TSTP Solution File: ALG222+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG222+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 16:09:20 EDT 2022
% Result : Theorem 0.76s 0.72s
% Output : Proof 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG222+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 13:57:45 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.76/0.72 % SZS status Theorem
% 0.76/0.72 % SZS output start Proof
% 0.76/0.72 tff(m1_rmod_2_type, type, (
% 0.76/0.72 m1_rmod_2: ( $i * $i * $i ) > $o)).
% 0.76/0.72 tff(k2_rmod_3_type, type, (
% 0.76/0.72 k2_rmod_3: ( $i * $i * $i * $i ) > $i)).
% 0.76/0.72 tff(g1_vectsp_2_type, type, (
% 0.76/0.72 g1_vectsp_2: ( $i * $i * $i * $i * $i ) > $i)).
% 0.76/0.72 tff(u1_vectsp_2_type, type, (
% 0.76/0.72 u1_vectsp_2: ( $i * $i ) > $i)).
% 0.76/0.72 tff(k1_rmod_5_type, type, (
% 0.76/0.72 k1_rmod_5: ( $i * $i * $i ) > $i)).
% 0.76/0.72 tff(tptp_fun_D_3_type, type, (
% 0.76/0.72 tptp_fun_D_3: $i)).
% 0.76/0.72 tff(tptp_fun_B_1_type, type, (
% 0.76/0.72 tptp_fun_B_1: $i)).
% 0.76/0.72 tff(tptp_fun_A_0_type, type, (
% 0.76/0.72 tptp_fun_A_0: $i)).
% 0.76/0.72 tff(u2_struct_0_type, type, (
% 0.76/0.72 u2_struct_0: $i > $i)).
% 0.76/0.72 tff(u1_rlvect_1_type, type, (
% 0.76/0.72 u1_rlvect_1: $i > $i)).
% 0.76/0.72 tff(u1_struct_0_type, type, (
% 0.76/0.72 u1_struct_0: $i > $i)).
% 0.76/0.72 tff(tptp_fun_C_2_type, type, (
% 0.76/0.72 tptp_fun_C_2: $i)).
% 0.76/0.72 tff(k5_subset_1_type, type, (
% 0.76/0.72 k5_subset_1: ( $i * $i * $i ) > $i)).
% 0.76/0.72 tff(l1_vectsp_2_type, type, (
% 0.76/0.72 l1_vectsp_2: ( $i * $i ) > $o)).
% 0.76/0.72 tff(v5_vectsp_2_type, type, (
% 0.76/0.72 v5_vectsp_2: ( $i * $i ) > $o)).
% 0.76/0.72 tff(v6_rlvect_1_type, type, (
% 0.76/0.72 v6_rlvect_1: $i > $o)).
% 0.76/0.72 tff(v5_rlvect_1_type, type, (
% 0.76/0.72 v5_rlvect_1: $i > $o)).
% 0.76/0.72 tff(v4_rlvect_1_type, type, (
% 0.76/0.72 v4_rlvect_1: $i > $o)).
% 0.76/0.72 tff(v3_rlvect_1_type, type, (
% 0.76/0.72 v3_rlvect_1: $i > $o)).
% 0.76/0.72 tff(v3_struct_0_type, type, (
% 0.76/0.72 v3_struct_0: $i > $o)).
% 0.76/0.72 tff(v3_vectsp_2_type, type, (
% 0.76/0.72 v3_vectsp_2: ( $i * $i ) > $o)).
% 0.76/0.72 tff(l3_vectsp_1_type, type, (
% 0.76/0.72 l3_vectsp_1: $i > $o)).
% 0.76/0.72 tff(v2_vectsp_2_type, type, (
% 0.76/0.72 v2_vectsp_2: $i > $o)).
% 0.76/0.72 tff(v8_vectsp_1_type, type, (
% 0.76/0.72 v8_vectsp_1: $i > $o)).
% 0.76/0.72 tff(v7_vectsp_1_type, type, (
% 0.76/0.72 v7_vectsp_1: $i > $o)).
% 0.76/0.72 tff(v6_vectsp_1_type, type, (
% 0.76/0.72 v6_vectsp_1: $i > $o)).
% 0.76/0.72 tff(v7_group_1_type, type, (
% 0.76/0.72 v7_group_1: $i > $o)).
% 0.76/0.72 tff(v4_group_1_type, type, (
% 0.76/0.72 v4_group_1: $i > $o)).
% 0.76/0.72 tff(m1_subset_1_type, type, (
% 0.76/0.72 m1_subset_1: ( $i * $i ) > $o)).
% 0.76/0.72 tff(k1_zfmisc_1_type, type, (
% 0.76/0.72 k1_zfmisc_1: $i > $i)).
% 0.76/0.72 tff(v10_vectsp_1_type, type, (
% 0.76/0.72 v10_vectsp_1: $i > $o)).
% 0.76/0.72 tff(l1_struct_0_type, type, (
% 0.76/0.72 l1_struct_0: $i > $o)).
% 0.76/0.72 tff(l2_struct_0_type, type, (
% 0.76/0.72 l2_struct_0: $i > $o)).
% 0.76/0.72 tff(l1_rlvect_1_type, type, (
% 0.76/0.72 l1_rlvect_1: $i > $o)).
% 0.76/0.72 tff(l2_vectsp_1_type, type, (
% 0.76/0.72 l2_vectsp_1: $i > $o)).
% 0.76/0.72 tff(k3_xboole_0_type, type, (
% 0.76/0.72 k3_xboole_0: ( $i * $i ) > $i)).
% 0.76/0.72 tff(r1_tarski_type, type, (
% 0.76/0.72 r1_tarski: ( $i * $i ) > $o)).
% 0.76/0.72 tff(1,plain,
% 0.76/0.72 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B))))) <=> (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B))))))),
% 0.76/0.72 inference(bind,[status(th)],[])).
% 0.76/0.72 tff(2,plain,
% 0.76/0.72 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))),
% 0.76/0.72 inference(quant_intro,[status(thm)],[1])).
% 0.76/0.72 tff(3,plain,
% 0.76/0.72 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) <=> (~(v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) <=> (~(~(v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))))))), rewrite((~(~(v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))))) <=> (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) <=> (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))))), rewrite((v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B)) <=> (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), 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) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B))) <=> ((v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B))))))), rewrite(((v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A))) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B))))) <=> (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), 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) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B))) <=> (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))))),
% 0.76/0.72 inference(bind,[status(th)],[])).
% 0.76/0.72 tff(4,plain,
% 0.76/0.72 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))),
% 0.76/0.72 inference(quant_intro,[status(thm)],[3])).
% 0.76/0.72 tff(5,plain,
% 0.76/0.72 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(6,plain,
% 0.76/0.72 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(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)))), (((((((((((((((~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(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)) & (~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) & 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(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) & (~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)) & 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(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) & (~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)) & 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(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) & 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(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) & 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(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) & 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(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)) & 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(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) & 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(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)) & 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(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) & 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(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) & 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(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) & 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(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)) & 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(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) & 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(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)) & 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(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) & 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(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) & 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(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) & 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(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)) & 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(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) & 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(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)) & 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(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) & 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(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) & 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(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) & 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(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)) & 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(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) & 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(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)) & 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(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) & 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(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) & 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(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) & 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(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)) & 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(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) & 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(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)) & 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(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) & 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(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) & 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(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) & 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(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)) & 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(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) & 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(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)) & 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(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))), ((((((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & 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(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))))), (((((((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & 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(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), 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) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), 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) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), 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) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), 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)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), 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) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(7,plain,
% 0.76/0.73 (![A: $i, B: $i, C: $i] : ((((((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & 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(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B)))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[6])).
% 0.76/0.73 tff(8,axiom,(![A: $i, B: $i, C: $i] : ((((((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & 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(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_rmod_5')).
% 0.76/0.73 tff(9,plain,
% 0.76/0.73 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.76/0.73 tff(10,plain,
% 0.76/0.73 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.76/0.73 tff(11,plain,(
% 0.76/0.73 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))) | (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B)))),
% 0.76/0.73 inference(skolemize,[status(sab)],[10])).
% 0.76/0.73 tff(12,plain,
% 0.76/0.73 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.76/0.73 tff(13,plain,
% 0.76/0.73 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.76/0.73 tff(14,plain,
% 0.76/0.73 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & 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) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))) <=> ((~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) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(15,plain,
% 0.76/0.73 ((((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))) <=> ((~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) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(16,plain,
% 0.76/0.73 (((~(~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))))) <=> (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(17,plain,
% 0.76/0.73 ((~(~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) <=> ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(18,plain,
% 0.76/0.73 (((~(~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & ((~(~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))) <=> (((~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)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))))))),
% 0.76/0.73 inference(monotonicity,[status(thm)],[17, 16])).
% 0.76/0.73 tff(19,plain,
% 0.76/0.73 (((~(~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & ((~(~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))) <=> ((~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) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))),
% 0.76/0.73 inference(transitivity,[status(thm)],[18, 15])).
% 0.76/0.73 tff(20,plain,
% 0.76/0.73 ((~(~((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & 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))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(21,plain,
% 0.76/0.73 (((~(~((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & 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) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & ((~(~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))))))) <=> (((~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) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))))))),
% 0.76/0.73 inference(monotonicity,[status(thm)],[20, 19])).
% 0.76/0.73 tff(22,plain,
% 0.76/0.73 (((~(~((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & 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) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & ((~(~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))))))) <=> ((~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) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))),
% 0.76/0.73 inference(transitivity,[status(thm)],[21, 14])).
% 0.76/0.73 tff(23,plain,
% 0.76/0.73 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D))))))))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(24,plain,
% 0.76/0.73 ((~![A: $i] : ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & 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] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D))))))))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 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)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t18_rmod_5')).
% 0.76/0.73 tff(26,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.76/0.73 tff(27,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.76/0.73 tff(28,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.76/0.73 tff(29,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.76/0.73 tff(30,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.76/0.73 tff(31,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.76/0.73 tff(32,plain,
% 0.76/0.73 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[31, 23])).
% 0.76/0.73 tff(33,plain,
% 0.76/0.73 ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & 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) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.76/0.73 tff(34,plain,
% 0.76/0.73 (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))),
% 0.76/0.73 inference(and_elim,[status(thm)],[33])).
% 0.76/0.73 tff(35,plain,
% 0.76/0.73 (m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.76/0.73 inference(or_elim,[status(thm)],[34])).
% 0.76/0.73 tff(36,plain,
% 0.76/0.73 (l1_vectsp_2(B!1, A!0)),
% 0.76/0.73 inference(and_elim,[status(thm)],[33])).
% 0.76/0.73 tff(37,plain,
% 0.76/0.73 (v5_vectsp_2(B!1, A!0)),
% 0.76/0.73 inference(and_elim,[status(thm)],[33])).
% 0.76/0.73 tff(38,plain,
% 0.76/0.73 (v6_rlvect_1(B!1)),
% 0.76/0.73 inference(and_elim,[status(thm)],[33])).
% 0.76/0.73 tff(39,plain,
% 0.76/0.73 (v5_rlvect_1(B!1)),
% 0.76/0.73 inference(and_elim,[status(thm)],[33])).
% 0.76/0.73 tff(40,plain,
% 0.76/0.73 (v4_rlvect_1(B!1)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(41,plain,
% 0.76/0.74 (v3_rlvect_1(B!1)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(42,plain,
% 0.76/0.74 (~v3_struct_0(B!1)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(43,plain,
% 0.76/0.74 (l3_vectsp_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(44,plain,
% 0.76/0.74 (v2_vectsp_2(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(45,plain,
% 0.76/0.74 (~v10_vectsp_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(46,plain,
% 0.76/0.74 (v8_vectsp_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(47,plain,
% 0.76/0.74 (v7_vectsp_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(48,plain,
% 0.76/0.74 (v6_vectsp_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(49,plain,
% 0.76/0.74 (v7_group_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(50,plain,
% 0.76/0.74 (v4_group_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(51,plain,
% 0.76/0.74 (v6_rlvect_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(52,plain,
% 0.76/0.74 (v5_rlvect_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(53,plain,
% 0.76/0.74 (v4_rlvect_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(54,plain,
% 0.76/0.74 (v3_rlvect_1(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(55,plain,
% 0.76/0.74 (~v3_struct_0(A!0)),
% 0.76/0.74 inference(and_elim,[status(thm)],[33])).
% 0.76/0.74 tff(56,plain,
% 0.76/0.74 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)))))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(57,plain,
% 0.76/0.74 ((v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1))))) <=> (v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)))))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(58,plain,
% 0.76/0.74 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1))))))),
% 0.76/0.74 inference(monotonicity,[status(thm)],[57])).
% 0.76/0.74 tff(59,plain,
% 0.76/0.74 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)))))),
% 0.76/0.74 inference(transitivity,[status(thm)],[58, 56])).
% 0.76/0.74 tff(60,plain,
% 0.76/0.74 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)))))),
% 0.76/0.74 inference(quant_inst,[status(thm)],[])).
% 0.76/0.74 tff(61,plain,
% 0.76/0.74 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1))))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.76/0.74 tff(62,plain,
% 0.76/0.74 (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)))),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[61, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 13])).
% 0.76/0.74 tff(63,plain,
% 0.76/0.74 (((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1))) | m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)),
% 0.76/0.74 inference(tautology,[status(thm)],[])).
% 0.76/0.74 tff(64,plain,
% 0.76/0.74 (m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.76/0.74 tff(65,plain,
% 0.76/0.74 (^[A: $i, B: $i] : refl((v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(66,plain,
% 0.76/0.74 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[65])).
% 0.76/0.74 tff(67,plain,
% 0.76/0.74 (^[A: $i, B: $i] : rewrite((v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(68,plain,
% 0.76/0.74 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[67])).
% 0.76/0.74 tff(69,plain,
% 0.76/0.74 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))),
% 0.76/0.74 inference(transitivity,[status(thm)],[68, 66])).
% 0.76/0.74 tff(70,plain,
% 0.76/0.74 (^[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(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & 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(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))), rewrite((~(~(v3_struct_0(B) | v3_struct_0(A) | (~l1_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_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_struct_0(A) | (~l1_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_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(B) | v3_struct_0(A) | (~l1_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_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_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))) <=> ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))), (![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))) <=> ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, 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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))) <=> ((v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))))), rewrite(((v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, 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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(71,plain,
% 0.76/0.74 (![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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[70])).
% 0.76/0.74 tff(72,plain,
% 0.76/0.74 (![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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))) <=> ![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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(73,plain,
% 0.76/0.74 (^[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)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) <=> ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C))), (((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) <=> (((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C)) & v5_rlvect_1(C)))), rewrite((((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C)) & v5_rlvect_1(C)) <=> ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C))), (((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) <=> ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C)))), ((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) <=> (((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C)) & v6_rlvect_1(C)))), rewrite((((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C)) & v6_rlvect_1(C)) <=> ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C))), ((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) <=> ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C)))), (((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) <=> (((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)))), rewrite((((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) <=> ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A))), (((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) <=> ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A)))), ((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) <=> (((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)))), rewrite((((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) <=> ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))), ((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) <=> ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))), ((m1_rmod_2(C, A, B) => (((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A))) <=> (m1_rmod_2(C, A, B) => ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))), rewrite((m1_rmod_2(C, A, B) => ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))) <=> ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))), ((m1_rmod_2(C, A, B) => (((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A))) <=> ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))))), (![C: $i] : (m1_rmod_2(C, A, B) => (((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A))) <=> ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, 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)) => ![C: $i] : (m1_rmod_2(C, A, B) => (((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, 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)) => ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, 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)) => ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, 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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, 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)) => ![C: $i] : (m1_rmod_2(C, A, B) => (((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, 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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(74,plain,
% 0.76/0.75 (![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)) => ![C: $i] : (m1_rmod_2(C, A, B) => (((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)))) <=> ![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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[73])).
% 0.76/0.75 tff(75,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)) => ![C: $i] : (m1_rmod_2(C, A, B) => (((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_rmod_2')).
% 0.76/0.75 tff(76,plain,
% 0.76/0.75 (![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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.76/0.75 tff(77,plain,
% 0.76/0.75 (![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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.76/0.75 tff(78,plain,(
% 0.76/0.75 ![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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))),
% 0.76/0.75 inference(skolemize,[status(sab)],[77])).
% 0.76/0.75 tff(79,plain,
% 0.76/0.75 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.76/0.75 tff(80,plain,
% 0.76/0.75 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[79, 69])).
% 0.76/0.75 tff(81,plain,
% 0.76/0.75 (((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_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_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_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_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_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_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0))))))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(82,plain,
% 0.76/0.75 ((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_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_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_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0))))))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(83,plain,
% 0.76/0.75 ((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_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_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A))))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_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_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_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.76/0.75 tff(84,plain,
% 0.76/0.75 (![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[83, 55, 54, 53, 52, 51, 50, 48, 47, 46, 43, 42, 41, 40, 39, 38, 37, 36, 80])).
% 0.76/0.75 tff(85,plain,
% 0.76/0.75 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(86,plain,
% 0.76/0.75 (((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))))) <=> ((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(87,plain,
% 0.76/0.75 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))))))),
% 0.76/0.75 inference(monotonicity,[status(thm)],[86])).
% 0.76/0.75 tff(88,plain,
% 0.76/0.75 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))),
% 0.76/0.75 inference(transitivity,[status(thm)],[87, 85])).
% 0.76/0.75 tff(89,plain,
% 0.76/0.75 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(90,plain,
% 0.76/0.75 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.76/0.75 tff(91,plain,
% 0.76/0.75 (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[90, 84, 64])).
% 0.76/0.75 tff(92,plain,
% 0.76/0.75 (((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))) | l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.76/0.75 inference(tautology,[status(thm)],[])).
% 0.76/0.75 tff(93,plain,
% 0.76/0.75 (l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.76/0.75 tff(94,plain,
% 0.76/0.75 (^[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))))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(95,plain,
% 0.76/0.75 (![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)))))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[94])).
% 0.76/0.75 tff(96,plain,
% 0.76/0.75 (^[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))))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(97,plain,
% 0.76/0.75 (![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)))))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[96])).
% 0.76/0.75 tff(98,plain,
% 0.76/0.75 (![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)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(99,plain,
% 0.76/0.75 (^[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))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(100,plain,
% 0.76/0.75 (![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)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[99])).
% 0.76/0.75 tff(101,axiom,(![A: $i] : (l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_vectsp_1')).
% 0.76/0.75 tff(102,plain,
% 0.76/0.75 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.76/0.75 tff(103,plain,
% 0.76/0.75 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.76/0.75 tff(104,plain,(
% 0.76/0.75 ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.76/0.75 inference(skolemize,[status(sab)],[103])).
% 0.76/0.75 tff(105,plain,
% 0.76/0.75 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.76/0.75 tff(106,plain,
% 0.76/0.75 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[105, 95])).
% 0.76/0.75 tff(107,plain,
% 0.76/0.75 (((~![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)))))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(108,plain,
% 0.76/0.75 ((~![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)))))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(109,plain,
% 0.76/0.75 ((~![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))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.76/0.75 tff(110,plain,
% 0.76/0.75 (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[109, 43, 106])).
% 0.76/0.75 tff(111,plain,
% 0.76/0.75 (((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0))) | l1_rlvect_1(A!0)),
% 0.76/0.75 inference(tautology,[status(thm)],[])).
% 0.76/0.75 tff(112,plain,
% 0.76/0.75 (l1_rlvect_1(A!0)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.76/0.75 tff(113,plain,
% 0.76/0.75 (^[A: $i] : refl((l2_struct_0(A) | (~l1_rlvect_1(A))) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(114,plain,
% 0.76/0.75 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[113])).
% 0.76/0.75 tff(115,plain,
% 0.76/0.75 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(116,plain,
% 0.76/0.75 (^[A: $i] : rewrite((l1_rlvect_1(A) => l2_struct_0(A)) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(117,plain,
% 0.76/0.75 (![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A)) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[116])).
% 0.76/0.75 tff(118,axiom,(![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_rlvect_1')).
% 0.76/0.75 tff(119,plain,
% 0.76/0.75 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.76/0.75 tff(120,plain,
% 0.76/0.75 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.76/0.75 tff(121,plain,(
% 0.76/0.75 ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.76/0.75 inference(skolemize,[status(sab)],[120])).
% 0.76/0.75 tff(122,plain,
% 0.76/0.75 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.76/0.75 tff(123,plain,
% 0.76/0.75 (((~![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)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(124,plain,
% 0.76/0.75 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(125,plain,
% 0.76/0.75 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(A!0) | (~l1_rlvect_1(A!0))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.76/0.75 tff(126,plain,
% 0.76/0.75 (l2_struct_0(A!0)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[125, 122, 112])).
% 0.76/0.75 tff(127,plain,
% 0.76/0.75 (^[A: $i] : refl((l1_struct_0(A) | (~l2_struct_0(A))) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(128,plain,
% 0.76/0.75 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[127])).
% 0.76/0.75 tff(129,plain,
% 0.76/0.75 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(130,plain,
% 0.76/0.75 (^[A: $i] : rewrite((l2_struct_0(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(131,plain,
% 0.76/0.75 (![A: $i] : (l2_struct_0(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[130])).
% 0.76/0.75 tff(132,axiom,(![A: $i] : (l2_struct_0(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l2_struct_0')).
% 0.76/0.75 tff(133,plain,
% 0.76/0.75 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.76/0.75 tff(134,plain,
% 0.76/0.75 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.76/0.75 tff(135,plain,(
% 0.76/0.75 ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.76/0.75 inference(skolemize,[status(sab)],[134])).
% 0.76/0.75 tff(136,plain,
% 0.76/0.75 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.76/0.75 tff(137,plain,
% 0.76/0.75 (((~![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)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(138,plain,
% 0.76/0.75 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | (l1_struct_0(A!0) | (~l2_struct_0(A!0)))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(139,plain,
% 0.76/0.75 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | l1_struct_0(A!0) | (~l2_struct_0(A!0))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.76/0.75 tff(140,plain,
% 0.76/0.75 (l1_struct_0(A!0)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[139, 136, 126])).
% 0.76/0.75 tff(141,plain,
% 0.76/0.75 (((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1))) | v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.76/0.75 inference(tautology,[status(thm)],[])).
% 0.76/0.75 tff(142,plain,
% 0.76/0.75 (v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[141, 62])).
% 0.76/0.75 tff(143,plain,
% 0.76/0.75 (^[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))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(144,plain,
% 0.76/0.75 (![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)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[143])).
% 0.76/0.75 tff(145,plain,
% 0.76/0.75 (^[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)))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(146,plain,
% 0.76/0.75 (![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)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[145])).
% 0.76/0.75 tff(147,plain,
% 0.76/0.75 (![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))))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(148,plain,
% 0.76/0.75 (^[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))))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(149,plain,
% 0.76/0.75 (![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))))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[148])).
% 0.76/0.75 tff(150,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/sandbox/benchmark/theBenchmark.p','abstractness_v3_vectsp_2')).
% 0.76/0.75 tff(151,plain,
% 0.76/0.75 (![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))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.76/0.75 tff(152,plain,
% 0.76/0.75 (![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))))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.76/0.75 tff(153,plain,(
% 0.76/0.75 ![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))))),
% 0.76/0.75 inference(skolemize,[status(sab)],[152])).
% 0.76/0.75 tff(154,plain,
% 0.76/0.75 (![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)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.76/0.75 tff(155,plain,
% 0.76/0.75 (![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)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[154, 144])).
% 0.76/0.75 tff(156,plain,
% 0.76/0.75 (((~![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)))) | ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), 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)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(157,plain,
% 0.76/0.76 (((k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_struct_0(A!0))) <=> ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(158,plain,
% 0.76/0.76 (((~![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)))) | ((k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), 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)))) | ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))))),
% 0.76/0.76 inference(monotonicity,[status(thm)],[157])).
% 0.76/0.76 tff(159,plain,
% 0.76/0.76 (((~![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)))) | ((k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), 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)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))),
% 0.76/0.76 inference(transitivity,[status(thm)],[158, 156])).
% 0.76/0.76 tff(160,plain,
% 0.76/0.76 ((~![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)))) | ((k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_struct_0(A!0)))),
% 0.76/0.76 inference(quant_inst,[status(thm)],[])).
% 0.76/0.76 tff(161,plain,
% 0.76/0.76 ((~![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)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.76/0.76 tff(162,plain,
% 0.76/0.76 ((~l1_struct_0(A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[161, 155, 142])).
% 0.76/0.76 tff(163,plain,
% 0.76/0.76 (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[162, 140, 93])).
% 0.76/0.76 tff(164,plain,
% 0.76/0.76 (g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))) = k1_rmod_5(A!0, B!1, D!3)),
% 0.76/0.76 inference(symmetry,[status(thm)],[163])).
% 0.76/0.76 tff(165,plain,
% 0.76/0.76 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.76/0.76 inference(and_elim,[status(thm)],[33])).
% 0.76/0.76 tff(166,plain,
% 0.76/0.76 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(167,plain,
% 0.76/0.76 ((v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1))))) <=> (v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(168,plain,
% 0.76/0.76 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1))))))),
% 0.76/0.76 inference(monotonicity,[status(thm)],[167])).
% 0.76/0.76 tff(169,plain,
% 0.76/0.76 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))),
% 0.76/0.76 inference(transitivity,[status(thm)],[168, 166])).
% 0.76/0.76 tff(170,plain,
% 0.76/0.76 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))),
% 0.76/0.76 inference(quant_inst,[status(thm)],[])).
% 0.76/0.76 tff(171,plain,
% 0.76/0.76 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1))))),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.76/0.77 tff(172,plain,
% 0.76/0.77 (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[171, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 165, 13])).
% 0.76/0.77 tff(173,plain,
% 0.76/0.77 (((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)),
% 0.76/0.77 inference(tautology,[status(thm)],[])).
% 0.76/0.77 tff(174,plain,
% 0.76/0.77 (m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.76/0.77 tff(175,plain,
% 0.76/0.77 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(176,plain,
% 0.76/0.77 (((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))))) <=> ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(177,plain,
% 0.76/0.77 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))))))),
% 0.82/0.77 inference(monotonicity,[status(thm)],[176])).
% 0.82/0.77 tff(178,plain,
% 0.82/0.77 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))),
% 0.82/0.77 inference(transitivity,[status(thm)],[177, 175])).
% 0.82/0.77 tff(179,plain,
% 0.82/0.77 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))),
% 0.82/0.77 inference(quant_inst,[status(thm)],[])).
% 0.82/0.77 tff(180,plain,
% 0.82/0.77 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.82/0.77 tff(181,plain,
% 0.82/0.77 (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[180, 84, 174])).
% 0.82/0.77 tff(182,plain,
% 0.82/0.77 (((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))) | l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)),
% 0.82/0.77 inference(tautology,[status(thm)],[])).
% 0.82/0.77 tff(183,plain,
% 0.82/0.77 (l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.82/0.77 tff(184,plain,
% 0.82/0.77 (((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1))) | v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)),
% 0.82/0.77 inference(tautology,[status(thm)],[])).
% 0.82/0.77 tff(185,plain,
% 0.82/0.77 (v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[184, 172])).
% 0.82/0.77 tff(186,plain,
% 0.82/0.77 (((~![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)))) | ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), 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)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(187,plain,
% 0.82/0.77 (((k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_struct_0(A!0))) <=> ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(188,plain,
% 0.82/0.77 (((~![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)))) | ((k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), 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)))) | ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))))),
% 0.82/0.77 inference(monotonicity,[status(thm)],[187])).
% 0.82/0.77 tff(189,plain,
% 0.82/0.77 (((~![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)))) | ((k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), 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)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))),
% 0.82/0.77 inference(transitivity,[status(thm)],[188, 186])).
% 0.82/0.77 tff(190,plain,
% 0.82/0.77 ((~![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)))) | ((k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_struct_0(A!0)))),
% 0.82/0.77 inference(quant_inst,[status(thm)],[])).
% 0.82/0.77 tff(191,plain,
% 0.82/0.77 ((~![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)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.82/0.77 tff(192,plain,
% 0.82/0.77 ((~l1_struct_0(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[191, 155, 185])).
% 0.82/0.77 tff(193,plain,
% 0.82/0.77 (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[192, 140, 183])).
% 0.82/0.77 tff(194,plain,
% 0.82/0.77 (g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))) = k1_rmod_5(A!0, B!1, C!2)),
% 0.82/0.77 inference(symmetry,[status(thm)],[193])).
% 0.82/0.77 tff(195,plain,
% 0.82/0.77 (k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) = k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))),
% 0.82/0.77 inference(monotonicity,[status(thm)],[194, 164])).
% 0.82/0.77 tff(196,plain,
% 0.82/0.77 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))),
% 0.82/0.77 inference(monotonicity,[status(thm)],[195])).
% 0.82/0.77 tff(197,plain,
% 0.82/0.77 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))),
% 0.82/0.77 inference(symmetry,[status(thm)],[196])).
% 0.82/0.77 tff(198,plain,
% 0.82/0.77 ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))) <=> (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))),
% 0.82/0.77 inference(monotonicity,[status(thm)],[197])).
% 0.82/0.77 tff(199,plain,
% 0.82/0.77 (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))),
% 0.82/0.77 inference(or_elim,[status(thm)],[34])).
% 0.82/0.77 tff(200,plain,
% 0.82/0.77 (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.82/0.77 tff(201,plain,
% 0.82/0.77 (^[A: $i, B: $i, C: $i] : refl(((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.82/0.77 inference(bind,[status(th)],[])).
% 0.82/0.77 tff(202,plain,
% 0.82/0.77 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.82/0.77 inference(quant_intro,[status(thm)],[201])).
% 0.82/0.77 tff(203,plain,
% 0.82/0.77 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.82/0.77 inference(bind,[status(th)],[])).
% 0.82/0.77 tff(204,plain,
% 0.82/0.77 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.82/0.77 inference(quant_intro,[status(thm)],[203])).
% 0.82/0.77 tff(205,plain,
% 0.82/0.77 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(206,plain,
% 0.82/0.77 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))))),
% 0.82/0.78 inference(bind,[status(th)],[])).
% 0.82/0.78 tff(207,plain,
% 0.82/0.78 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 0.82/0.78 inference(quant_intro,[status(thm)],[206])).
% 0.82/0.78 tff(208,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k5_subset_1')).
% 0.82/0.78 tff(209,plain,
% 0.82/0.78 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.82/0.78 tff(210,plain,
% 0.82/0.78 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.82/0.78 tff(211,plain,(
% 0.82/0.78 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 0.82/0.78 inference(skolemize,[status(sab)],[210])).
% 0.82/0.78 tff(212,plain,
% 0.82/0.78 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[211, 204])).
% 0.82/0.78 tff(213,plain,
% 0.82/0.78 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[212, 202])).
% 0.82/0.78 tff(214,plain,
% 0.82/0.78 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)))),
% 0.82/0.78 inference(rewrite,[status(thm)],[])).
% 0.82/0.78 tff(215,plain,
% 0.82/0.78 (((k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)))),
% 0.82/0.78 inference(rewrite,[status(thm)],[])).
% 0.82/0.78 tff(216,plain,
% 0.82/0.78 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3))))),
% 0.82/0.78 inference(monotonicity,[status(thm)],[215])).
% 0.82/0.78 tff(217,plain,
% 0.82/0.78 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)))),
% 0.82/0.78 inference(transitivity,[status(thm)],[216, 214])).
% 0.82/0.78 tff(218,plain,
% 0.82/0.78 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.82/0.78 inference(quant_inst,[status(thm)],[])).
% 0.82/0.78 tff(219,plain,
% 0.82/0.78 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.82/0.78 tff(220,plain,
% 0.82/0.78 (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[219, 165, 35, 213])).
% 0.82/0.78 tff(221,plain,
% 0.82/0.78 (k3_xboole_0(C!2, D!3) = k5_subset_1(u1_struct_0(B!1), C!2, D!3)),
% 0.82/0.78 inference(symmetry,[status(thm)],[220])).
% 0.82/0.78 tff(222,plain,
% 0.82/0.78 (k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)) = k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3))),
% 0.82/0.78 inference(monotonicity,[status(thm)],[221])).
% 0.82/0.78 tff(223,plain,
% 0.82/0.78 (k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)) = k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3))),
% 0.82/0.78 inference(symmetry,[status(thm)],[222])).
% 0.82/0.78 tff(224,plain,
% 0.82/0.78 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.82/0.78 inference(monotonicity,[status(thm)],[223, 164])).
% 0.82/0.78 tff(225,plain,
% 0.82/0.78 (m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3)) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))),
% 0.82/0.78 inference(symmetry,[status(thm)],[224])).
% 0.82/0.78 tff(226,plain,
% 0.82/0.78 (^[A: $i, B: $i] : refl((k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> (k3_xboole_0(A, B) = k3_xboole_0(B, A)))),
% 0.82/0.78 inference(bind,[status(th)],[])).
% 0.82/0.78 tff(227,plain,
% 0.82/0.78 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.82/0.78 inference(quant_intro,[status(thm)],[226])).
% 0.82/0.78 tff(228,plain,
% 0.82/0.78 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.82/0.78 inference(rewrite,[status(thm)],[])).
% 0.82/0.78 tff(229,axiom,(![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.82/0.78 tff(230,plain,
% 0.82/0.78 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.82/0.78 tff(231,plain,(
% 0.82/0.78 ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.82/0.78 inference(skolemize,[status(sab)],[230])).
% 0.82/0.78 tff(232,plain,
% 0.82/0.78 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.82/0.78 tff(233,plain,
% 0.82/0.78 ((~![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))) | (k3_xboole_0(C!2, D!3) = k3_xboole_0(D!3, C!2))),
% 0.82/0.78 inference(quant_inst,[status(thm)],[])).
% 0.82/0.78 tff(234,plain,
% 0.82/0.78 (k3_xboole_0(C!2, D!3) = k3_xboole_0(D!3, C!2)),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.82/0.78 tff(235,plain,
% 0.82/0.78 (r1_tarski(k3_xboole_0(C!2, D!3), D!3) <=> r1_tarski(k3_xboole_0(D!3, C!2), D!3)),
% 0.82/0.78 inference(monotonicity,[status(thm)],[234])).
% 0.82/0.78 tff(236,plain,
% 0.82/0.78 (r1_tarski(k3_xboole_0(D!3, C!2), D!3) <=> r1_tarski(k3_xboole_0(C!2, D!3), D!3)),
% 0.82/0.78 inference(symmetry,[status(thm)],[235])).
% 0.82/0.78 tff(237,plain,
% 0.82/0.78 (^[A: $i, B: $i] : refl(r1_tarski(k3_xboole_0(A, B), A) <=> r1_tarski(k3_xboole_0(A, B), A))),
% 0.82/0.78 inference(bind,[status(th)],[])).
% 0.82/0.78 tff(238,plain,
% 0.82/0.78 (![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A) <=> ![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)),
% 0.82/0.78 inference(quant_intro,[status(thm)],[237])).
% 0.82/0.78 tff(239,plain,
% 0.82/0.78 (![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A) <=> ![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)),
% 0.82/0.78 inference(rewrite,[status(thm)],[])).
% 0.82/0.78 tff(240,axiom,(![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_xboole_1')).
% 0.82/0.78 tff(241,plain,
% 0.82/0.78 (![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.82/0.78 tff(242,plain,(
% 0.82/0.78 ![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)),
% 0.82/0.78 inference(skolemize,[status(sab)],[241])).
% 0.82/0.78 tff(243,plain,
% 0.82/0.78 (![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[242, 238])).
% 0.82/0.78 tff(244,plain,
% 0.82/0.78 ((~![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)) | r1_tarski(k3_xboole_0(D!3, C!2), D!3)),
% 0.82/0.78 inference(quant_inst,[status(thm)],[])).
% 0.82/0.78 tff(245,plain,
% 0.82/0.78 (r1_tarski(k3_xboole_0(D!3, C!2), D!3)),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.82/0.78 tff(246,plain,
% 0.82/0.78 (r1_tarski(k3_xboole_0(C!2, D!3), D!3)),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[245, 236])).
% 0.82/0.78 tff(247,plain,
% 0.82/0.78 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))), (![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))), ((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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, 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)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))))))), 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))))) <=> (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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))), ((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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, 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)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))))),
% 0.82/0.78 inference(bind,[status(th)],[])).
% 0.82/0.78 tff(248,plain,
% 0.82/0.78 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))),
% 0.82/0.78 inference(quant_intro,[status(thm)],[247])).
% 0.82/0.78 tff(249,plain,
% 0.82/0.78 (^[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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, 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)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))),
% 0.82/0.78 inference(bind,[status(th)],[])).
% 0.82/0.78 tff(250,plain,
% 0.82/0.78 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.78 inference(quant_intro,[status(thm)],[249])).
% 0.82/0.78 tff(251,plain,
% 0.82/0.78 (^[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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, 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)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))),
% 0.82/0.78 inference(bind,[status(th)],[])).
% 0.82/0.78 tff(252,plain,
% 0.82/0.78 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.78 inference(quant_intro,[status(thm)],[251])).
% 0.82/0.78 tff(253,plain,
% 0.82/0.78 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.78 inference(transitivity,[status(thm)],[252, 250])).
% 0.82/0.78 tff(254,plain,
% 0.82/0.78 (^[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))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))) <=> ((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))), rewrite(((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~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) & 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))))) <=> ((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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, 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))) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, 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)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~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) & 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))))) <=> (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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))),
% 0.82/0.78 inference(bind,[status(th)],[])).
% 0.82/0.78 tff(255,plain,
% 0.82/0.78 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))))) <=> ![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.78 inference(quant_intro,[status(thm)],[254])).
% 0.82/0.78 tff(256,plain,
% 0.82/0.78 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))),
% 0.82/0.78 inference(rewrite,[status(thm)],[])).
% 0.82/0.78 tff(257,plain,
% 0.82/0.78 (^[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((r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D))) <=> ((~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)))) <=> (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)))))), rewrite((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)))) <=> (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)))) <=> (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)))) <=> ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D))))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(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] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(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] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(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] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(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] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))))))), 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(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] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))))),
% 0.82/0.79 inference(bind,[status(th)],[])).
% 0.82/0.79 tff(258,plain,
% 0.82/0.79 (![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] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, 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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))),
% 0.82/0.79 inference(quant_intro,[status(thm)],[257])).
% 0.82/0.79 tff(259,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] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (r1_tarski(C, D) => m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t15_rmod_5')).
% 0.82/0.79 tff(260,plain,
% 0.82/0.79 (![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.82/0.79 tff(261,plain,
% 0.82/0.79 (![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.82/0.79 tff(262,plain,(
% 0.82/0.79 ![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))),
% 0.82/0.79 inference(skolemize,[status(sab)],[261])).
% 0.82/0.79 tff(263,plain,
% 0.82/0.79 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[262, 255])).
% 0.82/0.79 tff(264,plain,
% 0.82/0.79 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[263, 253])).
% 0.82/0.79 tff(265,plain,
% 0.82/0.79 (![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[264, 248])).
% 0.82/0.79 tff(266,plain,
% 0.82/0.79 (((~![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))) | (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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D))))))) <=> ((~![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))) | 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D))))))),
% 0.82/0.79 inference(rewrite,[status(thm)],[])).
% 0.82/0.79 tff(267,plain,
% 0.82/0.79 ((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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))) <=> (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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D))))))),
% 0.82/0.79 inference(rewrite,[status(thm)],[])).
% 0.82/0.79 tff(268,plain,
% 0.82/0.79 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))), (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D))))))), rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, 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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))))),
% 0.82/0.79 inference(bind,[status(th)],[])).
% 0.82/0.79 tff(269,plain,
% 0.82/0.79 (![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))),
% 0.82/0.79 inference(quant_intro,[status(thm)],[268])).
% 0.82/0.79 tff(270,plain,
% 0.82/0.79 ((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] : (m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))))) <=> (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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D))))))),
% 0.82/0.79 inference(monotonicity,[status(thm)],[269])).
% 0.82/0.79 tff(271,plain,
% 0.82/0.79 ((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] : (m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))))) <=> (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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D))))))),
% 0.82/0.79 inference(transitivity,[status(thm)],[270, 267])).
% 0.82/0.79 tff(272,plain,
% 0.82/0.79 (((~![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))) | (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] : (m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))) <=> ((~![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))) | (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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))))),
% 0.82/0.79 inference(monotonicity,[status(thm)],[271])).
% 0.82/0.79 tff(273,plain,
% 0.82/0.79 (((~![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))) | (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] : (m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))) <=> ((~![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))) | 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D))))))),
% 0.82/0.79 inference(transitivity,[status(thm)],[272, 266])).
% 0.82/0.79 tff(274,plain,
% 0.82/0.79 ((~![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))) | (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] : (m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))),
% 0.82/0.79 inference(quant_inst,[status(thm)],[])).
% 0.82/0.79 tff(275,plain,
% 0.82/0.79 ((~![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] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D))))))) | 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.82/0.79 tff(276,plain,
% 0.82/0.79 (![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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))),
% 0.82/0.80 inference(unit_resolution,[status(thm)],[275, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 265])).
% 0.82/0.80 tff(277,plain,
% 0.82/0.80 (((~![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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, 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] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, 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] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D)))))),
% 0.82/0.80 inference(rewrite,[status(thm)],[])).
% 0.82/0.80 tff(278,plain,
% 0.82/0.80 ((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] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, 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] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D)))))),
% 0.82/0.80 inference(rewrite,[status(thm)],[])).
% 0.82/0.80 tff(279,plain,
% 0.82/0.80 (^[C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D)))))),
% 0.82/0.80 inference(bind,[status(th)],[])).
% 0.82/0.80 tff(280,plain,
% 0.82/0.80 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D)))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))),
% 0.82/0.80 inference(quant_intro,[status(thm)],[279])).
% 0.82/0.80 tff(281,plain,
% 0.82/0.80 ((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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))) <=> (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] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D)))))),
% 0.82/0.80 inference(monotonicity,[status(thm)],[280])).
% 0.82/0.80 tff(282,plain,
% 0.82/0.80 ((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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, 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] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D)))))),
% 0.82/0.80 inference(transitivity,[status(thm)],[281, 278])).
% 0.82/0.80 tff(283,plain,
% 0.82/0.80 (((~![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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))) | (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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, 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] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))))),
% 0.82/0.80 inference(monotonicity,[status(thm)],[282])).
% 0.82/0.80 tff(284,plain,
% 0.82/0.80 (((~![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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))) | (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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, 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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, 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] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D)))))),
% 0.82/0.80 inference(transitivity,[status(thm)],[283, 277])).
% 0.82/0.80 tff(285,plain,
% 0.82/0.80 ((~![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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, D)))))) | (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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D)))))),
% 0.82/0.80 inference(quant_inst,[status(thm)],[])).
% 0.82/0.80 tff(286,plain,
% 0.82/0.80 ((~![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] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)) | m1_rmod_2(k1_rmod_5(A!0, B, C), A!0, k1_rmod_5(A!0, B, 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] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.82/0.80 tff(287,plain,
% 0.82/0.80 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))),
% 0.82/0.80 inference(unit_resolution,[status(thm)],[286, 42, 41, 40, 39, 38, 37, 36, 276])).
% 0.82/0.80 tff(288,plain,
% 0.82/0.80 (m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.82/0.80 inference(monotonicity,[status(thm)],[221])).
% 0.82/0.80 tff(289,plain,
% 0.82/0.80 (m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.82/0.80 inference(symmetry,[status(thm)],[288])).
% 0.82/0.80 tff(290,plain,
% 0.82/0.80 (^[A: $i, B: $i, C: $i] : refl((m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.82/0.80 inference(bind,[status(th)],[])).
% 0.82/0.80 tff(291,plain,
% 0.82/0.80 (![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.82/0.80 inference(quant_intro,[status(thm)],[290])).
% 0.82/0.80 tff(292,plain,
% 0.82/0.80 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.82/0.80 inference(bind,[status(th)],[])).
% 0.82/0.80 tff(293,plain,
% 0.82/0.80 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.82/0.80 inference(quant_intro,[status(thm)],[292])).
% 0.82/0.80 tff(294,plain,
% 0.82/0.80 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 0.82/0.80 inference(rewrite,[status(thm)],[])).
% 0.82/0.80 tff(295,plain,
% 0.82/0.80 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))))),
% 0.82/0.80 inference(bind,[status(th)],[])).
% 0.82/0.80 tff(296,plain,
% 0.82/0.80 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 0.82/0.80 inference(quant_intro,[status(thm)],[295])).
% 0.82/0.80 tff(297,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_subset_1')).
% 0.82/0.80 tff(298,plain,
% 0.82/0.80 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.82/0.80 tff(299,plain,
% 0.82/0.80 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.82/0.80 tff(300,plain,(
% 0.82/0.80 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 0.82/0.80 inference(skolemize,[status(sab)],[299])).
% 0.82/0.80 tff(301,plain,
% 0.82/0.80 (![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[300, 293])).
% 0.82/0.80 tff(302,plain,
% 0.82/0.80 (![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[301, 291])).
% 0.82/0.80 tff(303,plain,
% 0.82/0.80 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))))),
% 0.82/0.80 inference(rewrite,[status(thm)],[])).
% 0.82/0.80 tff(304,plain,
% 0.82/0.80 ((m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))))),
% 0.82/0.80 inference(rewrite,[status(thm)],[])).
% 0.82/0.80 tff(305,plain,
% 0.82/0.80 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.82/0.80 inference(monotonicity,[status(thm)],[304])).
% 0.82/0.80 tff(306,plain,
% 0.82/0.80 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))))),
% 0.82/0.80 inference(transitivity,[status(thm)],[305, 303])).
% 0.82/0.80 tff(307,plain,
% 0.82/0.80 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.82/0.80 inference(quant_inst,[status(thm)],[])).
% 0.82/0.80 tff(308,plain,
% 0.82/0.80 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.82/0.80 tff(309,plain,
% 0.82/0.80 (m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.82/0.80 inference(unit_resolution,[status(thm)],[308, 165, 35, 302])).
% 0.82/0.80 tff(310,plain,
% 0.82/0.80 (m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[309, 289])).
% 0.82/0.80 tff(311,plain,
% 0.82/0.80 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))) | ((~m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))) | (~m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D))))),
% 0.82/0.80 inference(rewrite,[status(thm)],[])).
% 0.82/0.80 tff(312,plain,
% 0.82/0.80 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))) | ((~m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D))))),
% 0.82/0.80 inference(quant_inst,[status(thm)],[])).
% 0.82/0.80 tff(313,plain,
% 0.82/0.80 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))) | (~m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.82/0.80 tff(314,plain,
% 0.82/0.80 (![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))),
% 0.82/0.80 inference(unit_resolution,[status(thm)],[313, 310, 287])).
% 0.82/0.80 tff(315,plain,
% 0.82/0.80 (((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | ((~r1_tarski(k3_xboole_0(C!2, D!3), D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3)))) <=> ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | (~r1_tarski(k3_xboole_0(C!2, D!3), D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3)))),
% 0.82/0.80 inference(rewrite,[status(thm)],[])).
% 0.82/0.80 tff(316,plain,
% 0.82/0.80 ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | ((~r1_tarski(k3_xboole_0(C!2, D!3), D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3)))),
% 0.82/0.80 inference(quant_inst,[status(thm)],[])).
% 0.82/0.80 tff(317,plain,
% 0.82/0.80 ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | (~r1_tarski(k3_xboole_0(C!2, D!3), D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.82/0.80 tff(318,plain,
% 0.82/0.80 ((~r1_tarski(k3_xboole_0(C!2, D!3), D!3)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.82/0.80 inference(unit_resolution,[status(thm)],[317, 35, 314])).
% 0.82/0.80 tff(319,plain,
% 0.82/0.80 (m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.82/0.80 inference(unit_resolution,[status(thm)],[318, 246])).
% 0.82/0.80 tff(320,plain,
% 0.82/0.80 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[319, 225])).
% 0.82/0.80 tff(321,plain,
% 0.82/0.80 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2))),
% 0.82/0.81 inference(monotonicity,[status(thm)],[223, 194])).
% 0.82/0.81 tff(322,plain,
% 0.82/0.81 (m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2)) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))),
% 0.82/0.81 inference(symmetry,[status(thm)],[321])).
% 0.82/0.81 tff(323,plain,
% 0.82/0.81 ((~![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)) | r1_tarski(k3_xboole_0(C!2, D!3), C!2)),
% 0.82/0.81 inference(quant_inst,[status(thm)],[])).
% 0.82/0.81 tff(324,plain,
% 0.82/0.81 (r1_tarski(k3_xboole_0(C!2, D!3), C!2)),
% 0.82/0.81 inference(unit_resolution,[status(thm)],[323, 243])).
% 0.82/0.81 tff(325,plain,
% 0.82/0.81 (((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | ((~r1_tarski(k3_xboole_0(C!2, D!3), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2)))) <=> ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | (~r1_tarski(k3_xboole_0(C!2, D!3), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2)))),
% 0.82/0.81 inference(rewrite,[status(thm)],[])).
% 0.82/0.81 tff(326,plain,
% 0.82/0.81 ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | ((~r1_tarski(k3_xboole_0(C!2, D!3), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2)))),
% 0.82/0.81 inference(quant_inst,[status(thm)],[])).
% 0.82/0.81 tff(327,plain,
% 0.82/0.81 ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | (~r1_tarski(k3_xboole_0(C!2, D!3), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2))),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.82/0.81 tff(328,plain,
% 0.82/0.81 (m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2))),
% 0.82/0.81 inference(unit_resolution,[status(thm)],[327, 165, 324, 314])).
% 0.82/0.81 tff(329,plain,
% 0.82/0.81 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[328, 322])).
% 0.82/0.81 tff(330,plain,
% 0.82/0.81 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)),
% 0.82/0.81 inference(monotonicity,[status(thm)],[164])).
% 0.82/0.81 tff(331,plain,
% 0.82/0.81 (m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1) <=> m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)),
% 0.82/0.81 inference(symmetry,[status(thm)],[330])).
% 0.82/0.81 tff(332,plain,
% 0.82/0.81 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[64, 331])).
% 0.82/0.81 tff(333,plain,
% 0.82/0.81 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)),
% 0.82/0.81 inference(monotonicity,[status(thm)],[194])).
% 0.82/0.81 tff(334,plain,
% 0.82/0.81 (m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1) <=> m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)),
% 0.82/0.81 inference(symmetry,[status(thm)],[333])).
% 0.82/0.81 tff(335,plain,
% 0.82/0.81 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[174, 334])).
% 0.82/0.81 tff(336,plain,
% 0.82/0.81 (^[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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> (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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))))),
% 0.82/0.81 inference(bind,[status(th)],[])).
% 0.82/0.81 tff(337,plain,
% 0.82/0.81 (![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> ![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.82/0.81 inference(quant_intro,[status(thm)],[336])).
% 0.82/0.81 tff(338,plain,
% 0.82/0.81 (^[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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> (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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))))),
% 0.82/0.81 inference(bind,[status(th)],[])).
% 0.82/0.81 tff(339,plain,
% 0.82/0.81 (![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> ![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.82/0.81 inference(quant_intro,[status(thm)],[338])).
% 0.82/0.81 tff(340,plain,
% 0.82/0.81 (![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> ![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.82/0.81 inference(transitivity,[status(thm)],[339, 337])).
% 0.82/0.81 tff(341,plain,
% 0.82/0.81 (^[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))))), quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))) <=> ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))), (![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))) <=> ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))), (((~((~v3_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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))), 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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))) <=> (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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))), (((~((~v3_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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))))), (![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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))))), 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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> (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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))))),
% 0.82/0.81 inference(bind,[status(th)],[])).
% 0.82/0.81 tff(342,plain,
% 0.82/0.81 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.82/0.81 inference(quant_intro,[status(thm)],[341])).
% 0.82/0.81 tff(343,plain,
% 0.82/0.81 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))),
% 0.82/0.81 inference(rewrite,[status(thm)],[])).
% 0.82/0.81 tff(344,plain,
% 0.82/0.81 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite(((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))) <=> ((~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))), ((m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))) <=> (m1_rmod_2(E, A, B) => ((~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))), rewrite((m1_rmod_2(E, A, B) => ((~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))) <=> (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))), ((m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))) <=> (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))), (![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))) <=> ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))), ((m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))) <=> (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))), rewrite((m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))) <=> ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))), ((m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))) <=> ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))), (![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))) <=> ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))), ((m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))) <=> (m1_rmod_2(C, A, B) => ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))), rewrite((m1_rmod_2(C, A, B) => ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))) <=> ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))), ((m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))) <=> ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))), (![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))) <=> ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))))) <=> (((~v3_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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))))) <=> ((~((~v3_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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))))) <=> ![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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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)) => ![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, 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)) => ![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))))),
% 0.82/0.81 inference(bind,[status(th)],[])).
% 0.82/0.81 tff(345,plain,
% 0.82/0.81 (![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))),
% 0.82/0.81 inference(quant_intro,[status(thm)],[344])).
% 0.82/0.81 tff(346,axiom,(![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t24_rmod_3')).
% 0.82/0.81 tff(347,plain,
% 0.82/0.81 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.82/0.81 tff(348,plain,
% 0.82/0.81 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[347, 343])).
% 0.82/0.81 tff(349,plain,(
% 0.82/0.81 ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))),
% 0.82/0.82 inference(skolemize,[status(sab)],[348])).
% 0.82/0.82 tff(350,plain,
% 0.82/0.82 (![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[349, 342])).
% 0.82/0.82 tff(351,plain,
% 0.82/0.82 (![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[350, 340])).
% 0.82/0.82 tff(352,plain,
% 0.82/0.82 (((~![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | (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)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))) <=> ((~![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | 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)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(353,plain,
% 0.82/0.82 ((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)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) <=> (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)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(354,plain,
% 0.82/0.82 (^[B: $i] : rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))) <=> (v3_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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(355,plain,
% 0.82/0.82 (![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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))) <=> ![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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[354])).
% 0.82/0.82 tff(356,plain,
% 0.82/0.82 ((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) | (~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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) <=> (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)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.82/0.82 inference(monotonicity,[status(thm)],[355])).
% 0.82/0.82 tff(357,plain,
% 0.82/0.82 ((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) | (~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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) <=> (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)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.82/0.82 inference(transitivity,[status(thm)],[356, 353])).
% 0.82/0.82 tff(358,plain,
% 0.82/0.82 (((~![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | (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) | (~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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))) <=> ((~![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | (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)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))))),
% 0.82/0.82 inference(monotonicity,[status(thm)],[357])).
% 0.82/0.82 tff(359,plain,
% 0.82/0.82 (((~![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | (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) | (~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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))) <=> ((~![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | 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)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.82/0.82 inference(transitivity,[status(thm)],[358, 352])).
% 0.82/0.82 tff(360,plain,
% 0.82/0.82 ((~![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | (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) | (~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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.82/0.82 inference(quant_inst,[status(thm)],[])).
% 0.82/0.82 tff(361,plain,
% 0.82/0.82 ((~![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) | (~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_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | 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)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.82/0.82 tff(362,plain,
% 0.82/0.82 (![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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))),
% 0.82/0.82 inference(unit_resolution,[status(thm)],[361, 55, 54, 53, 52, 51, 50, 48, 47, 46, 43, 351])).
% 0.82/0.82 tff(363,plain,
% 0.82/0.82 (((~![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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | (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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))) <=> ((~![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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | 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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(364,plain,
% 0.82/0.82 ((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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))) <=> (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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(365,plain,
% 0.82/0.82 (^[C: $i] : rewrite(((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))) <=> ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(366,plain,
% 0.82/0.82 (![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))) <=> ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))),
% 0.82/0.83 inference(quant_intro,[status(thm)],[365])).
% 0.82/0.83 tff(367,plain,
% 0.82/0.83 ((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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))) <=> (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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.82/0.83 inference(monotonicity,[status(thm)],[366])).
% 0.82/0.83 tff(368,plain,
% 0.82/0.83 ((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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))) <=> (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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.82/0.83 inference(transitivity,[status(thm)],[367, 364])).
% 0.82/0.83 tff(369,plain,
% 0.82/0.83 (((~![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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | (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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) <=> ((~![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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | (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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))))),
% 0.82/0.83 inference(monotonicity,[status(thm)],[368])).
% 0.82/0.83 tff(370,plain,
% 0.82/0.83 (((~![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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | (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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) <=> ((~![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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | 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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.82/0.83 inference(transitivity,[status(thm)],[369, 363])).
% 0.82/0.83 tff(371,plain,
% 0.82/0.83 ((~![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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | (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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))),
% 0.82/0.83 inference(quant_inst,[status(thm)],[])).
% 0.82/0.83 tff(372,plain,
% 0.82/0.83 ((~![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_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | 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_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))),
% 0.82/0.83 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.82/0.83 tff(373,plain,
% 0.82/0.83 (![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))),
% 0.82/0.83 inference(unit_resolution,[status(thm)],[372, 42, 41, 40, 39, 38, 37, 36, 362])).
% 0.82/0.83 tff(374,plain,
% 0.82/0.83 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v10_vectsp_1(A!0) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))),
% 0.82/0.83 inference(rewrite,[status(thm)],[])).
% 0.82/0.83 tff(375,plain,
% 0.82/0.83 ((v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1))))) <=> (v10_vectsp_1(A!0) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))),
% 0.82/0.83 inference(rewrite,[status(thm)],[])).
% 0.82/0.83 tff(376,plain,
% 0.82/0.83 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v10_vectsp_1(A!0) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1))))))),
% 0.82/0.83 inference(monotonicity,[status(thm)],[375])).
% 0.82/0.83 tff(377,plain,
% 0.82/0.83 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))),
% 0.82/0.83 inference(transitivity,[status(thm)],[376, 374])).
% 0.82/0.83 tff(378,plain,
% 0.82/0.83 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))),
% 0.82/0.83 inference(quant_inst,[status(thm)],[])).
% 0.82/0.83 tff(379,plain,
% 0.82/0.83 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_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_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)) | (~v7_group_1(A!0)) | (~v2_vectsp_2(A!0)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1))))),
% 0.82/0.83 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.82/0.83 tff(380,plain,
% 0.82/0.83 (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))),
% 0.82/0.83 inference(unit_resolution,[status(thm)],[379, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 13, 309])).
% 0.82/0.83 tff(381,plain,
% 0.82/0.83 (((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)),
% 0.82/0.83 inference(tautology,[status(thm)],[])).
% 0.82/0.83 tff(382,plain,
% 0.82/0.83 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)),
% 0.82/0.83 inference(unit_resolution,[status(thm)],[381, 380])).
% 0.82/0.83 tff(383,plain,
% 0.82/0.83 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E)))))),
% 0.82/0.83 inference(rewrite,[status(thm)],[])).
% 0.82/0.83 tff(384,plain,
% 0.82/0.83 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E)))))),
% 0.82/0.83 inference(quant_inst,[status(thm)],[])).
% 0.82/0.83 tff(385,plain,
% 0.82/0.83 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))),
% 0.82/0.83 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.82/0.83 tff(386,plain,
% 0.82/0.83 (![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))),
% 0.82/0.83 inference(unit_resolution,[status(thm)],[385, 382, 373])).
% 0.82/0.83 tff(387,plain,
% 0.82/0.83 (((~![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))) | ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E))))) <=> ((~![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E))))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(388,plain,
% 0.82/0.84 ((~![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))) | ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E))))),
% 0.82/0.84 inference(quant_inst,[status(thm)],[])).
% 0.82/0.84 tff(389,plain,
% 0.82/0.84 ((~![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.82/0.84 tff(390,plain,
% 0.82/0.84 ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[389, 386])).
% 0.82/0.84 tff(391,plain,
% 0.82/0.84 (![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[390, 335])).
% 0.82/0.84 tff(392,plain,
% 0.82/0.84 (((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))) <=> ((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(393,plain,
% 0.82/0.84 (((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))) <=> ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(394,plain,
% 0.82/0.84 (((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))) <=> ((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))))),
% 0.82/0.84 inference(monotonicity,[status(thm)],[393])).
% 0.82/0.84 tff(395,plain,
% 0.82/0.84 (((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))) <=> ((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))),
% 0.82/0.85 inference(transitivity,[status(thm)],[394, 392])).
% 0.82/0.85 tff(396,plain,
% 0.82/0.85 ((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(397,plain,
% 0.82/0.85 ((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.82/0.85 tff(398,plain,
% 0.82/0.85 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[397, 391, 332, 329, 320])).
% 0.82/0.85 tff(399,plain,
% 0.82/0.85 ($false),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[398, 200])).
% 0.82/0.85 % SZS output end Proof
%------------------------------------------------------------------------------