1_rmod_5(k1_xboole_0, A!0, B!1)),
% 0.76/0.73 inference(symmetry,[status(thm)],[69])).
% 0.76/0.73 tff(71,plain,
% 0.76/0.73 ((~v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1)) <=> (~v1_rmod_5(k1_xboole_0, A!0, B!1))),
% 0.76/0.73 inference(monotonicity,[status(thm)],[70])).
% 0.76/0.73 tff(72,plain,
% 0.76/0.73 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)) & (~((~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))) | v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1)))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0) & (~((~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))) | v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1))))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(73,plain,
% 0.76/0.73 ((~(~((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(74,plain,
% 0.76/0.73 (((~(~((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)))) & (~((~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))) | v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1)))) <=> (((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)) & (~((~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))) | v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1))))),
% 0.76/0.73 inference(monotonicity,[status(thm)],[73])).
% 0.76/0.73 tff(75,plain,
% 0.76/0.73 (((~(~((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)))) & (~((~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))) | v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1)))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0) & (~((~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))) | v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1))))),
% 0.76/0.73 inference(transitivity,[status(thm)],[74, 72])).
% 0.76/0.73 tff(76,plain,
% 0.76/0.73 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B)))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B))))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(77,plain,
% 0.76/0.73 ((~![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B)))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B))))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(78,axiom,(~![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_rmod_5')).
% 0.76/0.73 tff(79,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.76/0.73 tff(80,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.76/0.73 tff(81,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.76/0.73 tff(82,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[81, 76])).
% 0.76/0.73 tff(83,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[82, 76])).
% 0.76/0.73 tff(84,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.76/0.73 tff(85,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | v1_rmod_5(k1_subset_1(u1_struct_0(B)), A, B)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[84, 76])).
% 0.76/0.73 tff(86,plain,
% 0.76/0.73 ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0) & (~((~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))) | v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.76/0.73 tff(87,plain,
% 0.76/0.73 (~((~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))) | v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1))),
% 0.76/0.73 inference(and_elim,[status(thm)],[86])).
% 0.76/0.73 tff(88,plain,
% 0.76/0.73 (~v1_rmod_5(k1_subset_1(u1_struct_0(B!1)), A!0, B!1)),
% 0.76/0.73 inference(or_elim,[status(thm)],[87])).
% 0.76/0.73 tff(89,plain,
% 0.76/0.73 (~v1_rmod_5(k1_xboole_0, A!0, B!1)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[88, 71])).
% 0.76/0.73 tff(90,plain,
% 0.76/0.73 (m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(k1_subset_1(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.76/0.73 inference(monotonicity,[status(thm)],[68])).
% 0.76/0.73 tff(91,plain,
% 0.76/0.73 (m1_subset_1(k1_subset_1(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.76/0.73 inference(symmetry,[status(thm)],[90])).
% 0.76/0.73 tff(92,plain,
% 0.76/0.73 (((~v1_xboole_0(k1_subset_1(u1_struct_0(B!1)))) | (~m1_subset_1(k1_subset_1(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | m1_subset_1(k1_subset_1(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.76/0.73 inference(tautology,[status(thm)],[])).
% 0.76/0.73 tff(93,plain,
% 0.76/0.73 (m1_subset_1(k1_subset_1(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[92, 61])).
% 0.76/0.73 tff(94,plain,
% 0.76/0.73 (m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[93, 91])).
% 0.76/0.73 tff(95,plain,
% 0.76/0.73 (^[A: $i] : refl((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(96,plain,
% 0.76/0.73 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[95])).
% 0.76/0.73 tff(97,plain,
% 0.76/0.73 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(98,plain,
% 0.76/0.73 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[97])).
% 0.76/0.73 tff(99,plain,
% 0.76/0.73 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))),
% 0.76/0.73 inference(transitivity,[status(thm)],[98, 96])).
% 0.76/0.73 tff(100,plain,
% 0.76/0.73 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) <=> (~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) <=> (~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))), (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))) <=> ((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))), rewrite(((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))) <=> ((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))))), rewrite(((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(101,plain,
% 0.76/0.74 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[100])).
% 0.76/0.74 tff(102,plain,
% 0.76/0.74 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(103,plain,
% 0.76/0.74 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0)))) <=> (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0)))))) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0)))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))))), (![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0)))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(104,plain,
% 0.76/0.74 (![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[103])).
% 0.76/0.74 tff(105,axiom,(![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_rmod_5')).
% 0.76/0.74 tff(106,plain,
% 0.76/0.74 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.76/0.74 tff(107,plain,
% 0.76/0.74 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.76/0.74 tff(108,plain,(
% 0.76/0.74 ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))),
% 0.76/0.74 inference(skolemize,[status(sab)],[107])).
% 0.76/0.74 tff(109,plain,
% 0.76/0.74 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.76/0.74 tff(110,plain,
% 0.76/0.74 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[109, 99])).
% 0.76/0.74 tff(111,plain,
% 0.76/0.74 (l3_vectsp_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[86])).
% 0.76/0.74 tff(112,plain,
% 0.76/0.74 (v8_vectsp_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[86])).
% 0.76/0.74 tff(113,plain,
% 0.76/0.74 (v7_vectsp_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[86])).
% 0.76/0.74 tff(114,plain,
% 0.76/0.74 (v6_vectsp_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[86])).
% 0.76/0.74 tff(115,plain,
% 0.76/0.74 (v4_group_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[86])).
% 0.76/0.74 tff(116,plain,
% 0.76/0.74 (v6_rlvect_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[86])).
% 0.76/0.74 tff(117,plain,
% 0.76/0.74 (v5_rlvect_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[86])).
% 0.76/0.74 tff(118,plain,
% 0.76/0.74 (v4_rlvect_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[86])).
% 0.76/0.74 tff(119,plain,
% 0.76/0.74 (v3_rlvect_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[86])).
% 0.76/0.74 tff(120,plain,
% 0.76/0.74 (~v3_struct_0(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[86])).
% 0.76/0.74 tff(121,plain,
% 0.76/0.74 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(122,plain,
% 0.76/0.74 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C))))))))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(123,plain,
% 0.76/0.74 (^[B: $i] : rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(124,plain,
% 0.76/0.75 (![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))) <=> ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C))))))))))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[123])).
% 0.76/0.75 tff(125,plain,
% 0.76/0.75 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C))))))))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))))),
% 0.76/0.75 inference(monotonicity,[status(thm)],[124])).
% 0.76/0.75 tff(126,plain,
% 0.76/0.75 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C))))))))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))))),
% 0.76/0.75 inference(transitivity,[status(thm)],[125, 122])).
% 0.76/0.75 tff(127,plain,
% 0.76/0.75 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C))))))))))))),
% 0.76/0.75 inference(monotonicity,[status(thm)],[126])).
% 0.76/0.75 tff(128,plain,
% 0.76/0.75 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))))),
% 0.76/0.75 inference(transitivity,[status(thm)],[127, 121])).
% 0.76/0.75 tff(129,plain,
% 0.76/0.75 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C)))))))))))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(130,plain,
% 0.76/0.75 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_2(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A), A, B, C)))))))))))) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C))))))))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.76/0.75 tff(131,plain,
% 0.76/0.75 (![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C))))))))))),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[130, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110])).
% 0.76/0.75 tff(132,plain,
% 0.76/0.75 ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)),
% 0.76/0.75 inference(or_elim,[status(thm)],[87])).
% 0.76/0.75 tff(133,plain,
% 0.76/0.75 (l1_vectsp_2(B!1, A!0)),
% 0.76/0.75 inference(and_elim,[status(thm)],[132])).
% 0.76/0.75 tff(134,plain,
% 0.76/0.75 (v5_vectsp_2(B!1, A!0)),
% 0.76/0.75 inference(and_elim,[status(thm)],[132])).
% 0.76/0.75 tff(135,plain,
% 0.76/0.75 (v6_rlvect_1(B!1)),
% 0.76/0.75 inference(and_elim,[status(thm)],[132])).
% 0.76/0.75 tff(136,plain,
% 0.76/0.75 (v5_rlvect_1(B!1)),
% 0.76/0.75 inference(and_elim,[status(thm)],[132])).
% 0.76/0.75 tff(137,plain,
% 0.76/0.75 (v4_rlvect_1(B!1)),
% 0.76/0.75 inference(and_elim,[status(thm)],[132])).
% 0.76/0.75 tff(138,plain,
% 0.76/0.75 (v3_rlvect_1(B!1)),
% 0.76/0.75 inference(and_elim,[status(thm)],[132])).
% 0.76/0.75 tff(139,plain,
% 0.76/0.75 (~v3_struct_0(B!1)),
% 0.76/0.75 inference(and_elim,[status(thm)],[132])).
% 0.76/0.75 tff(140,plain,
% 0.76/0.75 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C))))))))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(C, B!1, A!0), A!0, B!1, C))))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C))))))))))) | v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(C, B!1, A!0), A!0, B!1, C))))))))))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(141,plain,
% 0.76/0.75 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C))))))))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(C, B!1, A!0), A!0, B!1, C))))))))))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(142,plain,
% 0.76/0.75 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_2(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_2(C, B, A!0), A!0, B, C))))))))))) | v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(C, B!1, A!0), A!0, B!1, C)))))))))),
% 0.82/0.75 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.82/0.75 tff(143,plain,
% 0.82/0.75 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(C, B!1, A!0), A!0, B!1, C)))))))))),
% 0.82/0.75 inference(unit_resolution,[status(thm)],[142, 139, 138, 137, 136, 135, 134, 133, 131])).
% 0.82/0.75 tff(144,plain,
% 0.82/0.75 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(C, B!1, A!0), A!0, B!1, C)))))))))) | ((~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(k1_xboole_0, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, k1_xboole_0))))) | (~(v1_rmod_5(k1_xboole_0, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0)))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(C, B!1, A!0), A!0, B!1, C)))))))))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(k1_xboole_0, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, k1_xboole_0))))) | (~(v1_rmod_5(k1_xboole_0, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0)))))))))),
% 0.82/0.75 inference(rewrite,[status(thm)],[])).
% 0.82/0.75 tff(145,plain,
% 0.82/0.75 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(C, B!1, A!0), A!0, B!1, C)))))))))) | ((~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(k1_xboole_0, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, k1_xboole_0))))) | (~(v1_rmod_5(k1_xboole_0, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0)))))))))),
% 0.82/0.76 inference(quant_inst,[status(thm)],[])).
% 0.82/0.76 tff(146,plain,
% 0.82/0.76 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(C, B!1, A!0), A!0, B!1, C)))))))))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(k1_xboole_0, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, k1_xboole_0))))) | (~(v1_rmod_5(k1_xboole_0, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0))))))))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.82/0.76 tff(147,plain,
% 0.82/0.76 ((~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(k1_xboole_0, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, k1_xboole_0))))) | (~(v1_rmod_5(k1_xboole_0, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0))))))))),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[146, 143])).
% 0.82/0.76 tff(148,plain,
% 0.82/0.76 (~((~((~v1_rmod_5(k1_xboole_0, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, k1_xboole_0))))) | (~(v1_rmod_5(k1_xboole_0, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0)))))))),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[147, 94])).
% 0.82/0.76 tff(149,plain,
% 0.82/0.76 (((~((~v1_rmod_5(k1_xboole_0, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, k1_xboole_0))))) | (~(v1_rmod_5(k1_xboole_0, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0))))))) | (v1_rmod_5(k1_xboole_0, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0)))))),
% 0.82/0.76 inference(tautology,[status(thm)],[])).
% 0.82/0.76 tff(150,plain,
% 0.82/0.76 (v1_rmod_5(k1_xboole_0, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0))))),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.82/0.76 tff(151,plain,
% 0.82/0.76 ((~(v1_rmod_5(k1_xboole_0, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0)))))) | v1_rmod_5(k1_xboole_0, A!0, B!1) | (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0))))),
% 0.82/0.76 inference(tautology,[status(thm)],[])).
% 0.82/0.76 tff(152,plain,
% 0.82/0.76 (~((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0)))),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[151, 150, 89])).
% 0.82/0.76 tff(153,plain,
% 0.82/0.76 (((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0))) | m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0)),
% 0.82/0.76 inference(tautology,[status(thm)],[])).
% 0.82/0.76 tff(154,plain,
% 0.82/0.76 (m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0)),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.82/0.76 tff(155,plain,
% 0.82/0.76 (m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[154, 49])).
% 0.82/0.76 tff(156,plain,
% 0.82/0.76 (((~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_xboole_0(tptp_fun_B_22(u1_struct_0(B!1))))) | m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.82/0.76 inference(tautology,[status(thm)],[])).
% 0.82/0.76 tff(157,plain,
% 0.82/0.76 (m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[156, 36])).
% 0.82/0.76 tff(158,plain,
% 0.82/0.76 (^[A: $i, B: $i, C: $i] : rewrite((v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B))))),
% 0.82/0.76 inference(bind,[status(th)],[])).
% 0.82/0.76 tff(159,plain,
% 0.82/0.76 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))),
% 0.82/0.76 inference(quant_intro,[status(thm)],[158])).
% 0.82/0.76 tff(160,plain,
% 0.82/0.76 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))))),
% 0.82/0.76 inference(bind,[status(th)],[])).
% 0.82/0.76 tff(161,plain,
% 0.82/0.76 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)))),
% 0.82/0.76 inference(quant_intro,[status(thm)],[160])).
% 0.82/0.76 tff(162,plain,
% 0.82/0.76 (^[A: $i, B: $i, C: $i] : rewrite((v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))))),
% 0.82/0.76 inference(bind,[status(th)],[])).
% 0.82/0.76 tff(163,plain,
% 0.82/0.76 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)))),
% 0.82/0.76 inference(quant_intro,[status(thm)],[162])).
% 0.82/0.76 tff(164,plain,
% 0.82/0.76 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)))),
% 0.82/0.76 inference(transitivity,[status(thm)],[163, 161])).
% 0.82/0.76 tff(165,plain,
% 0.82/0.76 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) <=> (~(v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) <=> (~(~(v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))))))), rewrite((~(~(v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B))) <=> ((v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B))))), rewrite(((v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)))))),
% 0.82/0.76 inference(bind,[status(th)],[])).
% 0.82/0.76 tff(166,plain,
% 0.82/0.76 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)))),
% 0.82/0.76 inference(quant_intro,[status(thm)],[165])).
% 0.82/0.76 tff(167,plain,
% 0.82/0.76 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))),
% 0.82/0.76 inference(rewrite,[status(thm)],[])).
% 0.82/0.76 tff(168,plain,
% 0.82/0.76 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B))))), (((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B))) & v3_rlvect_1(B)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B))) & v3_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B))), (((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B)))), ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B))), ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)))), (((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B))), (((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)))), ((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B))), ((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)))), (((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A))), (((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)))), ((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))), ((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))), (((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))), (((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))))), quant_intro(proof_bind(^[D: $i] : rewrite((m2_rmod_4(D, A, B, C) => m1_rmod_4(D, A, B)) <=> ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))), (![D: $i] : (m2_rmod_4(D, A, B, C) => m1_rmod_4(D, A, B)) <=> ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))), ((((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => ![D: $i] : (m2_rmod_4(D, A, B, C) => m1_rmod_4(D, A, B))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))), ((((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => ![D: $i] : (m2_rmod_4(D, A, B, C) => m1_rmod_4(D, A, B))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))))),
% 0.82/0.76 inference(bind,[status(th)],[])).
% 0.82/0.76 tff(169,plain,
% 0.82/0.76 (![A: $i, B: $i, C: $i] : (((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => ![D: $i] : (m2_rmod_4(D, A, B, C) => m1_rmod_4(D, A, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))),
% 0.82/0.76 inference(quant_intro,[status(thm)],[168])).
% 0.82/0.76 tff(170,axiom,(![A: $i, B: $i, C: $i] : (((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => ![D: $i] : (m2_rmod_4(D, A, B, C) => m1_rmod_4(D, A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_rmod_4')).
% 0.82/0.76 tff(171,plain,
% 0.82/0.76 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.82/0.76 tff(172,plain,
% 0.82/0.76 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.82/0.77 tff(173,plain,(
% 0.82/0.77 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))),
% 0.82/0.77 inference(skolemize,[status(sab)],[172])).
% 0.82/0.77 tff(174,plain,
% 0.82/0.77 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.82/0.77 tff(175,plain,
% 0.82/0.77 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[174, 164])).
% 0.82/0.77 tff(176,plain,
% 0.82/0.77 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[175, 159])).
% 0.82/0.77 tff(177,plain,
% 0.82/0.77 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | (~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | (~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1)))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(178,plain,
% 0.82/0.77 ((v3_struct_0(B!1) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1))) <=> (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | (~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1)))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(179,plain,
% 0.82/0.77 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | (~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1))))),
% 0.82/0.77 inference(monotonicity,[status(thm)],[178])).
% 0.82/0.77 tff(180,plain,
% 0.82/0.77 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | (~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1)))),
% 0.82/0.77 inference(transitivity,[status(thm)],[179, 177])).
% 0.82/0.77 tff(181,plain,
% 0.82/0.77 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1)))),
% 0.82/0.77 inference(quant_inst,[status(thm)],[])).
% 0.82/0.77 tff(182,plain,
% 0.82/0.77 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | ![D: $i] : ((~m2_rmod_4(D, A, B, C)) | m1_rmod_4(D, A, B)))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | (~m1_subset_1(tptp_fun_B_22(u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.82/0.77 tff(183,plain,
% 0.82/0.77 (![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1))),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[182, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 139, 138, 137, 136, 135, 134, 133, 176, 157])).
% 0.82/0.77 tff(184,plain,
% 0.82/0.77 (((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1))) | ((~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1))) <=> ((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(185,plain,
% 0.82/0.77 ((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1))) | ((~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1))),
% 0.82/0.77 inference(quant_inst,[status(thm)],[])).
% 0.82/0.77 tff(186,plain,
% 0.82/0.77 ((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(D, A!0, B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1)),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.82/0.77 tff(187,plain,
% 0.82/0.77 ((~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, tptp_fun_B_22(u1_struct_0(B!1)))) | m1_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1)),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[186, 183])).
% 0.82/0.77 tff(188,plain,
% 0.82/0.77 (m1_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1)),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[187, 155])).
% 0.82/0.77 tff(189,plain,
% 0.82/0.77 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))), (![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))), ((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))))), rewrite((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))), ((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))))),
% 0.82/0.77 inference(bind,[status(th)],[])).
% 0.82/0.77 tff(190,plain,
% 0.82/0.77 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))),
% 0.82/0.77 inference(quant_intro,[status(thm)],[189])).
% 0.82/0.77 tff(191,plain,
% 0.82/0.77 (^[A: $i] : refl((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))),
% 0.82/0.77 inference(bind,[status(th)],[])).
% 0.82/0.77 tff(192,plain,
% 0.82/0.77 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.77 inference(quant_intro,[status(thm)],[191])).
% 0.82/0.77 tff(193,plain,
% 0.82/0.77 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))),
% 0.82/0.77 inference(bind,[status(th)],[])).
% 0.82/0.77 tff(194,plain,
% 0.82/0.77 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.77 inference(quant_intro,[status(thm)],[193])).
% 0.82/0.77 tff(195,plain,
% 0.82/0.77 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.77 inference(transitivity,[status(thm)],[194, 192])).
% 0.82/0.77 tff(196,plain,
% 0.82/0.77 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) <=> (~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) <=> (~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))) <=> ((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))), rewrite(((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))) <=> (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))) <=> (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))) <=> ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))) <=> ((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))), rewrite(((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))),
% 0.82/0.77 inference(bind,[status(th)],[])).
% 0.82/0.77 tff(197,plain,
% 0.82/0.77 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.77 inference(quant_intro,[status(thm)],[196])).
% 0.82/0.77 tff(198,plain,
% 0.82/0.77 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(199,plain,
% 0.82/0.77 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite((m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))) <=> ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))), (![D: $i] : (m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))) <=> ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))))), (![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))))),
% 0.82/0.78 inference(bind,[status(th)],[])).
% 0.82/0.78 tff(200,plain,
% 0.82/0.78 (![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))),
% 0.82/0.78 inference(quant_intro,[status(thm)],[199])).
% 0.82/0.78 tff(201,axiom,(![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_4(D, A, B) => (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_rmod_4')).
% 0.82/0.78 tff(202,plain,
% 0.82/0.78 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.82/0.78 tff(203,plain,
% 0.82/0.78 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.82/0.78 tff(204,plain,(
% 0.82/0.78 ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))),
% 0.82/0.78 inference(skolemize,[status(sab)],[203])).
% 0.82/0.78 tff(205,plain,
% 0.82/0.78 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.82/0.78 tff(206,plain,
% 0.82/0.78 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C)))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[205, 195])).
% 0.82/0.78 tff(207,plain,
% 0.82/0.78 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[206, 190])).
% 0.82/0.78 tff(208,plain,
% 0.82/0.78 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))))),
% 0.82/0.78 inference(rewrite,[status(thm)],[])).
% 0.82/0.78 tff(209,plain,
% 0.82/0.78 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C)))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))))),
% 0.82/0.78 inference(rewrite,[status(thm)],[])).
% 0.82/0.78 tff(210,plain,
% 0.82/0.78 (^[B: $i] : rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))))),
% 0.82/0.78 inference(bind,[status(th)],[])).
% 0.82/0.78 tff(211,plain,
% 0.82/0.78 (![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))) <=> ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C)))))),
% 0.82/0.78 inference(quant_intro,[status(thm)],[210])).
% 0.82/0.78 tff(212,plain,
% 0.82/0.78 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C)))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))))),
% 0.82/0.78 inference(monotonicity,[status(thm)],[211])).
% 0.82/0.78 tff(213,plain,
% 0.82/0.78 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C)))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))))),
% 0.82/0.78 inference(transitivity,[status(thm)],[212, 209])).
% 0.82/0.78 tff(214,plain,
% 0.82/0.78 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C)))))))),
% 0.82/0.78 inference(monotonicity,[status(thm)],[213])).
% 0.82/0.78 tff(215,plain,
% 0.82/0.78 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))))),
% 0.82/0.78 inference(transitivity,[status(thm)],[214, 208])).
% 0.82/0.78 tff(216,plain,
% 0.82/0.78 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C))))))),
% 0.82/0.78 inference(quant_inst,[status(thm)],[])).
% 0.82/0.78 tff(217,plain,
% 0.82/0.78 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A, B)) | (m2_rmod_4(D, A, B, C) <=> r1_tarski(k2_rmod_4(A, B, D), C))))))) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C)))))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.82/0.78 tff(218,plain,
% 0.82/0.78 (![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C)))))),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[217, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 207])).
% 0.82/0.78 tff(219,plain,
% 0.82/0.78 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, C) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), C)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C)))))) | v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, C) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), C)))))),
% 0.82/0.78 inference(rewrite,[status(thm)],[])).
% 0.82/0.78 tff(220,plain,
% 0.82/0.78 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, C) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), C)))))),
% 0.82/0.78 inference(quant_inst,[status(thm)],[])).
% 0.82/0.78 tff(221,plain,
% 0.82/0.78 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B)) | (m2_rmod_4(D, A!0, B, C) <=> r1_tarski(k2_rmod_4(A!0, B, D), C)))))) | v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, C) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), C))))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.82/0.79 tff(222,plain,
% 0.82/0.79 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, C) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), C))))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[221, 139, 138, 137, 136, 135, 134, 133, 218])).
% 0.82/0.79 tff(223,plain,
% 0.82/0.79 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, C) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), C))))) | ((~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), k1_xboole_0))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, C) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), C))))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), k1_xboole_0))))),
% 0.82/0.79 inference(rewrite,[status(thm)],[])).
% 0.82/0.79 tff(224,plain,
% 0.82/0.79 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, C) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), C))))) | ((~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), k1_xboole_0))))),
% 0.82/0.79 inference(quant_inst,[status(thm)],[])).
% 0.82/0.79 tff(225,plain,
% 0.82/0.79 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, C) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), C))))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), k1_xboole_0)))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.82/0.79 tff(226,plain,
% 0.82/0.79 ((~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), k1_xboole_0)))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[225, 222])).
% 0.82/0.79 tff(227,plain,
% 0.82/0.79 (![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), k1_xboole_0)))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[226, 94])).
% 0.82/0.79 tff(228,plain,
% 0.82/0.79 (((~![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), k1_xboole_0)))) | ((~m1_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1)) | (m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0)))) <=> ((~![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), k1_xboole_0)))) | (~m1_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1)) | (m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0)))),
% 0.82/0.79 inference(rewrite,[status(thm)],[])).
% 0.82/0.79 tff(229,plain,
% 0.82/0.79 ((~![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), k1_xboole_0)))) | ((~m1_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1)) | (m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0)))),
% 0.82/0.79 inference(quant_inst,[status(thm)],[])).
% 0.82/0.79 tff(230,plain,
% 0.82/0.79 ((~![D: $i] : ((~m1_rmod_4(D, A!0, B!1)) | (m2_rmod_4(D, A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, D), k1_xboole_0)))) | (~m1_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1)) | (m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.82/0.79 tff(231,plain,
% 0.82/0.79 ((~m1_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1)) | (m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.82/0.79 tff(232,plain,
% 0.82/0.79 (m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0)),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[231, 188])).
% 0.82/0.79 tff(233,plain,
% 0.82/0.79 ((~(m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0)) | r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0)),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(234,plain,
% 0.82/0.79 ((~(m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0) <=> r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0))) | r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0)),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[233, 154])).
% 0.82/0.79 tff(235,plain,
% 0.82/0.79 (r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0)),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[234, 232])).
% 0.82/0.79 tff(236,plain,
% 0.82/0.79 (((k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_2(k1_xboole_0, B!1, A!0), A!0, B!1, k1_xboole_0))) | (~(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0))),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(237,plain,
% 0.82/0.79 (~(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0)),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[236, 152])).
% 0.82/0.79 tff(238,plain,
% 0.82/0.79 (^[A: $i] : refl(((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0)) <=> ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0)))),
% 0.82/0.79 inference(bind,[status(th)],[])).
% 0.82/0.79 tff(239,plain,
% 0.82/0.79 (![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0)) <=> ![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0))),
% 0.82/0.79 inference(quant_intro,[status(thm)],[238])).
% 0.82/0.79 tff(240,plain,
% 0.82/0.79 (![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0)) <=> ![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0))),
% 0.82/0.79 inference(rewrite,[status(thm)],[])).
% 0.82/0.79 tff(241,plain,
% 0.82/0.79 (^[A: $i] : rewrite((r1_tarski(A, k1_xboole_0) => (A = k1_xboole_0)) <=> ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0)))),
% 0.82/0.79 inference(bind,[status(th)],[])).
% 0.82/0.79 tff(242,plain,
% 0.82/0.79 (![A: $i] : (r1_tarski(A, k1_xboole_0) => (A = k1_xboole_0)) <=> ![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0))),
% 0.82/0.79 inference(quant_intro,[status(thm)],[241])).
% 0.82/0.79 tff(243,axiom,(![A: $i] : (r1_tarski(A, k1_xboole_0) => (A = k1_xboole_0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_xboole_1')).
% 0.82/0.79 tff(244,plain,
% 0.82/0.79 (![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.82/0.79 tff(245,plain,
% 0.82/0.79 (![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[244, 240])).
% 0.82/0.79 tff(246,plain,(
% 0.82/0.79 ![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0))),
% 0.82/0.79 inference(skolemize,[status(sab)],[245])).
% 0.82/0.79 tff(247,plain,
% 0.82/0.79 (![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[246, 239])).
% 0.82/0.79 tff(248,plain,
% 0.82/0.79 (((~![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0))) | ((~r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0)) | (k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0))) <=> ((~![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0))) | (~r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0)) | (k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0))),
% 0.82/0.80 inference(rewrite,[status(thm)],[])).
% 0.82/0.80 tff(249,plain,
% 0.82/0.80 ((~![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0))) | ((~r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0)) | (k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0))),
% 0.82/0.80 inference(quant_inst,[status(thm)],[])).
% 0.82/0.80 tff(250,plain,
% 0.82/0.80 ((~![A: $i] : ((~r1_tarski(A, k1_xboole_0)) | (A = k1_xboole_0))) | (~r1_tarski(k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)), k1_xboole_0)) | (k2_rmod_4(A!0, B!1, tptp_fun_D_2(k1_xboole_0, B!1, A!0)) = k1_xboole_0)),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.82/0.80 tff(251,plain,
% 0.82/0.80 ($false),
% 0.82/0.80 inference(unit_resolution,[status(thm)],[250, 247, 237, 235])).
% 0.82/0.80 % SZS output end Proof
%------------------------------------------------------------------------------