TSTP Solution File: ALG219+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG219+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 16:09:18 EDT 2022
% Result : Theorem 0.50s 0.57s
% Output : Proof 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ALG219+1 : TPTP v8.1.0. Released v3.4.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 29 14:05:48 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.50/0.57 % SZS status Theorem
% 0.50/0.57 % SZS output start Proof
% 0.50/0.57 tff(g1_vectsp_2_type, type, (
% 0.50/0.57 g1_vectsp_2: ( $i * $i * $i * $i * $i ) > $i)).
% 0.50/0.57 tff(u1_vectsp_2_type, type, (
% 0.50/0.57 u1_vectsp_2: ( $i * $i ) > $i)).
% 0.50/0.57 tff(tptp_fun_B_1_type, type, (
% 0.50/0.57 tptp_fun_B_1: $i)).
% 0.50/0.57 tff(tptp_fun_A_0_type, type, (
% 0.50/0.57 tptp_fun_A_0: $i)).
% 0.50/0.57 tff(u2_struct_0_type, type, (
% 0.50/0.57 u2_struct_0: $i > $i)).
% 0.50/0.57 tff(u1_rlvect_1_type, type, (
% 0.50/0.57 u1_rlvect_1: $i > $i)).
% 0.50/0.57 tff(u1_struct_0_type, type, (
% 0.50/0.57 u1_struct_0: $i > $i)).
% 0.50/0.57 tff(k1_rmod_5_type, type, (
% 0.50/0.57 k1_rmod_5: ( $i * $i * $i ) > $i)).
% 0.50/0.57 tff(tptp_fun_C_2_type, type, (
% 0.50/0.57 tptp_fun_C_2: $i)).
% 0.50/0.57 tff(l1_struct_0_type, type, (
% 0.50/0.57 l1_struct_0: $i > $o)).
% 0.50/0.57 tff(l2_struct_0_type, type, (
% 0.50/0.57 l2_struct_0: $i > $o)).
% 0.50/0.57 tff(l1_rlvect_1_type, type, (
% 0.50/0.57 l1_rlvect_1: $i > $o)).
% 0.50/0.57 tff(l2_vectsp_1_type, type, (
% 0.50/0.57 l2_vectsp_1: $i > $o)).
% 0.50/0.57 tff(l3_vectsp_1_type, type, (
% 0.50/0.57 l3_vectsp_1: $i > $o)).
% 0.50/0.57 tff(m1_subset_1_type, type, (
% 0.50/0.57 m1_subset_1: ( $i * $i ) > $o)).
% 0.50/0.57 tff(k1_zfmisc_1_type, type, (
% 0.50/0.57 k1_zfmisc_1: $i > $i)).
% 0.50/0.57 tff(k2_group_1_type, type, (
% 0.50/0.57 k2_group_1: $i > $i)).
% 0.50/0.57 tff(k1_rlvect_1_type, type, (
% 0.50/0.57 k1_rlvect_1: $i > $i)).
% 0.50/0.57 tff(l1_vectsp_2_type, type, (
% 0.50/0.57 l1_vectsp_2: ( $i * $i ) > $o)).
% 0.50/0.57 tff(v5_vectsp_2_type, type, (
% 0.50/0.57 v5_vectsp_2: ( $i * $i ) > $o)).
% 0.50/0.57 tff(v3_vectsp_2_type, type, (
% 0.50/0.57 v3_vectsp_2: ( $i * $i ) > $o)).
% 0.50/0.57 tff(v6_rlvect_1_type, type, (
% 0.50/0.57 v6_rlvect_1: $i > $o)).
% 0.50/0.57 tff(v5_rlvect_1_type, type, (
% 0.50/0.57 v5_rlvect_1: $i > $o)).
% 0.50/0.57 tff(v4_rlvect_1_type, type, (
% 0.50/0.57 v4_rlvect_1: $i > $o)).
% 0.50/0.57 tff(v3_rlvect_1_type, type, (
% 0.50/0.57 v3_rlvect_1: $i > $o)).
% 0.50/0.57 tff(v3_struct_0_type, type, (
% 0.50/0.57 v3_struct_0: $i > $o)).
% 0.50/0.57 tff(v2_vectsp_2_type, type, (
% 0.50/0.57 v2_vectsp_2: $i > $o)).
% 0.50/0.57 tff(v10_vectsp_1_type, type, (
% 0.50/0.57 v10_vectsp_1: $i > $o)).
% 0.50/0.57 tff(v8_vectsp_1_type, type, (
% 0.50/0.57 v8_vectsp_1: $i > $o)).
% 0.50/0.57 tff(v7_vectsp_1_type, type, (
% 0.50/0.57 v7_vectsp_1: $i > $o)).
% 0.50/0.57 tff(v6_vectsp_1_type, type, (
% 0.50/0.57 v6_vectsp_1: $i > $o)).
% 0.50/0.57 tff(v7_group_1_type, type, (
% 0.50/0.57 v7_group_1: $i > $o)).
% 0.50/0.57 tff(v4_group_1_type, type, (
% 0.50/0.57 v4_group_1: $i > $o)).
% 0.50/0.57 tff(m1_rmod_2_type, type, (
% 0.50/0.57 m1_rmod_2: ( $i * $i * $i ) > $o)).
% 0.50/0.57 tff(k2_rmod_2_type, type, (
% 0.50/0.57 k2_rmod_2: ( $i * $i ) > $i)).
% 0.50/0.57 tff(1,plain,
% 0.50/0.57 (^[A: $i] : refl(((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))) <=> ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(2,plain,
% 0.50/0.57 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[1])).
% 0.50/0.57 tff(3,plain,
% 0.50/0.57 (^[A: $i] : rewrite(((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(4,plain,
% 0.50/0.57 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[3])).
% 0.50/0.57 tff(5,plain,
% 0.50/0.57 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(6,plain,
% 0.50/0.57 (^[A: $i] : rewrite((l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(7,plain,
% 0.50/0.57 (![A: $i] : (l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[6])).
% 0.50/0.57 tff(8,axiom,(![A: $i] : (l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_vectsp_1')).
% 0.50/0.57 tff(9,plain,
% 0.50/0.57 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.50/0.57 tff(10,plain,
% 0.50/0.57 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.50/0.57 tff(11,plain,(
% 0.50/0.57 ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.50/0.57 inference(skolemize,[status(sab)],[10])).
% 0.50/0.57 tff(12,plain,
% 0.50/0.57 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.50/0.57 tff(13,plain,
% 0.50/0.57 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.50/0.57 tff(14,plain,
% 0.50/0.57 ((((~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) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = B!1) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_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) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = B!1) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(15,plain,
% 0.50/0.57 ((((~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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = B!1) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))))))) <=> ((~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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = B!1) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(16,plain,
% 0.50/0.57 ((~((k1_rmod_5(A!0, B!1, C!2) = B!1) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))))) <=> (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = B!1) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(17,plain,
% 0.50/0.57 ((~(~((~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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(18,plain,
% 0.50/0.57 (((~(~((~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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & (~((k1_rmod_5(A!0, B!1, C!2) = B!1) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))))))) <=> (((~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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = B!1) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.50/0.57 inference(monotonicity,[status(thm)],[17, 16])).
% 0.50/0.57 tff(19,plain,
% 0.50/0.57 (((~(~((~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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & (~((k1_rmod_5(A!0, B!1, C!2) = B!1) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))))))) <=> ((~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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = B!1) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.50/0.57 inference(transitivity,[status(thm)],[18, 15])).
% 0.50/0.57 tff(20,plain,
% 0.50/0.57 ((~(~((~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) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(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) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(21,plain,
% 0.50/0.57 (((~(~((~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) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & (~((k1_rmod_5(A!0, B!1, C!2) = B!1) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_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) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = B!1) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))))))))),
% 0.50/0.57 inference(monotonicity,[status(thm)],[20, 19])).
% 0.50/0.57 tff(22,plain,
% 0.50/0.57 (((~(~((~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) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & (~((k1_rmod_5(A!0, B!1, C!2) = B!1) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_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) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = B!1) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.50/0.57 inference(transitivity,[status(thm)],[21, 14])).
% 0.50/0.57 tff(23,plain,
% 0.50/0.57 ((~![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((k1_rmod_5(A, B, C) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((k1_rmod_5(A, B, C) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(24,plain,
% 0.50/0.57 ((~![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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(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)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ((C = u1_struct_0(B)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = 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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((k1_rmod_5(A, B, C) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(25,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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(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)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ((C = u1_struct_0(B)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t14_rmod_5')).
% 0.50/0.57 tff(26,plain,
% 0.50/0.57 (~![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((k1_rmod_5(A, B, C) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.50/0.57 tff(27,plain,
% 0.50/0.57 (~![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((k1_rmod_5(A, B, C) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.50/0.57 tff(28,plain,
% 0.50/0.57 (~![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((k1_rmod_5(A, B, C) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.50/0.58 tff(29,plain,
% 0.50/0.58 (~![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((k1_rmod_5(A, B, C) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.50/0.58 tff(30,plain,
% 0.50/0.58 (~![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((k1_rmod_5(A, B, C) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.50/0.58 tff(31,plain,
% 0.50/0.58 (~![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((k1_rmod_5(A, B, C) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.50/0.58 tff(32,plain,
% 0.50/0.58 (~![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((k1_rmod_5(A, B, C) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[31, 23])).
% 0.50/0.58 tff(33,plain,
% 0.50/0.58 ((~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) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(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) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = B!1) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.50/0.58 tff(34,plain,
% 0.50/0.58 (l3_vectsp_1(A!0)),
% 0.50/0.58 inference(and_elim,[status(thm)],[33])).
% 0.50/0.58 tff(35,plain,
% 0.50/0.58 (((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | ((~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))) <=> ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | (~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(36,plain,
% 0.50/0.58 ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | ((~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(37,plain,
% 0.50/0.58 ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | (~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.50/0.58 tff(38,plain,
% 0.50/0.58 (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[37, 34, 13])).
% 0.50/0.58 tff(39,plain,
% 0.50/0.58 (((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0))) | l1_rlvect_1(A!0)),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(40,plain,
% 0.50/0.58 (l1_rlvect_1(A!0)),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.50/0.58 tff(41,plain,
% 0.50/0.58 (^[A: $i] : refl((l2_struct_0(A) | (~l1_rlvect_1(A))) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(42,plain,
% 0.50/0.58 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[41])).
% 0.50/0.58 tff(43,plain,
% 0.50/0.58 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(44,plain,
% 0.50/0.58 (^[A: $i] : rewrite((l1_rlvect_1(A) => l2_struct_0(A)) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(45,plain,
% 0.50/0.58 (![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A)) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[44])).
% 0.50/0.58 tff(46,axiom,(![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_rlvect_1')).
% 0.50/0.58 tff(47,plain,
% 0.50/0.58 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.50/0.58 tff(48,plain,
% 0.50/0.58 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.50/0.58 tff(49,plain,(
% 0.50/0.58 ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.50/0.58 inference(skolemize,[status(sab)],[48])).
% 0.50/0.58 tff(50,plain,
% 0.50/0.58 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.50/0.58 tff(51,plain,
% 0.50/0.58 (((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))) <=> ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(52,plain,
% 0.50/0.58 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(53,plain,
% 0.50/0.58 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(A!0) | (~l1_rlvect_1(A!0))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.50/0.58 tff(54,plain,
% 0.50/0.58 (l2_struct_0(A!0)),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[53, 50, 40])).
% 0.50/0.58 tff(55,plain,
% 0.50/0.58 (^[A: $i] : refl((l1_struct_0(A) | (~l2_struct_0(A))) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(56,plain,
% 0.50/0.58 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[55])).
% 0.50/0.58 tff(57,plain,
% 0.50/0.58 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(58,plain,
% 0.50/0.58 (^[A: $i] : rewrite((l2_struct_0(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(59,plain,
% 0.50/0.58 (![A: $i] : (l2_struct_0(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[58])).
% 0.50/0.58 tff(60,axiom,(![A: $i] : (l2_struct_0(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_struct_0')).
% 0.50/0.58 tff(61,plain,
% 0.50/0.58 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.50/0.58 tff(62,plain,
% 0.50/0.58 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.50/0.58 tff(63,plain,(
% 0.50/0.58 ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.50/0.58 inference(skolemize,[status(sab)],[62])).
% 0.50/0.58 tff(64,plain,
% 0.50/0.58 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.50/0.58 tff(65,plain,
% 0.50/0.58 (((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | (l1_struct_0(A!0) | (~l2_struct_0(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | l1_struct_0(A!0) | (~l2_struct_0(A!0)))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(66,plain,
% 0.50/0.58 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | (l1_struct_0(A!0) | (~l2_struct_0(A!0)))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(67,plain,
% 0.50/0.58 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | l1_struct_0(A!0) | (~l2_struct_0(A!0))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.50/0.58 tff(68,plain,
% 0.50/0.58 (l1_struct_0(A!0)),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[67, 64, 54])).
% 0.50/0.58 tff(69,plain,
% 0.50/0.58 (^[A: $i, B: $i] : refl(((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(70,plain,
% 0.50/0.58 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[69])).
% 0.50/0.58 tff(71,plain,
% 0.50/0.58 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_struct_0(A) & l1_vectsp_2(B, A)) <=> (~((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))), ((~(l1_struct_0(A) & l1_vectsp_2(B, A))) <=> (~(~((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))))), rewrite((~(~((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))) <=> ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A)))), ((~(l1_struct_0(A) & l1_vectsp_2(B, A))) <=> ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))), (((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A)))))), rewrite(((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A)))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))), (((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(72,plain,
% 0.50/0.58 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[71])).
% 0.50/0.58 tff(73,plain,
% 0.50/0.58 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(74,plain,
% 0.50/0.58 (^[A: $i, B: $i] : trans(monotonicity(rewrite((v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> ((~v3_vectsp_2(B, A)) | (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))), (((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((l1_struct_0(A) & l1_vectsp_2(B, A)) => ((~v3_vectsp_2(B, A)) | (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))))), rewrite(((l1_struct_0(A) & l1_vectsp_2(B, A)) => ((~v3_vectsp_2(B, A)) | (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))), (((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(75,plain,
% 0.50/0.58 (![A: $i, B: $i] : ((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[74])).
% 0.50/0.58 tff(76,axiom,(![A: $i, B: $i] : ((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v3_vectsp_2')).
% 0.50/0.58 tff(77,plain,
% 0.50/0.58 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.50/0.58 tff(78,plain,
% 0.50/0.58 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.50/0.58 tff(79,plain,(
% 0.50/0.58 ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.50/0.58 inference(skolemize,[status(sab)],[78])).
% 0.50/0.58 tff(80,plain,
% 0.50/0.58 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.50/0.58 tff(81,plain,
% 0.50/0.58 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.53/0.58 tff(82,plain,
% 0.53/0.58 (l1_vectsp_2(B!1, A!0)),
% 0.53/0.58 inference(and_elim,[status(thm)],[33])).
% 0.53/0.58 tff(83,plain,
% 0.53/0.58 (v3_vectsp_2(B!1, A!0)),
% 0.53/0.58 inference(and_elim,[status(thm)],[33])).
% 0.53/0.58 tff(84,plain,
% 0.53/0.58 (((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | (B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~l1_struct_0(A!0)))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(85,plain,
% 0.53/0.58 ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~l1_struct_0(A!0)))),
% 0.53/0.58 inference(quant_inst,[status(thm)],[])).
% 0.53/0.58 tff(86,plain,
% 0.53/0.58 ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | (B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~l1_struct_0(A!0))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.53/0.58 tff(87,plain,
% 0.53/0.58 ((B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) | (~l1_struct_0(A!0))),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[86, 83, 82, 81])).
% 0.53/0.58 tff(88,plain,
% 0.53/0.58 (B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[87, 68])).
% 0.53/0.58 tff(89,plain,
% 0.53/0.58 (g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)) = B!1),
% 0.53/0.58 inference(symmetry,[status(thm)],[88])).
% 0.53/0.58 tff(90,plain,
% 0.53/0.58 (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = B!1) | (~(C!2 = u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.53/0.58 inference(and_elim,[status(thm)],[33])).
% 0.53/0.58 tff(91,plain,
% 0.53/0.58 (C!2 = u1_struct_0(B!1)),
% 0.53/0.58 inference(or_elim,[status(thm)],[90])).
% 0.53/0.58 tff(92,plain,
% 0.53/0.58 (u1_struct_0(B!1) = C!2),
% 0.53/0.58 inference(symmetry,[status(thm)],[91])).
% 0.53/0.58 tff(93,plain,
% 0.53/0.58 (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = k1_rmod_5(A!0, B!1, C!2)),
% 0.53/0.58 inference(monotonicity,[status(thm)],[92])).
% 0.53/0.58 tff(94,plain,
% 0.53/0.58 ((k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) <=> (k1_rmod_5(A!0, B!1, C!2) = B!1)),
% 0.53/0.58 inference(monotonicity,[status(thm)],[93, 89])).
% 0.53/0.58 tff(95,plain,
% 0.53/0.58 ((k1_rmod_5(A!0, B!1, C!2) = B!1) <=> (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.53/0.58 inference(symmetry,[status(thm)],[94])).
% 0.53/0.58 tff(96,plain,
% 0.53/0.58 ((~(k1_rmod_5(A!0, B!1, C!2) = B!1)) <=> (~(k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.53/0.58 inference(monotonicity,[status(thm)],[95])).
% 0.53/0.58 tff(97,plain,
% 0.53/0.58 (~(k1_rmod_5(A!0, B!1, C!2) = B!1)),
% 0.53/0.58 inference(or_elim,[status(thm)],[90])).
% 0.53/0.58 tff(98,plain,
% 0.53/0.58 (~(k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.53/0.58 tff(99,plain,
% 0.53/0.58 (^[A: $i] : refl((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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)))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(100,plain,
% 0.53/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[99])).
% 0.53/0.58 tff(101,plain,
% 0.53/0.58 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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)))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(102,plain,
% 0.53/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[101])).
% 0.53/0.58 tff(103,plain,
% 0.53/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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))))),
% 0.53/0.58 inference(transitivity,[status(thm)],[102, 100])).
% 0.53/0.58 tff(104,plain,
% 0.53/0.58 (^[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)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_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) & l3_vectsp_1(A))) <=> (~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_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) & l3_vectsp_1(A))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> ((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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))), 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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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)))))), (![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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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))))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(105,plain,
% 0.53/0.58 (![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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[104])).
% 0.53/0.58 tff(106,plain,
% 0.53/0.58 (![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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(107,plain,
% 0.53/0.58 (^[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)))), (((((((((~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)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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) & l1_vectsp_2(B, A)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))), 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)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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)) & l1_vectsp_2(B, A)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))))), (![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)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> ![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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(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)) => ![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)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(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)) => ![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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(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)) => ![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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(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))) | ![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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(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)) => ![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)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(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))) | ![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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(108,plain,
% 0.53/0.58 (![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)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[107])).
% 0.53/0.58 tff(109,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)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_rmod_2')).
% 0.53/0.58 tff(110,plain,
% 0.53/0.58 (![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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.53/0.59 tff(111,plain,
% 0.53/0.59 (![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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.53/0.59 tff(112,plain,(
% 0.53/0.59 ![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))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))),
% 0.53/0.59 inference(skolemize,[status(sab)],[111])).
% 0.53/0.59 tff(113,plain,
% 0.53/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.53/0.59 tff(114,plain,
% 0.53/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.53/0.59 tff(115,plain,
% 0.53/0.59 (v8_vectsp_1(A!0)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(116,plain,
% 0.53/0.59 (v7_vectsp_1(A!0)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(117,plain,
% 0.53/0.59 (v6_vectsp_1(A!0)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(118,plain,
% 0.53/0.59 (v4_group_1(A!0)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(119,plain,
% 0.53/0.59 (v6_rlvect_1(A!0)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(120,plain,
% 0.53/0.59 (v5_rlvect_1(A!0)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(121,plain,
% 0.53/0.59 (v4_rlvect_1(A!0)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(122,plain,
% 0.53/0.59 (v3_rlvect_1(A!0)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(123,plain,
% 0.53/0.59 (~v3_struct_0(A!0)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(124,plain,
% 0.53/0.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(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)) | ![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(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)) | ![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(125,plain,
% 0.53/0.59 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_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)) | (~v7_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)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) <=> (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)) | ![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(126,plain,
% 0.53/0.59 (^[B: $i] : rewrite((v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!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))) <=> (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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.53/0.59 inference(bind,[status(th)],[])).
% 0.53/0.59 tff(127,plain,
% 0.53/0.59 (![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!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))) <=> ![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))),
% 0.53/0.59 inference(quant_intro,[status(thm)],[126])).
% 0.53/0.59 tff(128,plain,
% 0.53/0.59 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_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)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!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)))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_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)) | (~v7_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)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.53/0.59 inference(monotonicity,[status(thm)],[127])).
% 0.53/0.59 tff(129,plain,
% 0.53/0.59 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_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)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!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)))) <=> (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)) | ![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.53/0.59 inference(transitivity,[status(thm)],[128, 125])).
% 0.53/0.59 tff(130,plain,
% 0.53/0.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_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)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!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))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(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)) | ![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))))),
% 0.53/0.59 inference(monotonicity,[status(thm)],[129])).
% 0.53/0.59 tff(131,plain,
% 0.53/0.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_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)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!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))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(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)) | ![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.53/0.59 inference(transitivity,[status(thm)],[130, 124])).
% 0.53/0.59 tff(132,plain,
% 0.53/0.59 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_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)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!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))))),
% 0.53/0.59 inference(quant_inst,[status(thm)],[])).
% 0.53/0.59 tff(133,plain,
% 0.53/0.59 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, 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(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)) | ![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.53/0.59 tff(134,plain,
% 0.53/0.59 (![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[133, 123, 122, 121, 120, 119, 118, 117, 116, 115, 34, 114])).
% 0.53/0.59 tff(135,plain,
% 0.53/0.59 (v5_vectsp_2(B!1, A!0)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(136,plain,
% 0.53/0.59 (v6_rlvect_1(B!1)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(137,plain,
% 0.53/0.59 (v5_rlvect_1(B!1)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(138,plain,
% 0.53/0.59 (v4_rlvect_1(B!1)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(139,plain,
% 0.53/0.59 (v3_rlvect_1(B!1)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(140,plain,
% 0.53/0.59 (~v3_struct_0(B!1)),
% 0.53/0.59 inference(and_elim,[status(thm)],[33])).
% 0.53/0.59 tff(141,plain,
% 0.53/0.59 (((~![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | (v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) <=> ((~![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(142,plain,
% 0.53/0.59 ((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)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))) <=> (v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(143,plain,
% 0.53/0.59 (((~![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | (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)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) <=> ((~![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | (v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))))),
% 0.53/0.59 inference(monotonicity,[status(thm)],[142])).
% 0.53/0.59 tff(144,plain,
% 0.53/0.59 (((~![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | (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)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) <=> ((~![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.53/0.59 inference(transitivity,[status(thm)],[143, 141])).
% 0.53/0.59 tff(145,plain,
% 0.53/0.59 ((~![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | (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)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.53/0.59 inference(quant_inst,[status(thm)],[])).
% 0.53/0.59 tff(146,plain,
% 0.53/0.59 ((~![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!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.53/0.59 tff(147,plain,
% 0.53/0.59 (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[146, 140, 139, 138, 137, 136, 135, 82, 134])).
% 0.53/0.59 tff(148,plain,
% 0.53/0.59 (g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)) = k2_rmod_2(A!0, B!1)),
% 0.53/0.59 inference(symmetry,[status(thm)],[147])).
% 0.53/0.59 tff(149,plain,
% 0.53/0.59 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1) <=> m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)),
% 0.53/0.59 inference(monotonicity,[status(thm)],[148])).
% 0.53/0.59 tff(150,plain,
% 0.53/0.59 (m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1) <=> m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)),
% 0.53/0.59 inference(symmetry,[status(thm)],[149])).
% 0.53/0.59 tff(151,plain,
% 0.53/0.59 (^[A: $i, B: $i] : refl((v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B))))))),
% 0.53/0.59 inference(bind,[status(th)],[])).
% 0.53/0.59 tff(152,plain,
% 0.53/0.59 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))),
% 0.53/0.59 inference(quant_intro,[status(thm)],[151])).
% 0.53/0.59 tff(153,plain,
% 0.53/0.59 (^[A: $i, B: $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)) <=> (~(v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_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) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_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) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)) <=> (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), 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))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> ((v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B))))))), rewrite(((v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), 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))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))))),
% 0.53/0.59 inference(bind,[status(th)],[])).
% 0.53/0.59 tff(154,plain,
% 0.53/0.59 (![A: $i, B: $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))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))),
% 0.53/0.59 inference(quant_intro,[status(thm)],[153])).
% 0.53/0.59 tff(155,plain,
% 0.53/0.59 (![A: $i, B: $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))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> ![A: $i, B: $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))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(156,plain,
% 0.53/0.59 (^[A: $i, B: $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(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)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), 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)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), 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)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), 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))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), 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)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), 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))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(157,plain,
% 0.53/0.60 (![A: $i, B: $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)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> ![A: $i, B: $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))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[156])).
% 0.53/0.60 tff(158,axiom,(![A: $i, B: $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)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_rmod_2')).
% 0.53/0.60 tff(159,plain,
% 0.53/0.60 (![A: $i, B: $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))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.53/0.60 tff(160,plain,
% 0.53/0.60 (![A: $i, B: $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))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.53/0.60 tff(161,plain,(
% 0.53/0.60 ![A: $i, B: $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))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))),
% 0.53/0.60 inference(skolemize,[status(sab)],[160])).
% 0.53/0.60 tff(162,plain,
% 0.53/0.60 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.53/0.60 tff(163,plain,
% 0.53/0.60 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[162, 152])).
% 0.53/0.60 tff(164,plain,
% 0.53/0.60 (((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_vectsp_2(B!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)) | (~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_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_vectsp_2(B!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)) | (~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_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(165,plain,
% 0.53/0.60 ((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_vectsp_2(B!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)) | (~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_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))))),
% 0.53/0.60 inference(quant_inst,[status(thm)],[])).
% 0.53/0.60 tff(166,plain,
% 0.53/0.60 ((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~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_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_vectsp_2(B!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)) | (~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_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1))))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.53/0.60 tff(167,plain,
% 0.53/0.60 (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[166, 123, 122, 121, 120, 119, 118, 117, 116, 115, 34, 140, 139, 138, 137, 136, 135, 82, 163])).
% 0.53/0.60 tff(168,plain,
% 0.53/0.60 (((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1))) | m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)),
% 0.53/0.60 inference(tautology,[status(thm)],[])).
% 0.53/0.60 tff(169,plain,
% 0.53/0.60 (m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.53/0.60 tff(170,plain,
% 0.53/0.60 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[169, 150])).
% 0.53/0.60 tff(171,plain,
% 0.53/0.60 (v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0) <=> v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)),
% 0.53/0.60 inference(monotonicity,[status(thm)],[148])).
% 0.53/0.60 tff(172,plain,
% 0.53/0.60 (v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0) <=> v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)),
% 0.53/0.60 inference(symmetry,[status(thm)],[171])).
% 0.53/0.60 tff(173,plain,
% 0.53/0.60 (((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1))) | v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)),
% 0.53/0.60 inference(tautology,[status(thm)],[])).
% 0.53/0.60 tff(174,plain,
% 0.53/0.60 (v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[173, 167])).
% 0.53/0.60 tff(175,plain,
% 0.53/0.60 (v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[174, 172])).
% 0.53/0.60 tff(176,plain,
% 0.53/0.60 (u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) = u1_struct_0(k2_rmod_2(A!0, B!1))),
% 0.53/0.60 inference(monotonicity,[status(thm)],[148])).
% 0.53/0.60 tff(177,plain,
% 0.53/0.60 (u1_struct_0(k2_rmod_2(A!0, B!1)) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.53/0.60 inference(symmetry,[status(thm)],[176])).
% 0.53/0.60 tff(178,plain,
% 0.53/0.60 (B!1 = k2_rmod_2(A!0, B!1)),
% 0.53/0.60 inference(transitivity,[status(thm)],[88, 148])).
% 0.53/0.60 tff(179,plain,
% 0.53/0.60 (u1_struct_0(B!1) = u1_struct_0(k2_rmod_2(A!0, B!1))),
% 0.53/0.60 inference(monotonicity,[status(thm)],[178])).
% 0.53/0.60 tff(180,plain,
% 0.53/0.60 (u1_struct_0(B!1) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.53/0.60 inference(transitivity,[status(thm)],[179, 177])).
% 0.53/0.60 tff(181,plain,
% 0.53/0.60 (^[A: $i] : refl((v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(182,plain,
% 0.53/0.60 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> ![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[181])).
% 0.53/0.60 tff(183,plain,
% 0.53/0.60 (^[A: $i] : rewrite((v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(184,plain,
% 0.53/0.60 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> ![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[183])).
% 0.53/0.60 tff(185,plain,
% 0.53/0.60 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> ![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.53/0.60 inference(transitivity,[status(thm)],[184, 182])).
% 0.53/0.60 tff(186,plain,
% 0.53/0.60 (^[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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A)) <=> (~(v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) <=> (~(~(v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A))))))), rewrite((~(~(v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A))))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))), (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, 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) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))) <=> ((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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))), 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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))) <=> (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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, 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) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))) <=> (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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))))), (![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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))) <=> ![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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))) <=> ((v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))))), rewrite(((v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(187,plain,
% 0.53/0.60 (![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))) <=> ![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[186])).
% 0.53/0.60 tff(188,plain,
% 0.53/0.60 (![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, 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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(189,plain,
% 0.53/0.60 (^[A: $i] : 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)) & v7_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)) & v7_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)) & v7_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) & v7_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)) & v7_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) & v7_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)) & v7_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) & v7_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) & v7_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) & v7_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)) & v7_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) & v7_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)) & v7_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) & v7_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) & v7_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) & v7_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)) & v7_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) & v7_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)) & v7_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) & v7_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) & v7_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) & v7_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)) & v7_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) & v7_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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & (~v10_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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & (~v10_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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A))) & v2_vectsp_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A))) & v2_vectsp_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : trans(monotonicity(rewrite(((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))) <=> ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))))), (((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))) <=> ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))))))), rewrite(((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))))) <=> ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))), (((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))) <=> ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))), (![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))) <=> ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, 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)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))))) <=> (((~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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))), 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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, 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) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, 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)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))))) <=> ((~((~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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))))), (![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] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))))) <=> ![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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(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] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(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] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(190,plain,
% 0.53/0.61 (![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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(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] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))))) <=> ![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[189])).
% 0.53/0.61 tff(191,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)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(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] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t13_rmod_5')).
% 0.53/0.61 tff(192,plain,
% 0.53/0.61 (![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.53/0.61 tff(193,plain,
% 0.53/0.61 (![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.53/0.61 tff(194,plain,(
% 0.53/0.61 ![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) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))),
% 0.53/0.61 inference(skolemize,[status(sab)],[193])).
% 0.53/0.61 tff(195,plain,
% 0.53/0.61 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.53/0.61 tff(196,plain,
% 0.53/0.61 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[195, 185])).
% 0.53/0.61 tff(197,plain,
% 0.53/0.61 (v2_vectsp_2(A!0)),
% 0.53/0.61 inference(and_elim,[status(thm)],[33])).
% 0.53/0.61 tff(198,plain,
% 0.53/0.61 (~v10_vectsp_1(A!0)),
% 0.53/0.61 inference(and_elim,[status(thm)],[33])).
% 0.53/0.61 tff(199,plain,
% 0.53/0.61 (v7_group_1(A!0)),
% 0.53/0.61 inference(and_elim,[status(thm)],[33])).
% 0.53/0.61 tff(200,plain,
% 0.53/0.61 (((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | (v10_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))) <=> ((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | v10_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(201,plain,
% 0.53/0.61 ((v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_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)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(A!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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) <=> (v10_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(202,plain,
% 0.53/0.61 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))), (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))), ((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] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))) <=> (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] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))), 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] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, 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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))), ((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] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, 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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(203,plain,
% 0.53/0.61 (![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] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))) <=> ![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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[202])).
% 0.53/0.61 tff(204,plain,
% 0.53/0.61 ((v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_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)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) <=> (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_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)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(A!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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.53/0.61 inference(monotonicity,[status(thm)],[203])).
% 0.53/0.61 tff(205,plain,
% 0.53/0.61 ((v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_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)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) <=> (v10_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.53/0.61 inference(transitivity,[status(thm)],[204, 201])).
% 0.53/0.61 tff(206,plain,
% 0.53/0.61 (((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_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)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))) <=> ((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | (v10_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))))),
% 0.53/0.61 inference(monotonicity,[status(thm)],[205])).
% 0.53/0.61 tff(207,plain,
% 0.53/0.61 (((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_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)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))) <=> ((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | v10_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.53/0.62 inference(transitivity,[status(thm)],[206, 200])).
% 0.53/0.62 tff(208,plain,
% 0.53/0.62 ((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_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)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.53/0.62 inference(quant_inst,[status(thm)],[])).
% 0.53/0.62 tff(209,plain,
% 0.53/0.62 ((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(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] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | v10_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.53/0.62 tff(210,plain,
% 0.53/0.62 (![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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[209, 123, 122, 121, 120, 119, 118, 199, 117, 116, 115, 198, 197, 34, 196])).
% 0.53/0.62 tff(211,plain,
% 0.53/0.62 (((~![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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | (v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))) <=> ((~![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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(212,plain,
% 0.53/0.62 ((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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) <=> (v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(213,plain,
% 0.53/0.62 (^[C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(214,plain,
% 0.53/0.62 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1)))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[213])).
% 0.53/0.62 tff(215,plain,
% 0.53/0.62 ((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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1))))) <=> (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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[214])).
% 0.53/0.62 tff(216,plain,
% 0.53/0.62 ((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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1))))) <=> (v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.53/0.62 inference(transitivity,[status(thm)],[215, 212])).
% 0.53/0.62 tff(217,plain,
% 0.53/0.62 (((~![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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | (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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1)))))) <=> ((~![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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | (v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[216])).
% 0.53/0.62 tff(218,plain,
% 0.53/0.62 (((~![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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | (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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1)))))) <=> ((~![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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.53/0.62 inference(transitivity,[status(thm)],[217, 211])).
% 0.53/0.62 tff(219,plain,
% 0.53/0.62 ((~![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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | (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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1)))))),
% 0.53/0.62 inference(quant_inst,[status(thm)],[])).
% 0.53/0.62 tff(220,plain,
% 0.53/0.62 ((~![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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.53/0.62 tff(221,plain,
% 0.53/0.62 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[220, 140, 139, 138, 137, 136, 135, 82, 210])).
% 0.53/0.62 tff(222,plain,
% 0.53/0.62 (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[92])).
% 0.53/0.62 tff(223,plain,
% 0.53/0.62 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.53/0.62 inference(symmetry,[status(thm)],[222])).
% 0.53/0.62 tff(224,plain,
% 0.53/0.62 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.53/0.62 inference(or_elim,[status(thm)],[90])).
% 0.53/0.62 tff(225,plain,
% 0.53/0.62 (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.53/0.62 tff(226,plain,
% 0.53/0.62 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(227,plain,
% 0.53/0.62 (((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(228,plain,
% 0.53/0.62 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[227])).
% 0.53/0.62 tff(229,plain,
% 0.53/0.62 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))),
% 0.53/0.62 inference(transitivity,[status(thm)],[228, 226])).
% 0.53/0.62 tff(230,plain,
% 0.53/0.62 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(231,plain,
% 0.53/0.63 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.53/0.63 tff(232,plain,
% 0.53/0.63 (![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[231, 225, 221])).
% 0.53/0.63 tff(233,plain,
% 0.53/0.63 (~(k1_rlvect_1(A!0) = k2_group_1(A!0))),
% 0.53/0.63 inference(or_elim,[status(thm)],[90])).
% 0.53/0.63 tff(234,plain,
% 0.53/0.63 (((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)) | (~v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) <=> ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)) | (~v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(235,plain,
% 0.53/0.63 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)) | (~v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(236,plain,
% 0.53/0.63 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)) | (~v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.53/0.63 tff(237,plain,
% 0.53/0.63 ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)) | (~v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[236, 233, 232, 180])).
% 0.53/0.63 tff(238,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[237, 175, 170, 98])).
% 0.53/0.63 % SZS output end Proof
%------------------------------------------------------------------------------