%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG220+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:58:45 AM UTC 2025
% Result : Theorem 0.22s 0.51s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ALG220+1 : TPTP v9.0.0. Released v3.4.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 10:48:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51 % SZS output start Proof
% 0.22/0.51 tff(m1_rmod_2_type, type, (
% 0.22/0.51 m1_rmod_2: ( $i * $i * $i ) > $o)).
% 0.22/0.51 tff(k1_rmod_5_type, type, (
% 0.22/0.51 k1_rmod_5: ( $i * $i * $i ) > $i)).
% 0.22/0.51 tff(tptp_fun_D_3_type, type, (
% 0.22/0.51 tptp_fun_D_3: $i)).
% 0.22/0.51 tff(tptp_fun_B_1_type, type, (
% 0.22/0.51 tptp_fun_B_1: $i)).
% 0.22/0.51 tff(tptp_fun_A_0_type, type, (
% 0.22/0.51 tptp_fun_A_0: $i)).
% 0.22/0.51 tff(tptp_fun_C_2_type, type, (
% 0.22/0.51 tptp_fun_C_2: $i)).
% 0.22/0.51 tff(r1_tarski_type, type, (
% 0.22/0.51 r1_tarski: ( $i * $i ) > $o)).
% 0.22/0.51 tff(m1_subset_1_type, type, (
% 0.22/0.51 m1_subset_1: ( $i * $i ) > $o)).
% 0.22/0.51 tff(k1_zfmisc_1_type, type, (
% 0.22/0.51 k1_zfmisc_1: $i > $i)).
% 0.22/0.51 tff(u1_struct_0_type, type, (
% 0.22/0.51 u1_struct_0: $i > $i)).
% 0.22/0.51 tff(l1_vectsp_2_type, type, (
% 0.22/0.51 l1_vectsp_2: ( $i * $i ) > $o)).
% 0.22/0.51 tff(v5_vectsp_2_type, type, (
% 0.22/0.51 v5_vectsp_2: ( $i * $i ) > $o)).
% 0.22/0.51 tff(v3_vectsp_2_type, type, (
% 0.22/0.51 v3_vectsp_2: ( $i * $i ) > $o)).
% 0.22/0.51 tff(v6_rlvect_1_type, type, (
% 0.22/0.51 v6_rlvect_1: $i > $o)).
% 0.22/0.51 tff(v5_rlvect_1_type, type, (
% 0.22/0.51 v5_rlvect_1: $i > $o)).
% 0.22/0.51 tff(v4_rlvect_1_type, type, (
% 0.22/0.51 v4_rlvect_1: $i > $o)).
% 0.22/0.51 tff(v3_rlvect_1_type, type, (
% 0.22/0.51 v3_rlvect_1: $i > $o)).
% 0.22/0.51 tff(v3_struct_0_type, type, (
% 0.22/0.51 v3_struct_0: $i > $o)).
% 0.22/0.51 tff(l3_vectsp_1_type, type, (
% 0.22/0.51 l3_vectsp_1: $i > $o)).
% 0.22/0.51 tff(v2_vectsp_2_type, type, (
% 0.22/0.51 v2_vectsp_2: $i > $o)).
% 0.22/0.51 tff(v10_vectsp_1_type, type, (
% 0.22/0.51 v10_vectsp_1: $i > $o)).
% 0.22/0.51 tff(v8_vectsp_1_type, type, (
% 0.22/0.51 v8_vectsp_1: $i > $o)).
% 0.22/0.51 tff(v7_vectsp_1_type, type, (
% 0.22/0.51 v7_vectsp_1: $i > $o)).
% 0.22/0.51 tff(v6_vectsp_1_type, type, (
% 0.22/0.51 v6_vectsp_1: $i > $o)).
% 0.22/0.51 tff(v7_group_1_type, type, (
% 0.22/0.51 v7_group_1: $i > $o)).
% 0.22/0.51 tff(v4_group_1_type, type, (
% 0.22/0.51 v4_group_1: $i > $o)).
% 0.22/0.51 tff(1,plain,
% 0.22/0.51 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(2,plain,
% 0.22/0.51 ((((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(3,plain,
% 0.22/0.51 ((~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))) <=> (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(4,plain,
% 0.22/0.52 ((m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~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))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[3])).
% 0.22/0.52 tff(5,plain,
% 0.22/0.52 ((((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))) <=> (((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[4])).
% 0.22/0.52 tff(6,plain,
% 0.22/0.52 ((((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.22/0.52 inference(transitivity,[status(thm)],[5, 2])).
% 0.22/0.52 tff(7,plain,
% 0.22/0.52 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & (((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))))) <=> (((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[6])).
% 0.22/0.52 tff(8,plain,
% 0.22/0.52 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & (((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.36/0.52 inference(transitivity,[status(thm)],[7, 1])).
% 0.36/0.52 tff(9,plain,
% 0.36/0.52 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, D) = B) | (~((k1_rmod_5(A, B, C) = B) & r1_tarski(C, D))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, D) = B) | (~((k1_rmod_5(A, B, C) = B) & r1_tarski(C, D))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))))))))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(10,plain,
% 0.36/0.52 ((~![A: $i] : ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) => ![B: $i] : (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (((k1_rmod_5(A, B, C) = B) & r1_tarski(C, D)) => (k1_rmod_5(A, B, D) = B))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, D) = B) | (~((k1_rmod_5(A, B, C) = B) & r1_tarski(C, D))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))))))))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(11,axiom,(~![A: $i] : ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) => ![B: $i] : (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => (((k1_rmod_5(A, B, C) = B) & r1_tarski(C, D)) => (k1_rmod_5(A, B, D) = B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t16_rmod_5')).
% 0.36/0.52 tff(12,plain,
% 0.36/0.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, D) = B) | (~((k1_rmod_5(A, B, C) = B) & r1_tarski(C, D))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.36/0.52 tff(13,plain,
% 0.36/0.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, D) = B) | (~((k1_rmod_5(A, B, C) = B) & r1_tarski(C, D))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.36/0.52 tff(14,plain,
% 0.36/0.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, D) = B) | (~((k1_rmod_5(A, B, C) = B) & r1_tarski(C, D))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.36/0.52 tff(15,plain,
% 0.36/0.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, D) = B) | (~((k1_rmod_5(A, B, C) = B) & r1_tarski(C, D))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.36/0.52 tff(16,plain,
% 0.36/0.52 ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.36/0.52 tff(17,plain,
% 0.36/0.52 (~((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.36/0.52 inference(and_elim,[status(thm)],[16])).
% 0.36/0.52 tff(18,plain,
% 0.36/0.52 ((k1_rmod_5(A!0, B!1, C!2) = B!1) & r1_tarski(C!2, D!3)),
% 0.36/0.52 inference(or_elim,[status(thm)],[17])).
% 0.36/0.52 tff(19,plain,
% 0.36/0.52 (k1_rmod_5(A!0, B!1, C!2) = B!1),
% 0.36/0.52 inference(and_elim,[status(thm)],[18])).
% 0.36/0.52 tff(20,plain,
% 0.36/0.52 (m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D!3)) <=> m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[19])).
% 0.36/0.52 tff(21,plain,
% 0.36/0.52 (m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3)) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.36/0.52 inference(symmetry,[status(thm)],[20])).
% 0.36/0.52 tff(22,plain,
% 0.36/0.52 ((~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3))) <=> (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D!3)))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[21])).
% 0.36/0.52 tff(23,plain,
% 0.36/0.52 (^[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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(24,plain,
% 0.36/0.52 (![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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[23])).
% 0.36/0.52 tff(25,plain,
% 0.36/0.52 (^[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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(26,plain,
% 0.36/0.52 (![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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[25])).
% 0.36/0.52 tff(27,plain,
% 0.36/0.52 (![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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))),
% 0.36/0.52 inference(transitivity,[status(thm)],[26, 24])).
% 0.36/0.52 tff(28,plain,
% 0.36/0.52 (^[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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) <=> (~(v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (~(~(v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) <=> (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) <=> (~((~m1_rmod_2(C, A, B)) | (~m1_rmod_2(B, A, C))))), ((~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) <=> (~(~((~m1_rmod_2(C, A, B)) | (~m1_rmod_2(B, A, C))))))), rewrite((~(~((~m1_rmod_2(C, A, B)) | (~m1_rmod_2(B, A, C))))) <=> ((~m1_rmod_2(C, A, B)) | (~m1_rmod_2(B, A, C)))), ((~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) <=> ((~m1_rmod_2(C, A, B)) | (~m1_rmod_2(B, A, C))))), trans(monotonicity(rewrite(((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & 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_vectsp_2(C, A))))), ((~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & 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_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_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_vectsp_2(C, A)))), ((~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & 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_vectsp_2(C, A))))), (((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))) <=> ((C = B) | ((~m1_rmod_2(C, A, B)) | (~m1_rmod_2(B, A, 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)) | (~l1_vectsp_2(C, A)) | (~v3_vectsp_2(C, A)))))), rewrite(((C = B) | ((~m1_rmod_2(C, A, B)) | (~m1_rmod_2(B, A, 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)) | (~l1_vectsp_2(C, A)) | (~v3_vectsp_2(C, A)))) <=> (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))), (((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))) <=> (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))), (![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))) <=> ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))) <=> ((v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))), rewrite(((v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))) <=> (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))) <=> (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))) <=> ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_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))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))))) <=> ((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))))), rewrite(((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_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))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(29,plain,
% 0.36/0.52 (![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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[28])).
% 0.36/0.52 tff(30,plain,
% 0.36/0.52 (![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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))))) <=> ![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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(31,plain,
% 0.36/0.52 (^[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(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)) & v3_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A)))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A)))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(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)) & v3_vectsp_2(C, A)) <=> (((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C)) & v3_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)) & v3_vectsp_2(C, A)) <=> ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A))), (((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v3_vectsp_2(C, A)) <=> ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A)))), ((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v3_vectsp_2(C, A)) & 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) & v3_vectsp_2(C, A)) & 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) & v3_vectsp_2(C, A)) & 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) & v3_vectsp_2(C, A) & 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)) & v3_vectsp_2(C, A)) & 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) & v3_vectsp_2(C, A) & 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)) & v3_vectsp_2(C, A)) & 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) & v3_vectsp_2(C, A) & 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) & v3_vectsp_2(C, A) & 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) & v3_vectsp_2(C, A) & 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)) & v3_vectsp_2(C, A)) & 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) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))), rewrite(((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) => (C = B)) <=> ((~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (C = B))), ((((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v3_vectsp_2(C, A)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) => ((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) => (C = B))) <=> (((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)) => ((~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (C = B))))), rewrite((((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)) => ((~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (C = B))) <=> ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & 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)) & v3_vectsp_2(C, A)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) => ((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) => (C = B))) <=> ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))))), (![C: $i] : (((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v3_vectsp_2(C, A)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) => ((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) => (C = B))) <=> ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))))), ((((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v3_vectsp_2(C, A)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) => ((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) => (C = B)))) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))))), ((((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v3_vectsp_2(C, A)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) => ((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) => (C = B)))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))))))), (![B: $i] : (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v3_vectsp_2(C, A)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) => ((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) => (C = B)))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & 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)) => ![B: $i] : (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v3_vectsp_2(C, A)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) => ((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) => (C = 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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & 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)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & 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))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & 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)) => ![B: $i] : (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v3_vectsp_2(C, A)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) => ((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) => (C = 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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(32,plain,
% 0.36/0.53 (![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)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v3_vectsp_2(C, A)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) => ((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) => (C = B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[31])).
% 0.36/0.53 tff(33,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)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (((((((((~v3_struct_0(C)) & v3_rlvect_1(C)) & v4_rlvect_1(C)) & v5_rlvect_1(C)) & v6_rlvect_1(C)) & v3_vectsp_2(C, A)) & v5_vectsp_2(C, A)) & l1_vectsp_2(C, A)) => ((m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C)) => (C = B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t33_rmod_2')).
% 0.36/0.53 tff(34,plain,
% 0.36/0.53 (![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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.36/0.53 tff(35,plain,
% 0.36/0.53 (![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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.36/0.53 tff(36,plain,(
% 0.36/0.53 ![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) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((C = B) | (~(m1_rmod_2(C, A, B) & m1_rmod_2(B, A, C))) | (~((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C, A) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A))))))),
% 0.36/0.53 inference(skolemize,[status(sab)],[35])).
% 0.36/0.53 tff(37,plain,
% 0.36/0.53 (![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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.36/0.53 tff(38,plain,
% 0.36/0.53 (![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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.36/0.53 tff(39,plain,
% 0.36/0.53 (l3_vectsp_1(A!0)),
% 0.36/0.53 inference(and_elim,[status(thm)],[16])).
% 0.36/0.53 tff(40,plain,
% 0.36/0.53 (v8_vectsp_1(A!0)),
% 0.36/0.53 inference(and_elim,[status(thm)],[16])).
% 0.36/0.53 tff(41,plain,
% 0.36/0.53 (v7_vectsp_1(A!0)),
% 0.36/0.53 inference(and_elim,[status(thm)],[16])).
% 0.36/0.53 tff(42,plain,
% 0.36/0.53 (v6_vectsp_1(A!0)),
% 0.36/0.53 inference(and_elim,[status(thm)],[16])).
% 0.36/0.53 tff(43,plain,
% 0.36/0.53 (v4_group_1(A!0)),
% 0.36/0.53 inference(and_elim,[status(thm)],[16])).
% 0.36/0.53 tff(44,plain,
% 0.36/0.53 (v6_rlvect_1(A!0)),
% 0.36/0.53 inference(and_elim,[status(thm)],[16])).
% 0.36/0.53 tff(45,plain,
% 0.36/0.53 (v5_rlvect_1(A!0)),
% 0.36/0.53 inference(and_elim,[status(thm)],[16])).
% 0.36/0.53 tff(46,plain,
% 0.36/0.53 (v4_rlvect_1(A!0)),
% 0.36/0.53 inference(and_elim,[status(thm)],[16])).
% 0.36/0.53 tff(47,plain,
% 0.36/0.53 (v3_rlvect_1(A!0)),
% 0.36/0.53 inference(and_elim,[status(thm)],[16])).
% 0.36/0.53 tff(48,plain,
% 0.36/0.53 (~v3_struct_0(A!0)),
% 0.36/0.53 inference(and_elim,[status(thm)],[16])).
% 0.36/0.53 tff(49,plain,
% 0.36/0.53 (((~![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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))) | (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(50,plain,
% 0.36/0.53 ((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)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))) <=> (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(51,plain,
% 0.36/0.53 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A!0, B)) | (~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(B, A!0, C)) | (~v3_vectsp_2(C, A!0))) <=> (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))), (![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A!0, B)) | (~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(B, A!0, C)) | (~v3_vectsp_2(C, A!0))) <=> ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))), ((v3_struct_0(B) | (~v3_vectsp_2(B, A!0)) | (~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] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A!0, B)) | (~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(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))) <=> (v3_struct_0(B) | (~v3_vectsp_2(B, A!0)) | (~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] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))))), rewrite((v3_struct_0(B) | (~v3_vectsp_2(B, A!0)) | (~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] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))), ((v3_struct_0(B) | (~v3_vectsp_2(B, A!0)) | (~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] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A!0, B)) | (~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(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(52,plain,
% 0.36/0.53 (![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A!0)) | (~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] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A!0, B)) | (~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(B, A!0, C)) | (~v3_vectsp_2(C, 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)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[51])).
% 0.36/0.53 tff(53,plain,
% 0.36/0.53 ((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_vectsp_2(B, A!0)) | (~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] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A!0, B)) | (~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(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[52])).
% 0.36/0.53 tff(54,plain,
% 0.36/0.53 ((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_vectsp_2(B, A!0)) | (~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] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A!0, B)) | (~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(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))) <=> (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))))),
% 0.36/0.53 inference(transitivity,[status(thm)],[53, 50])).
% 0.36/0.53 tff(55,plain,
% 0.36/0.53 (((~![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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A!0)) | (~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] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A!0, B)) | (~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(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))) | (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[54])).
% 0.36/0.53 tff(56,plain,
% 0.36/0.53 (((~![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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A!0)) | (~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] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A!0, B)) | (~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(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))))),
% 0.36/0.53 inference(transitivity,[status(thm)],[55, 49])).
% 0.36/0.53 tff(57,plain,
% 0.36/0.53 ((~![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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_vectsp_2(B, A!0)) | (~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] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A!0, B)) | (~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(B, A!0, C)) | (~v3_vectsp_2(C, A!0)))))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(58,plain,
% 0.36/0.53 ((~![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) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~m1_rmod_2(C, A, B)) | (~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(B, A, C)) | (~v3_vectsp_2(C, A)))))) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.36/0.54 tff(59,plain,
% 0.36/0.54 (![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)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[58, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38])).
% 0.36/0.54 tff(60,plain,
% 0.36/0.54 (l1_vectsp_2(B!1, A!0)),
% 0.36/0.54 inference(and_elim,[status(thm)],[16])).
% 0.36/0.54 tff(61,plain,
% 0.36/0.54 (v5_vectsp_2(B!1, A!0)),
% 0.36/0.54 inference(and_elim,[status(thm)],[16])).
% 0.36/0.54 tff(62,plain,
% 0.36/0.54 (v3_vectsp_2(B!1, A!0)),
% 0.36/0.54 inference(and_elim,[status(thm)],[16])).
% 0.36/0.54 tff(63,plain,
% 0.36/0.54 (v6_rlvect_1(B!1)),
% 0.36/0.54 inference(and_elim,[status(thm)],[16])).
% 0.36/0.54 tff(64,plain,
% 0.36/0.54 (v5_rlvect_1(B!1)),
% 0.36/0.54 inference(and_elim,[status(thm)],[16])).
% 0.36/0.54 tff(65,plain,
% 0.36/0.54 (v4_rlvect_1(B!1)),
% 0.36/0.54 inference(and_elim,[status(thm)],[16])).
% 0.36/0.54 tff(66,plain,
% 0.36/0.54 (v3_rlvect_1(B!1)),
% 0.36/0.54 inference(and_elim,[status(thm)],[16])).
% 0.36/0.54 tff(67,plain,
% 0.36/0.54 (~v3_struct_0(B!1)),
% 0.36/0.54 inference(and_elim,[status(thm)],[16])).
% 0.36/0.54 tff(68,plain,
% 0.36/0.54 (((~![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)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))) | (v3_struct_0(B!1) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))) | v3_struct_0(B!1) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C))))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(69,plain,
% 0.36/0.54 ((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_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))) <=> (v3_struct_0(B!1) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(70,plain,
% 0.37/0.54 (^[C: $i] : rewrite((v3_struct_0(C) | (C = B!1) | (~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(C, A!0, B!1)) | (~m1_rmod_2(B!1, A!0, C)) | (~v3_vectsp_2(C, A!0))) <=> (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(71,plain,
% 0.37/0.54 (![C: $i] : (v3_struct_0(C) | (C = B!1) | (~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(C, A!0, B!1)) | (~m1_rmod_2(B!1, A!0, C)) | (~v3_vectsp_2(C, A!0))) <=> ![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[70])).
% 0.37/0.54 tff(72,plain,
% 0.37/0.54 ((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_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B!1) | (~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(C, A!0, B!1)) | (~m1_rmod_2(B!1, A!0, C)) | (~v3_vectsp_2(C, 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)) | (~v3_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[71])).
% 0.37/0.54 tff(73,plain,
% 0.37/0.54 ((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_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B!1) | (~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(C, A!0, B!1)) | (~m1_rmod_2(B!1, A!0, C)) | (~v3_vectsp_2(C, A!0)))) <=> (v3_struct_0(B!1) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[72, 69])).
% 0.37/0.54 tff(74,plain,
% 0.37/0.54 (((~![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)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, 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)) | (~v3_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B!1) | (~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(C, A!0, B!1)) | (~m1_rmod_2(B!1, A!0, C)) | (~v3_vectsp_2(C, 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)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))) | (v3_struct_0(B!1) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[73])).
% 0.37/0.54 tff(75,plain,
% 0.37/0.54 (((~![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)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, 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)) | (~v3_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B!1) | (~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(C, A!0, B!1)) | (~m1_rmod_2(B!1, A!0, C)) | (~v3_vectsp_2(C, 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)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))) | v3_struct_0(B!1) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[74, 68])).
% 0.37/0.54 tff(76,plain,
% 0.37/0.54 ((~![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)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, 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)) | (~v3_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B!1) | (~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(C, A!0, B!1)) | (~m1_rmod_2(B!1, A!0, C)) | (~v3_vectsp_2(C, A!0))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(77,plain,
% 0.37/0.54 ((~![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)) | (~v3_vectsp_2(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (C = B) | (~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(C, A!0, B)) | (~m1_rmod_2(B, A!0, C)) | (~v3_vectsp_2(C, A!0))))) | v3_struct_0(B!1) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.37/0.54 tff(78,plain,
% 0.37/0.54 (![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[77, 67, 66, 65, 64, 63, 62, 61, 60, 59])).
% 0.37/0.54 tff(79,plain,
% 0.37/0.54 (^[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))))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(80,plain,
% 0.37/0.54 (![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)))))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[79])).
% 0.37/0.54 tff(81,plain,
% 0.37/0.54 (^[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)))))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(82,plain,
% 0.37/0.54 (![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)))))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[81])).
% 0.37/0.54 tff(83,plain,
% 0.37/0.54 (![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)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(84,plain,
% 0.37/0.54 (^[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)))))),
% 0.37/0.55 inference(bind,[status(th)],[])).
% 0.37/0.55 tff(85,plain,
% 0.37/0.55 (![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)))),
% 0.37/0.55 inference(quant_intro,[status(thm)],[84])).
% 0.37/0.55 tff(86,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/sandbox2/benchmark/theBenchmark.p','dt_k1_rmod_5')).
% 0.37/0.55 tff(87,plain,
% 0.37/0.55 (![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)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.37/0.55 tff(88,plain,
% 0.37/0.55 (![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)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.37/0.55 tff(89,plain,(
% 0.37/0.55 ![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)))),
% 0.37/0.55 inference(skolemize,[status(sab)],[88])).
% 0.37/0.55 tff(90,plain,
% 0.37/0.55 (![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)))))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.37/0.55 tff(91,plain,
% 0.37/0.55 (![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)))))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.37/0.55 tff(92,plain,
% 0.37/0.55 (m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.37/0.55 inference(or_elim,[status(thm)],[17])).
% 0.37/0.55 tff(93,plain,
% 0.37/0.55 (v2_vectsp_2(A!0)),
% 0.37/0.55 inference(and_elim,[status(thm)],[16])).
% 0.37/0.55 tff(94,plain,
% 0.37/0.55 (~v10_vectsp_1(A!0)),
% 0.37/0.55 inference(and_elim,[status(thm)],[16])).
% 0.37/0.55 tff(95,plain,
% 0.37/0.55 (v7_group_1(A!0)),
% 0.37/0.55 inference(and_elim,[status(thm)],[16])).
% 0.37/0.55 tff(96,plain,
% 0.37/0.55 (((~![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(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(97,plain,
% 0.37/0.55 ((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(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(98,plain,
% 0.37/0.55 (((~![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(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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))))))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[97])).
% 0.37/0.55 tff(99,plain,
% 0.37/0.55 (((~![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(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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)))))),
% 0.37/0.55 inference(transitivity,[status(thm)],[98, 96])).
% 0.37/0.55 tff(100,plain,
% 0.37/0.55 ((~![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)))))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(101,plain,
% 0.37/0.55 ((~![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(A!0) | v3_struct_0(B!1) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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))))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.37/0.55 tff(102,plain,
% 0.37/0.55 (~((~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)))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[101, 48, 47, 46, 45, 44, 43, 95, 42, 41, 40, 94, 93, 39, 67, 66, 65, 64, 63, 61, 60, 92, 91])).
% 0.37/0.55 tff(103,plain,
% 0.37/0.55 (((~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)),
% 0.37/0.55 inference(tautology,[status(thm)],[])).
% 0.37/0.55 tff(104,plain,
% 0.37/0.55 (m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.37/0.55 tff(105,plain,
% 0.37/0.55 (^[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)))))))),
% 0.37/0.55 inference(bind,[status(th)],[])).
% 0.37/0.55 tff(106,plain,
% 0.37/0.55 (![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))))))),
% 0.37/0.55 inference(quant_intro,[status(thm)],[105])).
% 0.37/0.55 tff(107,plain,
% 0.37/0.55 (^[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)))))))),
% 0.37/0.55 inference(bind,[status(th)],[])).
% 0.37/0.55 tff(108,plain,
% 0.37/0.55 (![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))))))),
% 0.37/0.55 inference(quant_intro,[status(thm)],[107])).
% 0.37/0.55 tff(109,plain,
% 0.37/0.55 (![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))))))),
% 0.37/0.55 inference(transitivity,[status(thm)],[108, 106])).
% 0.37/0.55 tff(110,plain,
% 0.37/0.55 (^[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))))))))),
% 0.37/0.55 inference(bind,[status(th)],[])).
% 0.37/0.55 tff(111,plain,
% 0.37/0.55 (![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))))))),
% 0.37/0.55 inference(quant_intro,[status(thm)],[110])).
% 0.37/0.55 tff(112,plain,
% 0.37/0.55 (![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))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(113,plain,
% 0.37/0.55 (^[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))))))),
% 0.37/0.56 inference(bind,[status(th)],[])).
% 0.37/0.56 tff(114,plain,
% 0.37/0.56 (![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))))),
% 0.37/0.56 inference(quant_intro,[status(thm)],[113])).
% 0.37/0.56 tff(115,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/sandbox2/benchmark/theBenchmark.p','dt_m1_rmod_2')).
% 0.37/0.56 tff(116,plain,
% 0.37/0.56 (![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))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.37/0.56 tff(117,plain,
% 0.37/0.56 (![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))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.37/0.56 tff(118,plain,(
% 0.37/0.56 ![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))))),
% 0.37/0.56 inference(skolemize,[status(sab)],[117])).
% 0.37/0.56 tff(119,plain,
% 0.37/0.56 (![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))))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.37/0.56 tff(120,plain,
% 0.37/0.56 (![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))))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[119, 109])).
% 0.37/0.56 tff(121,plain,
% 0.37/0.56 (((~![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(A!0) | v3_struct_0(B!1) | (~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(A!0) | v3_struct_0(B!1) | (~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))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(122,plain,
% 0.37/0.56 ((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)))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~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))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(123,plain,
% 0.37/0.56 (((~![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(A!0) | v3_struct_0(B!1) | (~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)))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[122])).
% 0.37/0.56 tff(124,plain,
% 0.37/0.56 (((~![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(A!0) | v3_struct_0(B!1) | (~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))))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[123, 121])).
% 0.37/0.56 tff(125,plain,
% 0.37/0.56 ((~![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))))))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(126,plain,
% 0.37/0.56 ((~![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(A!0) | v3_struct_0(B!1) | (~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)))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.37/0.56 tff(127,plain,
% 0.37/0.56 (![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)))))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[126, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 67, 66, 65, 64, 63, 61, 60, 120])).
% 0.37/0.56 tff(128,plain,
% 0.37/0.56 (((~![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)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)))))) <=> ((~![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)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(129,plain,
% 0.37/0.56 (((~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)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(130,plain,
% 0.37/0.56 (((~![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)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3))))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[129])).
% 0.37/0.57 tff(131,plain,
% 0.37/0.57 (((~![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)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[130, 128])).
% 0.37/0.57 tff(132,plain,
% 0.37/0.57 ((~![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)))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(133,plain,
% 0.37/0.57 ((~![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)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3))))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.37/0.57 tff(134,plain,
% 0.37/0.57 (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[133, 127, 104])).
% 0.37/0.57 tff(135,plain,
% 0.37/0.57 (((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3))) | (~v3_struct_0(k1_rmod_5(A!0, B!1, D!3)))),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(136,plain,
% 0.37/0.57 (~v3_struct_0(k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.37/0.57 tff(137,plain,
% 0.37/0.57 (((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3))) | v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(138,plain,
% 0.37/0.57 (v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[137, 134])).
% 0.37/0.57 tff(139,plain,
% 0.37/0.57 (((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3))) | v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(140,plain,
% 0.37/0.57 (v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[139, 134])).
% 0.37/0.57 tff(141,plain,
% 0.37/0.57 (((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3))) | v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(142,plain,
% 0.37/0.57 (v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[141, 134])).
% 0.37/0.57 tff(143,plain,
% 0.37/0.57 (((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3))) | v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(144,plain,
% 0.37/0.57 (v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[143, 134])).
% 0.37/0.57 tff(145,plain,
% 0.37/0.57 (((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3))) | v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(146,plain,
% 0.37/0.57 (v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[145, 134])).
% 0.37/0.57 tff(147,plain,
% 0.37/0.57 (((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3))) | l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(148,plain,
% 0.37/0.57 (l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[147, 134])).
% 0.37/0.57 tff(149,plain,
% 0.37/0.57 (((~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)),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(150,plain,
% 0.37/0.57 (v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[149, 102])).
% 0.37/0.57 tff(151,plain,
% 0.37/0.57 (~(k1_rmod_5(A!0, B!1, D!3) = B!1)),
% 0.37/0.57 inference(or_elim,[status(thm)],[17])).
% 0.37/0.57 tff(152,plain,
% 0.37/0.57 (((~![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))) | ((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~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)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))) | (k1_rmod_5(A!0, B!1, D!3) = B!1) | (~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)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(153,plain,
% 0.37/0.57 ((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))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~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)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = B!1) | (~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3)))) <=> ((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~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)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(154,plain,
% 0.37/0.57 (((~![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))) | (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))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~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)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = B!1) | (~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))) | ((k1_rmod_5(A!0, B!1, D!3) = B!1) | (~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)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3)))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[153])).
% 0.37/0.57 tff(155,plain,
% 0.37/0.57 (((~![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))) | (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))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~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)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = B!1) | (~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))) | (k1_rmod_5(A!0, B!1, D!3) = B!1) | (~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)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[154, 152])).
% 0.37/0.57 tff(156,plain,
% 0.37/0.57 ((~![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))) | (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))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~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)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = B!1) | (~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(157,plain,
% 0.37/0.57 ((~![C: $i] : (v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~m1_rmod_2(C, A!0, B!1)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)) | (~v3_vectsp_2(C, A!0)) | (C = B!1) | (~m1_rmod_2(B!1, A!0, C)))) | (k1_rmod_5(A!0, B!1, D!3) = B!1) | (~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)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.37/0.57 tff(158,plain,
% 0.37/0.57 (~m1_rmod_2(B!1, A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[157, 151, 150, 104, 148, 146, 144, 142, 140, 138, 136, 78])).
% 0.37/0.57 tff(159,plain,
% 0.37/0.57 (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[158, 22])).
% 0.37/0.57 tff(160,plain,
% 0.37/0.57 (^[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))))))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(161,plain,
% 0.37/0.57 (![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))))))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[160])).
% 0.37/0.57 tff(162,plain,
% 0.37/0.57 (^[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)))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(163,plain,
% 0.37/0.57 (![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))))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[162])).
% 0.37/0.57 tff(164,plain,
% 0.37/0.57 (^[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)))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(165,plain,
% 0.37/0.58 (![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))))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[164])).
% 0.37/0.58 tff(166,plain,
% 0.37/0.58 (![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))))),
% 0.37/0.58 inference(transitivity,[status(thm)],[165, 163])).
% 0.37/0.58 tff(167,plain,
% 0.37/0.58 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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))))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(168,plain,
% 0.37/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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))))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[167])).
% 0.37/0.58 tff(169,plain,
% 0.37/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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))))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(170,plain,
% 0.37/0.58 (^[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))))))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(171,plain,
% 0.37/0.58 (![A: $i] : ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & 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))))))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[170])).
% 0.37/0.58 tff(172,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/sandbox2/benchmark/theBenchmark.p','t15_rmod_5')).
% 0.37/0.58 tff(173,plain,
% 0.37/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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))))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.37/0.58 tff(174,plain,
% 0.37/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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))))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.37/0.58 tff(175,plain,(
% 0.37/0.58 ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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))))))),
% 0.37/0.58 inference(skolemize,[status(sab)],[174])).
% 0.37/0.58 tff(176,plain,
% 0.37/0.58 (![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))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.37/0.58 tff(177,plain,
% 0.37/0.58 (![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))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[176, 166])).
% 0.37/0.58 tff(178,plain,
% 0.37/0.58 (![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))))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[177, 161])).
% 0.37/0.58 tff(179,plain,
% 0.37/0.58 (((~![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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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_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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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_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))))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(180,plain,
% 0.37/0.58 ((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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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_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))))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(181,plain,
% 0.37/0.58 (^[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)))))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(182,plain,
% 0.37/0.59 (![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)))))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[181])).
% 0.37/0.59 tff(183,plain,
% 0.37/0.59 ((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))))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[182])).
% 0.37/0.59 tff(184,plain,
% 0.37/0.59 ((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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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_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))))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[183, 180])).
% 0.37/0.59 tff(185,plain,
% 0.37/0.59 (((~![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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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_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)))))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[184])).
% 0.37/0.59 tff(186,plain,
% 0.37/0.59 (((~![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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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_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))))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[185, 179])).
% 0.37/0.59 tff(187,plain,
% 0.37/0.59 ((~![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))))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(188,plain,
% 0.37/0.59 ((~![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)) | (~v2_vectsp_2(A!0)) | (~v7_group_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_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)))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.37/0.59 tff(189,plain,
% 0.37/0.59 (![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![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)))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[188, 48, 47, 46, 45, 44, 43, 95, 42, 41, 40, 94, 93, 39, 178])).
% 0.37/0.59 tff(190,plain,
% 0.37/0.59 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![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)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(191,plain,
% 0.37/0.59 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![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)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(192,plain,
% 0.37/0.59 (^[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)))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(193,plain,
% 0.37/0.59 (![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))))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[192])).
% 0.37/0.59 tff(194,plain,
% 0.37/0.59 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![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)))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[193])).
% 0.37/0.59 tff(195,plain,
% 0.37/0.59 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![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)))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[194, 191])).
% 0.37/0.59 tff(196,plain,
% 0.37/0.59 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![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))))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[195])).
% 0.37/0.59 tff(197,plain,
% 0.37/0.59 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![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)))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[196, 190])).
% 0.37/0.59 tff(198,plain,
% 0.37/0.59 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![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)))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(199,plain,
% 0.37/0.59 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![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))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.37/0.59 tff(200,plain,
% 0.37/0.59 (![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))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[199, 67, 66, 65, 64, 63, 61, 60, 189])).
% 0.37/0.59 tff(201,plain,
% 0.37/0.59 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.37/0.59 inference(and_elim,[status(thm)],[16])).
% 0.37/0.59 tff(202,plain,
% 0.37/0.59 (((~![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(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C!2, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), 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(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C!2, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(203,plain,
% 0.37/0.60 ((~![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(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C!2, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(204,plain,
% 0.37/0.60 ((~![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(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C!2, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.37/0.60 tff(205,plain,
% 0.37/0.60 (![D: $i] : ((~r1_tarski(C!2, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[204, 201, 200])).
% 0.37/0.60 tff(206,plain,
% 0.37/0.60 (r1_tarski(C!2, D!3)),
% 0.37/0.60 inference(and_elim,[status(thm)],[18])).
% 0.37/0.60 tff(207,plain,
% 0.37/0.60 (((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D)))) | ((~r1_tarski(C!2, 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, C!2), A!0, k1_rmod_5(A!0, B!1, D!3)))) <=> ((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D)))) | (~r1_tarski(C!2, 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, C!2), A!0, k1_rmod_5(A!0, B!1, D!3)))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(208,plain,
% 0.37/0.60 ((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D)))) | ((~r1_tarski(C!2, 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, C!2), A!0, k1_rmod_5(A!0, B!1, D!3)))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(209,plain,
% 0.37/0.60 ((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D)))) | (~r1_tarski(C!2, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.37/0.60 tff(210,plain,
% 0.37/0.60 (m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[209, 206, 92, 205])).
% 0.37/0.60 tff(211,plain,
% 0.37/0.60 ($false),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[210, 159])).
% 0.37/0.60 % SZS output end Proof
% 0.37/0.60 % E exiting
%------------------------------------------------------------------------------