%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG222+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 04:58:46 AM UTC 2025
% Result : Theorem 0.57s 0.74s
% Output : Proof 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG222+1 : TPTP v9.0.0. Released v3.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 10:49:10 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.57/0.74 % SZS status Theorem
% 0.57/0.74 % SZS output start Proof
% 0.57/0.74 tff(m1_rmod_2_type, type, (
% 0.57/0.74 m1_rmod_2: ( $i * $i * $i ) > $o)).
% 0.57/0.74 tff(k2_rmod_3_type, type, (
% 0.57/0.74 k2_rmod_3: ( $i * $i * $i * $i ) > $i)).
% 0.57/0.74 tff(g1_vectsp_2_type, type, (
% 0.57/0.74 g1_vectsp_2: ( $i * $i * $i * $i * $i ) > $i)).
% 0.57/0.74 tff(u1_vectsp_2_type, type, (
% 0.57/0.74 u1_vectsp_2: ( $i * $i ) > $i)).
% 0.57/0.74 tff(k1_rmod_5_type, type, (
% 0.57/0.74 k1_rmod_5: ( $i * $i * $i ) > $i)).
% 0.57/0.74 tff(tptp_fun_D_3_type, type, (
% 0.57/0.74 tptp_fun_D_3: $i)).
% 0.57/0.74 tff(tptp_fun_B_1_type, type, (
% 0.57/0.74 tptp_fun_B_1: $i)).
% 0.57/0.74 tff(tptp_fun_A_0_type, type, (
% 0.57/0.74 tptp_fun_A_0: $i)).
% 0.57/0.74 tff(u2_struct_0_type, type, (
% 0.57/0.74 u2_struct_0: $i > $i)).
% 0.57/0.74 tff(u1_rlvect_1_type, type, (
% 0.57/0.74 u1_rlvect_1: $i > $i)).
% 0.57/0.74 tff(u1_struct_0_type, type, (
% 0.57/0.74 u1_struct_0: $i > $i)).
% 0.57/0.74 tff(tptp_fun_C_2_type, type, (
% 0.57/0.74 tptp_fun_C_2: $i)).
% 0.57/0.74 tff(k5_subset_1_type, type, (
% 0.57/0.74 k5_subset_1: ( $i * $i * $i ) > $i)).
% 0.57/0.74 tff(l1_vectsp_2_type, type, (
% 0.57/0.74 l1_vectsp_2: ( $i * $i ) > $o)).
% 0.57/0.74 tff(v5_vectsp_2_type, type, (
% 0.57/0.74 v5_vectsp_2: ( $i * $i ) > $o)).
% 0.57/0.74 tff(v6_rlvect_1_type, type, (
% 0.57/0.74 v6_rlvect_1: $i > $o)).
% 0.57/0.74 tff(v5_rlvect_1_type, type, (
% 0.57/0.74 v5_rlvect_1: $i > $o)).
% 0.57/0.74 tff(v4_rlvect_1_type, type, (
% 0.57/0.74 v4_rlvect_1: $i > $o)).
% 0.57/0.74 tff(v3_rlvect_1_type, type, (
% 0.57/0.74 v3_rlvect_1: $i > $o)).
% 0.57/0.74 tff(v3_struct_0_type, type, (
% 0.57/0.74 v3_struct_0: $i > $o)).
% 0.57/0.74 tff(v3_vectsp_2_type, type, (
% 0.57/0.74 v3_vectsp_2: ( $i * $i ) > $o)).
% 0.57/0.74 tff(l3_vectsp_1_type, type, (
% 0.57/0.74 l3_vectsp_1: $i > $o)).
% 0.57/0.74 tff(v2_vectsp_2_type, type, (
% 0.57/0.74 v2_vectsp_2: $i > $o)).
% 0.57/0.74 tff(v8_vectsp_1_type, type, (
% 0.57/0.74 v8_vectsp_1: $i > $o)).
% 0.57/0.74 tff(v7_vectsp_1_type, type, (
% 0.57/0.74 v7_vectsp_1: $i > $o)).
% 0.57/0.74 tff(v6_vectsp_1_type, type, (
% 0.57/0.74 v6_vectsp_1: $i > $o)).
% 0.57/0.74 tff(v7_group_1_type, type, (
% 0.57/0.74 v7_group_1: $i > $o)).
% 0.57/0.74 tff(v4_group_1_type, type, (
% 0.57/0.74 v4_group_1: $i > $o)).
% 0.57/0.74 tff(m1_subset_1_type, type, (
% 0.57/0.74 m1_subset_1: ( $i * $i ) > $o)).
% 0.57/0.74 tff(k1_zfmisc_1_type, type, (
% 0.57/0.74 k1_zfmisc_1: $i > $i)).
% 0.57/0.74 tff(v10_vectsp_1_type, type, (
% 0.57/0.74 v10_vectsp_1: $i > $o)).
% 0.57/0.74 tff(l1_struct_0_type, type, (
% 0.57/0.74 l1_struct_0: $i > $o)).
% 0.57/0.74 tff(l2_struct_0_type, type, (
% 0.57/0.74 l2_struct_0: $i > $o)).
% 0.57/0.74 tff(l1_rlvect_1_type, type, (
% 0.57/0.74 l1_rlvect_1: $i > $o)).
% 0.57/0.74 tff(l2_vectsp_1_type, type, (
% 0.57/0.74 l2_vectsp_1: $i > $o)).
% 0.57/0.74 tff(k3_xboole_0_type, type, (
% 0.57/0.74 k3_xboole_0: ( $i * $i ) > $i)).
% 0.57/0.74 tff(r1_tarski_type, type, (
% 0.57/0.74 r1_tarski: ( $i * $i ) > $o)).
% 0.57/0.74 tff(1,plain,
% 0.57/0.74 (^[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))))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(2,plain,
% 0.57/0.74 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B))))) <=> ![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)))))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[1])).
% 0.57/0.74 tff(3,plain,
% 0.57/0.74 (^[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)))))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(4,plain,
% 0.57/0.74 (![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)))))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[3])).
% 0.57/0.74 tff(5,plain,
% 0.57/0.74 (![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)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(6,plain,
% 0.57/0.74 (^[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)))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(7,plain,
% 0.57/0.74 (![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)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[6])).
% 0.57/0.74 tff(8,axiom,(![A: $i, B: $i, C: $i] : ((((((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) => (v3_vectsp_2(k1_rmod_5(A, B, C), A) & m1_rmod_2(k1_rmod_5(A, B, C), A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_rmod_5')).
% 0.57/0.74 tff(9,plain,
% 0.57/0.74 (![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)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.57/0.74 tff(10,plain,
% 0.57/0.74 (![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)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.57/0.74 tff(11,plain,(
% 0.57/0.74 ![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)))),
% 0.57/0.74 inference(skolemize,[status(sab)],[10])).
% 0.57/0.74 tff(12,plain,
% 0.57/0.74 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.57/0.74 tff(13,plain,
% 0.57/0.74 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.57/0.74 tff(14,plain,
% 0.57/0.74 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(15,plain,
% 0.57/0.74 ((((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))) <=> ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(16,plain,
% 0.57/0.75 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & (((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))))))) <=> (((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[15])).
% 0.57/0.75 tff(17,plain,
% 0.57/0.75 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & (((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))))),
% 0.57/0.75 inference(transitivity,[status(thm)],[16, 14])).
% 0.57/0.75 tff(18,plain,
% 0.57/0.75 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D))))))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(19,plain,
% 0.57/0.75 ((~![A: $i] : ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D))))))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(20,axiom,(~![A: $i] : ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_rmod_5')).
% 0.57/0.75 tff(21,plain,
% 0.57/0.75 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.57/0.75 tff(22,plain,
% 0.57/0.75 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.57/0.75 tff(23,plain,
% 0.57/0.75 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.57/0.75 tff(24,plain,
% 0.57/0.75 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | m1_rmod_2(k1_rmod_5(A, B, k5_subset_1(u1_struct_0(B), C, D)), A, k2_rmod_3(A, B, k1_rmod_5(A, B, C), k1_rmod_5(A, B, D)))))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.57/0.75 tff(25,plain,
% 0.57/0.75 ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.57/0.75 tff(26,plain,
% 0.57/0.75 (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))))),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(27,plain,
% 0.57/0.75 (m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.57/0.75 inference(or_elim,[status(thm)],[26])).
% 0.57/0.75 tff(28,plain,
% 0.57/0.75 (l1_vectsp_2(B!1, A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(29,plain,
% 0.57/0.75 (v5_vectsp_2(B!1, A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(30,plain,
% 0.57/0.75 (v6_rlvect_1(B!1)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(31,plain,
% 0.57/0.75 (v5_rlvect_1(B!1)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(32,plain,
% 0.57/0.75 (v4_rlvect_1(B!1)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(33,plain,
% 0.57/0.75 (v3_rlvect_1(B!1)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(34,plain,
% 0.57/0.75 (~v3_struct_0(B!1)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(35,plain,
% 0.57/0.75 (l3_vectsp_1(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(36,plain,
% 0.57/0.75 (v2_vectsp_2(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(37,plain,
% 0.57/0.75 (~v10_vectsp_1(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(38,plain,
% 0.57/0.75 (v8_vectsp_1(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(39,plain,
% 0.57/0.75 (v7_vectsp_1(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(40,plain,
% 0.57/0.75 (v6_vectsp_1(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(41,plain,
% 0.57/0.75 (v7_group_1(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(42,plain,
% 0.57/0.75 (v4_group_1(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(43,plain,
% 0.57/0.75 (v6_rlvect_1(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(44,plain,
% 0.57/0.75 (v5_rlvect_1(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(45,plain,
% 0.57/0.75 (v4_rlvect_1(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(46,plain,
% 0.57/0.75 (v3_rlvect_1(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(47,plain,
% 0.57/0.75 (~v3_struct_0(A!0)),
% 0.57/0.75 inference(and_elim,[status(thm)],[25])).
% 0.57/0.75 tff(48,plain,
% 0.57/0.75 (((~![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)))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(49,plain,
% 0.57/0.75 ((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)))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(50,plain,
% 0.57/0.75 (((~![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))))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[49])).
% 0.57/0.75 tff(51,plain,
% 0.57/0.75 (((~![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)))))),
% 0.57/0.75 inference(transitivity,[status(thm)],[50, 48])).
% 0.57/0.75 tff(52,plain,
% 0.57/0.75 ((~![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)))))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(53,plain,
% 0.57/0.75 ((~![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))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.57/0.75 tff(54,plain,
% 0.57/0.75 (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[53, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 13])).
% 0.57/0.75 tff(55,plain,
% 0.57/0.75 (((~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1))) | m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)),
% 0.57/0.75 inference(tautology,[status(thm)],[])).
% 0.57/0.75 tff(56,plain,
% 0.57/0.75 (m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.57/0.75 tff(57,plain,
% 0.57/0.75 (^[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)))))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(58,plain,
% 0.57/0.75 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))) <=> ![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))))))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[57])).
% 0.57/0.75 tff(59,plain,
% 0.57/0.75 (^[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)))))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(60,plain,
% 0.57/0.75 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))) <=> ![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))))))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[59])).
% 0.57/0.75 tff(61,plain,
% 0.57/0.75 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A)) | (~l1_vectsp_2(C, A)))))) <=> ![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))))))),
% 0.57/0.75 inference(transitivity,[status(thm)],[60, 58])).
% 0.57/0.75 tff(62,plain,
% 0.57/0.75 (^[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))))))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(63,plain,
% 0.57/0.75 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ((~v3_struct_0(C)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C, A) & l1_vectsp_2(C, A)))) <=> ![A: $i, B: $i] : (v3_struct_0(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))))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[62])).
% 0.57/0.76 tff(64,plain,
% 0.57/0.76 (![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))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(65,plain,
% 0.57/0.76 (^[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))))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(66,plain,
% 0.57/0.76 (![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))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[65])).
% 0.57/0.76 tff(67,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')).
% 0.57/0.76 tff(68,plain,
% 0.57/0.76 (![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))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.57/0.76 tff(69,plain,
% 0.57/0.76 (![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))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.57/0.76 tff(70,plain,(
% 0.57/0.76 ![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))))),
% 0.57/0.76 inference(skolemize,[status(sab)],[69])).
% 0.57/0.76 tff(71,plain,
% 0.57/0.76 (![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))))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.57/0.76 tff(72,plain,
% 0.57/0.76 (![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))))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.57/0.76 tff(73,plain,
% 0.57/0.76 (((~![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))))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(74,plain,
% 0.57/0.76 ((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))))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(75,plain,
% 0.57/0.76 (((~![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)))))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[74])).
% 0.57/0.76 tff(76,plain,
% 0.57/0.76 (((~![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))))))),
% 0.57/0.76 inference(transitivity,[status(thm)],[75, 73])).
% 0.57/0.76 tff(77,plain,
% 0.57/0.76 ((~![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))))))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(78,plain,
% 0.57/0.76 ((~![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)))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.57/0.76 tff(79,plain,
% 0.57/0.76 (![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)))))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[78, 47, 46, 45, 44, 43, 42, 40, 39, 38, 35, 34, 33, 32, 31, 30, 29, 28, 72])).
% 0.57/0.76 tff(80,plain,
% 0.57/0.76 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(81,plain,
% 0.57/0.77 (((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))))) <=> ((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(82,plain,
% 0.57/0.77 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))))))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[81])).
% 0.57/0.77 tff(83,plain,
% 0.57/0.77 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))))),
% 0.57/0.77 inference(transitivity,[status(thm)],[82, 80])).
% 0.57/0.77 tff(84,plain,
% 0.57/0.77 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, 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)))))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(85,plain,
% 0.57/0.77 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.57/0.77 tff(86,plain,
% 0.57/0.77 (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[85, 79, 56])).
% 0.57/0.77 tff(87,plain,
% 0.57/0.77 (((~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, D!3)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, D!3))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))) | l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.57/0.77 inference(tautology,[status(thm)],[])).
% 0.57/0.77 tff(88,plain,
% 0.57/0.77 (l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.57/0.77 tff(89,plain,
% 0.57/0.77 (^[A: $i] : refl(((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))) <=> ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(90,plain,
% 0.57/0.77 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[89])).
% 0.57/0.77 tff(91,plain,
% 0.57/0.77 (^[A: $i] : rewrite(((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(92,plain,
% 0.57/0.77 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[91])).
% 0.57/0.77 tff(93,plain,
% 0.57/0.77 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(94,plain,
% 0.57/0.77 (^[A: $i] : rewrite((l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(95,plain,
% 0.57/0.77 (![A: $i] : (l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[94])).
% 0.57/0.77 tff(96,axiom,(![A: $i] : (l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_vectsp_1')).
% 0.57/0.77 tff(97,plain,
% 0.57/0.77 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.57/0.77 tff(98,plain,
% 0.57/0.77 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.57/0.77 tff(99,plain,(
% 0.57/0.77 ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.57/0.77 inference(skolemize,[status(sab)],[98])).
% 0.57/0.77 tff(100,plain,
% 0.57/0.77 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.57/0.77 tff(101,plain,
% 0.57/0.77 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.57/0.77 tff(102,plain,
% 0.57/0.77 (((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | ((~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))) <=> ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | (~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(103,plain,
% 0.57/0.77 ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | ((~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(104,plain,
% 0.57/0.77 ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | (~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0))))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.57/0.77 tff(105,plain,
% 0.57/0.77 (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[104, 35, 101])).
% 0.57/0.77 tff(106,plain,
% 0.57/0.77 (((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0))) | l1_rlvect_1(A!0)),
% 0.57/0.77 inference(tautology,[status(thm)],[])).
% 0.57/0.77 tff(107,plain,
% 0.57/0.77 (l1_rlvect_1(A!0)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.57/0.77 tff(108,plain,
% 0.57/0.77 (^[A: $i] : refl((l2_struct_0(A) | (~l1_rlvect_1(A))) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(109,plain,
% 0.57/0.77 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[108])).
% 0.57/0.77 tff(110,plain,
% 0.57/0.77 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(111,plain,
% 0.57/0.77 (^[A: $i] : rewrite((l1_rlvect_1(A) => l2_struct_0(A)) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(112,plain,
% 0.57/0.77 (![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A)) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[111])).
% 0.57/0.77 tff(113,axiom,(![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_rlvect_1')).
% 0.57/0.77 tff(114,plain,
% 0.57/0.77 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.57/0.77 tff(115,plain,
% 0.57/0.77 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.57/0.77 tff(116,plain,(
% 0.57/0.77 ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.57/0.77 inference(skolemize,[status(sab)],[115])).
% 0.57/0.77 tff(117,plain,
% 0.57/0.77 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.57/0.77 tff(118,plain,
% 0.57/0.77 (((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))) <=> ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(119,plain,
% 0.57/0.77 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(120,plain,
% 0.57/0.77 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(A!0) | (~l1_rlvect_1(A!0))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.57/0.77 tff(121,plain,
% 0.57/0.77 (l2_struct_0(A!0)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[120, 117, 107])).
% 0.57/0.77 tff(122,plain,
% 0.57/0.77 (^[A: $i] : refl((l1_struct_0(A) | (~l2_struct_0(A))) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(123,plain,
% 0.57/0.77 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[122])).
% 0.57/0.77 tff(124,plain,
% 0.57/0.77 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(125,plain,
% 0.57/0.77 (^[A: $i] : rewrite((l2_struct_0(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(126,plain,
% 0.57/0.77 (![A: $i] : (l2_struct_0(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[125])).
% 0.57/0.77 tff(127,axiom,(![A: $i] : (l2_struct_0(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_struct_0')).
% 0.57/0.77 tff(128,plain,
% 0.57/0.77 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.57/0.77 tff(129,plain,
% 0.57/0.77 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.57/0.77 tff(130,plain,(
% 0.57/0.77 ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.57/0.77 inference(skolemize,[status(sab)],[129])).
% 0.57/0.77 tff(131,plain,
% 0.57/0.77 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.57/0.77 tff(132,plain,
% 0.57/0.77 (((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | (l1_struct_0(A!0) | (~l2_struct_0(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | l1_struct_0(A!0) | (~l2_struct_0(A!0)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(133,plain,
% 0.57/0.77 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | (l1_struct_0(A!0) | (~l2_struct_0(A!0)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(134,plain,
% 0.57/0.77 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | l1_struct_0(A!0) | (~l2_struct_0(A!0))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.57/0.77 tff(135,plain,
% 0.57/0.77 (l1_struct_0(A!0)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[134, 131, 121])).
% 0.57/0.77 tff(136,plain,
% 0.57/0.77 (((~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)),
% 0.57/0.77 inference(tautology,[status(thm)],[])).
% 0.57/0.77 tff(137,plain,
% 0.57/0.77 (v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[136, 54])).
% 0.57/0.77 tff(138,plain,
% 0.57/0.77 (^[A: $i, B: $i] : refl(((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(139,plain,
% 0.57/0.77 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[138])).
% 0.57/0.77 tff(140,plain,
% 0.57/0.77 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_struct_0(A) & l1_vectsp_2(B, A)) <=> (~((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))), ((~(l1_struct_0(A) & l1_vectsp_2(B, A))) <=> (~(~((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))))), rewrite((~(~((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))) <=> ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A)))), ((~(l1_struct_0(A) & l1_vectsp_2(B, A))) <=> ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))), (((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A)))))), rewrite(((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A)))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))), (((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(141,plain,
% 0.57/0.77 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[140])).
% 0.57/0.77 tff(142,plain,
% 0.57/0.77 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(143,plain,
% 0.57/0.77 (^[A: $i, B: $i] : trans(monotonicity(rewrite((v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> ((~v3_vectsp_2(B, A)) | (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))), (((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((l1_struct_0(A) & l1_vectsp_2(B, A)) => ((~v3_vectsp_2(B, A)) | (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))))), rewrite(((l1_struct_0(A) & l1_vectsp_2(B, A)) => ((~v3_vectsp_2(B, A)) | (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))), (((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(144,plain,
% 0.57/0.77 (![A: $i, B: $i] : ((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[143])).
% 0.57/0.77 tff(145,axiom,(![A: $i, B: $i] : ((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v3_vectsp_2')).
% 0.57/0.77 tff(146,plain,
% 0.57/0.77 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.57/0.77 tff(147,plain,
% 0.57/0.77 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.57/0.77 tff(148,plain,(
% 0.57/0.77 ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.57/0.77 inference(skolemize,[status(sab)],[147])).
% 0.57/0.77 tff(149,plain,
% 0.57/0.77 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.57/0.77 tff(150,plain,
% 0.57/0.77 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[149, 139])).
% 0.57/0.77 tff(151,plain,
% 0.57/0.77 (((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))) <=> ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(152,plain,
% 0.57/0.77 (((k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_struct_0(A!0))) <=> ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(153,plain,
% 0.57/0.77 (((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[152])).
% 0.57/0.77 tff(154,plain,
% 0.57/0.77 (((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)))),
% 0.57/0.77 inference(transitivity,[status(thm)],[153, 151])).
% 0.57/0.77 tff(155,plain,
% 0.57/0.77 ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (~l1_struct_0(A!0)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(156,plain,
% 0.57/0.77 ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.57/0.77 tff(157,plain,
% 0.57/0.77 ((~l1_struct_0(A!0)) | (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, D!3), A!0))),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[156, 150, 137])).
% 0.57/0.77 tff(158,plain,
% 0.57/0.77 (k1_rmod_5(A!0, B!1, D!3) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[157, 135, 88])).
% 0.57/0.77 tff(159,plain,
% 0.57/0.77 (g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))) = k1_rmod_5(A!0, B!1, D!3)),
% 0.57/0.77 inference(symmetry,[status(thm)],[158])).
% 0.57/0.77 tff(160,plain,
% 0.57/0.77 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.57/0.77 inference(and_elim,[status(thm)],[25])).
% 0.57/0.77 tff(161,plain,
% 0.57/0.77 (((~![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(C!2, 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, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~m1_subset_1(C!2, 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, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(162,plain,
% 0.57/0.78 ((v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1))))) <=> (v10_vectsp_1(A!0) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~m1_subset_1(C!2, 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, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(163,plain,
% 0.57/0.78 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v10_vectsp_1(A!0) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~m1_subset_1(C!2, 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, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1))))))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[162])).
% 0.57/0.78 tff(164,plain,
% 0.57/0.78 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~m1_subset_1(C!2, 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, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))),
% 0.57/0.78 inference(transitivity,[status(thm)],[163, 161])).
% 0.57/0.78 tff(165,plain,
% 0.57/0.78 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))))),
% 0.57/0.78 inference(quant_inst,[status(thm)],[])).
% 0.57/0.78 tff(166,plain,
% 0.57/0.78 ((~![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(C!2, 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, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1))))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.57/0.78 tff(167,plain,
% 0.57/0.78 (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)))),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[166, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 160, 13])).
% 0.57/0.78 tff(168,plain,
% 0.57/0.78 (((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)),
% 0.57/0.78 inference(tautology,[status(thm)],[])).
% 0.57/0.78 tff(169,plain,
% 0.57/0.78 (m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.57/0.78 tff(170,plain,
% 0.57/0.78 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(171,plain,
% 0.57/0.78 (((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))))) <=> ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(172,plain,
% 0.57/0.78 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))))))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[171])).
% 0.57/0.78 tff(173,plain,
% 0.57/0.78 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))),
% 0.57/0.78 inference(transitivity,[status(thm)],[172, 170])).
% 0.57/0.78 tff(174,plain,
% 0.57/0.78 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~(v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))))),
% 0.57/0.78 inference(quant_inst,[status(thm)],[])).
% 0.57/0.78 tff(175,plain,
% 0.57/0.78 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | (~(v3_struct_0(C) | (~v3_rlvect_1(C)) | (~v4_rlvect_1(C)) | (~v5_rlvect_1(C)) | (~v6_rlvect_1(C)) | (~v5_vectsp_2(C, A!0)) | (~l1_vectsp_2(C, A!0)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)) | (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.57/0.78 tff(176,plain,
% 0.57/0.78 (~((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[175, 79, 169])).
% 0.57/0.78 tff(177,plain,
% 0.57/0.78 (((~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | v3_struct_0(k1_rmod_5(A!0, B!1, C!2)) | (~v3_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v4_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v6_rlvect_1(k1_rmod_5(A!0, B!1, C!2))) | (~v5_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))) | l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)),
% 0.57/0.78 inference(tautology,[status(thm)],[])).
% 0.57/0.78 tff(178,plain,
% 0.57/0.78 (l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.57/0.78 tff(179,plain,
% 0.57/0.78 (((~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1))) | v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)),
% 0.57/0.78 inference(tautology,[status(thm)],[])).
% 0.57/0.78 tff(180,plain,
% 0.57/0.78 (v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[179, 167])).
% 0.57/0.78 tff(181,plain,
% 0.57/0.78 (((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))) <=> ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(182,plain,
% 0.57/0.78 (((k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_struct_0(A!0))) <=> ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(183,plain,
% 0.57/0.78 (((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[182])).
% 0.57/0.78 tff(184,plain,
% 0.57/0.78 (((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)))),
% 0.57/0.79 inference(transitivity,[status(thm)],[183, 181])).
% 0.57/0.79 tff(185,plain,
% 0.57/0.79 ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (~l1_struct_0(A!0)))),
% 0.57/0.79 inference(quant_inst,[status(thm)],[])).
% 0.57/0.79 tff(186,plain,
% 0.57/0.79 ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | (~l1_struct_0(A!0)) | (~v3_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.57/0.79 tff(187,plain,
% 0.57/0.79 ((~l1_struct_0(A!0)) | (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) | (~l1_vectsp_2(k1_rmod_5(A!0, B!1, C!2), A!0))),
% 0.57/0.79 inference(unit_resolution,[status(thm)],[186, 150, 180])).
% 0.57/0.79 tff(188,plain,
% 0.57/0.79 (k1_rmod_5(A!0, B!1, C!2) = g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))),
% 0.57/0.79 inference(unit_resolution,[status(thm)],[187, 135, 178])).
% 0.57/0.79 tff(189,plain,
% 0.57/0.79 (g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))) = k1_rmod_5(A!0, B!1, C!2)),
% 0.57/0.79 inference(symmetry,[status(thm)],[188])).
% 0.57/0.79 tff(190,plain,
% 0.57/0.79 (k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) = k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))),
% 0.57/0.79 inference(monotonicity,[status(thm)],[189, 159])).
% 0.57/0.79 tff(191,plain,
% 0.57/0.79 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))),
% 0.57/0.79 inference(monotonicity,[status(thm)],[190])).
% 0.57/0.79 tff(192,plain,
% 0.57/0.79 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3))) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))),
% 0.57/0.79 inference(symmetry,[status(thm)],[191])).
% 0.57/0.79 tff(193,plain,
% 0.57/0.79 ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))) <=> (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))),
% 0.57/0.79 inference(monotonicity,[status(thm)],[192])).
% 0.57/0.79 tff(194,plain,
% 0.57/0.79 (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, k1_rmod_5(A!0, B!1, C!2), k1_rmod_5(A!0, B!1, D!3)))),
% 0.57/0.79 inference(or_elim,[status(thm)],[26])).
% 0.57/0.79 tff(195,plain,
% 0.57/0.79 (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.57/0.79 tff(196,plain,
% 0.57/0.79 (^[A: $i, B: $i, C: $i] : refl(((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.57/0.79 inference(bind,[status(th)],[])).
% 0.57/0.79 tff(197,plain,
% 0.57/0.79 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.57/0.79 inference(quant_intro,[status(thm)],[196])).
% 0.57/0.79 tff(198,plain,
% 0.57/0.79 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.57/0.79 inference(bind,[status(th)],[])).
% 0.57/0.79 tff(199,plain,
% 0.57/0.79 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.57/0.79 inference(quant_intro,[status(thm)],[198])).
% 0.57/0.79 tff(200,plain,
% 0.57/0.79 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 0.57/0.79 inference(rewrite,[status(thm)],[])).
% 0.57/0.79 tff(201,plain,
% 0.57/0.79 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))))),
% 0.57/0.79 inference(bind,[status(th)],[])).
% 0.57/0.79 tff(202,plain,
% 0.57/0.79 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 0.57/0.79 inference(quant_intro,[status(thm)],[201])).
% 0.57/0.79 tff(203,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k5_subset_1')).
% 0.57/0.79 tff(204,plain,
% 0.57/0.79 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.57/0.79 tff(205,plain,
% 0.57/0.79 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.57/0.79 tff(206,plain,(
% 0.57/0.79 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 0.57/0.79 inference(skolemize,[status(sab)],[205])).
% 0.57/0.79 tff(207,plain,
% 0.57/0.79 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[206, 199])).
% 0.57/0.79 tff(208,plain,
% 0.57/0.79 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[207, 197])).
% 0.57/0.79 tff(209,plain,
% 0.57/0.79 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)))),
% 0.57/0.79 inference(rewrite,[status(thm)],[])).
% 0.57/0.79 tff(210,plain,
% 0.57/0.79 (((k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)))),
% 0.57/0.79 inference(rewrite,[status(thm)],[])).
% 0.57/0.79 tff(211,plain,
% 0.57/0.79 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3))))),
% 0.57/0.79 inference(monotonicity,[status(thm)],[210])).
% 0.57/0.79 tff(212,plain,
% 0.57/0.79 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)))),
% 0.57/0.79 inference(transitivity,[status(thm)],[211, 209])).
% 0.57/0.79 tff(213,plain,
% 0.57/0.79 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.57/0.79 inference(quant_inst,[status(thm)],[])).
% 0.57/0.79 tff(214,plain,
% 0.57/0.79 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.57/0.79 tff(215,plain,
% 0.57/0.79 (k5_subset_1(u1_struct_0(B!1), C!2, D!3) = k3_xboole_0(C!2, D!3)),
% 0.57/0.79 inference(unit_resolution,[status(thm)],[214, 160, 27, 208])).
% 0.57/0.79 tff(216,plain,
% 0.57/0.79 (k3_xboole_0(C!2, D!3) = k5_subset_1(u1_struct_0(B!1), C!2, D!3)),
% 0.57/0.79 inference(symmetry,[status(thm)],[215])).
% 0.57/0.79 tff(217,plain,
% 0.57/0.79 (k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)) = k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3))),
% 0.57/0.79 inference(monotonicity,[status(thm)],[216])).
% 0.57/0.79 tff(218,plain,
% 0.57/0.79 (k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)) = k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3))),
% 0.57/0.79 inference(symmetry,[status(thm)],[217])).
% 0.57/0.79 tff(219,plain,
% 0.57/0.79 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.57/0.79 inference(monotonicity,[status(thm)],[218, 159])).
% 0.57/0.79 tff(220,plain,
% 0.57/0.79 (m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3)) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))),
% 0.57/0.79 inference(symmetry,[status(thm)],[219])).
% 0.57/0.79 tff(221,plain,
% 0.57/0.79 (^[A: $i, B: $i] : refl((k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> (k3_xboole_0(A, B) = k3_xboole_0(B, A)))),
% 0.57/0.79 inference(bind,[status(th)],[])).
% 0.57/0.79 tff(222,plain,
% 0.57/0.79 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.57/0.79 inference(quant_intro,[status(thm)],[221])).
% 0.57/0.79 tff(223,plain,
% 0.57/0.79 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.57/0.79 inference(rewrite,[status(thm)],[])).
% 0.57/0.79 tff(224,axiom,(![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.57/0.79 tff(225,plain,
% 0.57/0.79 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.57/0.79 tff(226,plain,(
% 0.57/0.79 ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.57/0.79 inference(skolemize,[status(sab)],[225])).
% 0.57/0.79 tff(227,plain,
% 0.57/0.79 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.57/0.79 tff(228,plain,
% 0.57/0.79 ((~![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))) | (k3_xboole_0(C!2, D!3) = k3_xboole_0(D!3, C!2))),
% 0.57/0.79 inference(quant_inst,[status(thm)],[])).
% 0.57/0.79 tff(229,plain,
% 0.57/0.79 (k3_xboole_0(C!2, D!3) = k3_xboole_0(D!3, C!2)),
% 0.57/0.79 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.57/0.79 tff(230,plain,
% 0.57/0.79 (r1_tarski(k3_xboole_0(C!2, D!3), D!3) <=> r1_tarski(k3_xboole_0(D!3, C!2), D!3)),
% 0.57/0.79 inference(monotonicity,[status(thm)],[229])).
% 0.57/0.79 tff(231,plain,
% 0.57/0.79 (r1_tarski(k3_xboole_0(D!3, C!2), D!3) <=> r1_tarski(k3_xboole_0(C!2, D!3), D!3)),
% 0.57/0.79 inference(symmetry,[status(thm)],[230])).
% 0.57/0.79 tff(232,plain,
% 0.57/0.79 (^[A: $i, B: $i] : refl(r1_tarski(k3_xboole_0(A, B), A) <=> r1_tarski(k3_xboole_0(A, B), A))),
% 0.57/0.79 inference(bind,[status(th)],[])).
% 0.57/0.79 tff(233,plain,
% 0.57/0.79 (![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A) <=> ![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)),
% 0.57/0.79 inference(quant_intro,[status(thm)],[232])).
% 0.57/0.79 tff(234,plain,
% 0.57/0.79 (![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A) <=> ![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)),
% 0.57/0.79 inference(rewrite,[status(thm)],[])).
% 0.57/0.79 tff(235,axiom,(![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t17_xboole_1')).
% 0.57/0.79 tff(236,plain,
% 0.57/0.79 (![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.57/0.79 tff(237,plain,(
% 0.57/0.79 ![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)),
% 0.57/0.79 inference(skolemize,[status(sab)],[236])).
% 0.57/0.79 tff(238,plain,
% 0.57/0.79 (![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[237, 233])).
% 0.57/0.79 tff(239,plain,
% 0.57/0.79 ((~![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)) | r1_tarski(k3_xboole_0(D!3, C!2), D!3)),
% 0.57/0.79 inference(quant_inst,[status(thm)],[])).
% 0.57/0.79 tff(240,plain,
% 0.57/0.79 (r1_tarski(k3_xboole_0(D!3, C!2), D!3)),
% 0.57/0.79 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.57/0.79 tff(241,plain,
% 0.57/0.79 (r1_tarski(k3_xboole_0(C!2, D!3), D!3)),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[240, 231])).
% 0.57/0.79 tff(242,plain,
% 0.57/0.79 (^[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))))))))),
% 0.57/0.79 inference(bind,[status(th)],[])).
% 0.57/0.79 tff(243,plain,
% 0.57/0.79 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![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))))))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[242])).
% 0.63/0.79 tff(244,plain,
% 0.63/0.79 (^[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)))))),
% 0.63/0.79 inference(bind,[status(th)],[])).
% 0.63/0.79 tff(245,plain,
% 0.63/0.79 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (m1_rmod_2(k1_rmod_5(A, B, C), A, k1_rmod_5(A, B, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~r1_tarski(C, D)))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![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))))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[244])).
% 0.63/0.79 tff(246,plain,
% 0.63/0.79 (^[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)))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(247,plain,
% 0.63/0.80 (![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))))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[246])).
% 0.63/0.80 tff(248,plain,
% 0.63/0.80 (![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))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[247, 245])).
% 0.63/0.80 tff(249,plain,
% 0.63/0.80 (^[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))))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(250,plain,
% 0.63/0.80 (![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))))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[249])).
% 0.63/0.80 tff(251,plain,
% 0.63/0.80 (![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))))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(252,plain,
% 0.63/0.80 (^[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))))))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(253,plain,
% 0.63/0.80 (![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))))))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[252])).
% 0.63/0.80 tff(254,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')).
% 0.63/0.80 tff(255,plain,
% 0.63/0.80 (![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))))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.63/0.80 tff(256,plain,
% 0.63/0.80 (![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))))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[255, 251])).
% 0.63/0.80 tff(257,plain,(
% 0.63/0.80 ![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))))))),
% 0.63/0.80 inference(skolemize,[status(sab)],[256])).
% 0.63/0.80 tff(258,plain,
% 0.63/0.80 (![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))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[257, 250])).
% 0.63/0.80 tff(259,plain,
% 0.63/0.80 (![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))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[258, 248])).
% 0.63/0.80 tff(260,plain,
% 0.63/0.80 (![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))))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[259, 243])).
% 0.63/0.80 tff(261,plain,
% 0.63/0.80 (((~![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))))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(262,plain,
% 0.63/0.80 ((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))))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(263,plain,
% 0.63/0.80 (^[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)))))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(264,plain,
% 0.63/0.81 (![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)))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[263])).
% 0.63/0.81 tff(265,plain,
% 0.63/0.81 ((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))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[264])).
% 0.63/0.81 tff(266,plain,
% 0.63/0.81 ((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))))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[265, 262])).
% 0.63/0.81 tff(267,plain,
% 0.63/0.81 (((~![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)))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[266])).
% 0.63/0.81 tff(268,plain,
% 0.63/0.81 (((~![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))))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[267, 261])).
% 0.63/0.81 tff(269,plain,
% 0.63/0.81 ((~![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))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(270,plain,
% 0.63/0.81 ((~![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)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.63/0.81 tff(271,plain,
% 0.63/0.81 (![B: $i] : (v3_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)))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[270, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 260])).
% 0.63/0.81 tff(272,plain,
% 0.63/0.81 (((~![B: $i] : (v3_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)))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(273,plain,
% 0.63/0.81 ((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)))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(274,plain,
% 0.63/0.81 (^[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)))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(275,plain,
% 0.63/0.81 (![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))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[274])).
% 0.63/0.81 tff(276,plain,
% 0.63/0.81 ((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)))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[275])).
% 0.63/0.81 tff(277,plain,
% 0.63/0.81 ((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)))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[276, 273])).
% 0.63/0.81 tff(278,plain,
% 0.63/0.81 (((~![B: $i] : (v3_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))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[277])).
% 0.63/0.81 tff(279,plain,
% 0.63/0.81 (((~![B: $i] : (v3_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)))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[278, 272])).
% 0.63/0.81 tff(280,plain,
% 0.63/0.81 ((~![B: $i] : (v3_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)))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(281,plain,
% 0.63/0.81 ((~![B: $i] : (v3_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))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.63/0.81 tff(282,plain,
% 0.63/0.81 (![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))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[281, 34, 33, 32, 31, 30, 29, 28, 271])).
% 0.63/0.81 tff(283,plain,
% 0.63/0.81 (m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[216])).
% 0.63/0.81 tff(284,plain,
% 0.63/0.81 (m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.63/0.81 inference(symmetry,[status(thm)],[283])).
% 0.63/0.81 tff(285,plain,
% 0.63/0.81 (^[A: $i, B: $i, C: $i] : refl((m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(286,plain,
% 0.63/0.81 (![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[285])).
% 0.63/0.81 tff(287,plain,
% 0.63/0.81 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(288,plain,
% 0.63/0.81 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[287])).
% 0.63/0.81 tff(289,plain,
% 0.63/0.81 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(290,plain,
% 0.63/0.81 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(291,plain,
% 0.63/0.81 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[290])).
% 0.63/0.81 tff(292,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_subset_1')).
% 0.63/0.81 tff(293,plain,
% 0.63/0.81 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.63/0.81 tff(294,plain,
% 0.63/0.81 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.63/0.81 tff(295,plain,(
% 0.63/0.81 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 0.63/0.81 inference(skolemize,[status(sab)],[294])).
% 0.63/0.81 tff(296,plain,
% 0.63/0.81 (![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.63/0.81 tff(297,plain,
% 0.63/0.81 (![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[296, 286])).
% 0.63/0.81 tff(298,plain,
% 0.63/0.81 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(299,plain,
% 0.63/0.82 ((m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(300,plain,
% 0.63/0.82 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[299])).
% 0.63/0.82 tff(301,plain,
% 0.63/0.82 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[300, 298])).
% 0.63/0.82 tff(302,plain,
% 0.63/0.82 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(303,plain,
% 0.63/0.82 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k5_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.63/0.82 tff(304,plain,
% 0.63/0.82 (m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[303, 160, 27, 297])).
% 0.63/0.82 tff(305,plain,
% 0.63/0.82 (m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[304, 284])).
% 0.63/0.82 tff(306,plain,
% 0.63/0.82 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))) | ((~m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))) | (~m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(307,plain,
% 0.63/0.82 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))) | ((~m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(308,plain,
% 0.63/0.82 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(C, D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, C), A!0, k1_rmod_5(A!0, B!1, D))))) | (~m1_subset_1(k3_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.63/0.82 tff(309,plain,
% 0.63/0.82 (![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[308, 305, 282])).
% 0.63/0.82 tff(310,plain,
% 0.63/0.82 (((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | ((~r1_tarski(k3_xboole_0(C!2, D!3), D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3)))) <=> ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | (~r1_tarski(k3_xboole_0(C!2, D!3), D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(311,plain,
% 0.63/0.82 ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | ((~r1_tarski(k3_xboole_0(C!2, D!3), D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(312,plain,
% 0.63/0.82 ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | (~r1_tarski(k3_xboole_0(C!2, D!3), D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.63/0.82 tff(313,plain,
% 0.63/0.82 ((~r1_tarski(k3_xboole_0(C!2, D!3), D!3)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[312, 27, 309])).
% 0.63/0.82 tff(314,plain,
% 0.63/0.82 (m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D!3))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[313, 241])).
% 0.63/0.82 tff(315,plain,
% 0.63/0.82 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[314, 220])).
% 0.63/0.82 tff(316,plain,
% 0.63/0.82 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2)))) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[218, 189])).
% 0.63/0.82 tff(317,plain,
% 0.63/0.82 (m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2)) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))),
% 0.63/0.82 inference(symmetry,[status(thm)],[316])).
% 0.63/0.82 tff(318,plain,
% 0.63/0.82 ((~![A: $i, B: $i] : r1_tarski(k3_xboole_0(A, B), A)) | r1_tarski(k3_xboole_0(C!2, D!3), C!2)),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(319,plain,
% 0.63/0.82 (r1_tarski(k3_xboole_0(C!2, D!3), C!2)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[318, 238])).
% 0.63/0.82 tff(320,plain,
% 0.63/0.82 (((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | ((~r1_tarski(k3_xboole_0(C!2, D!3), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2)))) <=> ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | (~r1_tarski(k3_xboole_0(C!2, D!3), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(321,plain,
% 0.63/0.82 ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | ((~r1_tarski(k3_xboole_0(C!2, D!3), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(322,plain,
% 0.63/0.82 ((~![D: $i] : ((~r1_tarski(k3_xboole_0(C!2, D!3), D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, D)))) | (~r1_tarski(k3_xboole_0(C!2, D!3), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.63/0.82 tff(323,plain,
% 0.63/0.82 (m1_rmod_2(k1_rmod_5(A!0, B!1, k3_xboole_0(C!2, D!3)), A!0, k1_rmod_5(A!0, B!1, C!2))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[322, 160, 319, 309])).
% 0.63/0.82 tff(324,plain,
% 0.63/0.82 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[323, 317])).
% 0.63/0.82 tff(325,plain,
% 0.63/0.82 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[159])).
% 0.63/0.82 tff(326,plain,
% 0.63/0.82 (m1_rmod_2(k1_rmod_5(A!0, B!1, D!3), A!0, B!1) <=> m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)),
% 0.63/0.82 inference(symmetry,[status(thm)],[325])).
% 0.63/0.82 tff(327,plain,
% 0.63/0.82 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[56, 326])).
% 0.63/0.82 tff(328,plain,
% 0.63/0.82 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1) <=> m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[189])).
% 0.63/0.82 tff(329,plain,
% 0.63/0.82 (m1_rmod_2(k1_rmod_5(A!0, B!1, C!2), A!0, B!1) <=> m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)),
% 0.63/0.82 inference(symmetry,[status(thm)],[328])).
% 0.63/0.82 tff(330,plain,
% 0.63/0.82 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[169, 329])).
% 0.63/0.82 tff(331,plain,
% 0.63/0.82 (^[A: $i] : refl((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(332,plain,
% 0.63/0.82 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[331])).
% 0.63/0.82 tff(333,plain,
% 0.63/0.82 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(334,plain,
% 0.63/0.82 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[333])).
% 0.63/0.82 tff(335,plain,
% 0.63/0.82 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[334, 332])).
% 0.63/0.82 tff(336,plain,
% 0.63/0.82 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) <=> (~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) <=> (~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))) <=> ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))), (![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))) <=> ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))) <=> ((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))), rewrite(((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))) <=> ((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))))), rewrite(((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(337,plain,
% 0.63/0.83 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[336])).
% 0.63/0.83 tff(338,plain,
% 0.63/0.83 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(339,plain,
% 0.63/0.83 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite(((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))) <=> ((~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))), ((m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))) <=> (m1_rmod_2(E, A, B) => ((~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))), rewrite((m1_rmod_2(E, A, B) => ((~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))) <=> (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))), ((m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))) <=> (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))), (![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))) <=> ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))), ((m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))) <=> (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))), rewrite((m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))) <=> ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))), ((m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))) <=> ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))), (![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))) <=> ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))), ((m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))) <=> (m1_rmod_2(C, A, B) => ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))), rewrite((m1_rmod_2(C, A, B) => ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))) <=> ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))), ((m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))) <=> ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))), (![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))) <=> ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))))) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))))), (![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(340,plain,
% 0.63/0.83 (![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[339])).
% 0.63/0.83 tff(341,axiom,(![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_rmod_2(C, A, B) => ![D: $i] : (m1_rmod_2(D, A, B) => ![E: $i] : (m1_rmod_2(E, A, B) => ((m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E)) => m1_rmod_2(C, A, k2_rmod_3(A, B, D, E))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_rmod_3')).
% 0.63/0.83 tff(342,plain,
% 0.63/0.83 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.63/0.83 tff(343,plain,
% 0.63/0.83 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[342, 338])).
% 0.63/0.83 tff(344,plain,(
% 0.63/0.83 ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~(m1_rmod_2(C, A, D) & m1_rmod_2(C, A, E))) | (~m1_rmod_2(E, A, B)))))))),
% 0.63/0.83 inference(skolemize,[status(sab)],[343])).
% 0.63/0.83 tff(345,plain,
% 0.63/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[344, 337])).
% 0.63/0.83 tff(346,plain,
% 0.63/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[345, 335])).
% 0.63/0.83 tff(347,plain,
% 0.63/0.83 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(348,plain,
% 0.63/0.83 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) <=> (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(349,plain,
% 0.63/0.83 (^[B: $i] : rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(350,plain,
% 0.63/0.83 (![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))) <=> ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[349])).
% 0.63/0.83 tff(351,plain,
% 0.63/0.83 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[350])).
% 0.63/0.83 tff(352,plain,
% 0.63/0.83 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) <=> (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[351, 348])).
% 0.63/0.83 tff(353,plain,
% 0.63/0.83 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[352])).
% 0.63/0.83 tff(354,plain,
% 0.63/0.83 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[353, 347])).
% 0.63/0.83 tff(355,plain,
% 0.63/0.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(356,plain,
% 0.63/0.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_rmod_2(C, A, B)) | ![D: $i] : ((~m1_rmod_2(D, A, B)) | ![E: $i] : (m1_rmod_2(C, A, k2_rmod_3(A, B, D, E)) | (~m1_rmod_2(E, A, B)) | (~m1_rmod_2(C, A, D)) | (~m1_rmod_2(C, A, E)))))))) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.63/0.84 tff(357,plain,
% 0.63/0.84 (![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[356, 47, 46, 45, 44, 43, 42, 40, 39, 38, 35, 346])).
% 0.63/0.84 tff(358,plain,
% 0.63/0.84 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | (v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(359,plain,
% 0.63/0.84 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))) <=> (v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(360,plain,
% 0.63/0.84 (^[C: $i] : rewrite(((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))) <=> ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(361,plain,
% 0.63/0.84 (![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))) <=> ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[360])).
% 0.63/0.84 tff(362,plain,
% 0.63/0.84 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))) <=> (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[361])).
% 0.63/0.84 tff(363,plain,
% 0.63/0.84 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)))))) <=> (v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[362, 359])).
% 0.63/0.84 tff(364,plain,
% 0.63/0.84 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | (v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[363])).
% 0.63/0.84 tff(365,plain,
% 0.63/0.84 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E))))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[364, 358])).
% 0.63/0.84 tff(366,plain,
% 0.63/0.84 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)) | (~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(367,plain,
% 0.63/0.84 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B)) | ![E: $i] : (m1_rmod_2(C, A!0, k2_rmod_3(A!0, B, D, E)) | (~m1_rmod_2(E, A!0, B)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E))))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.63/0.84 tff(368,plain,
% 0.63/0.84 (![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[367, 34, 33, 32, 31, 30, 29, 28, 357])).
% 0.63/0.84 tff(369,plain,
% 0.63/0.84 (((~![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) | (~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)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(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)) | (~v2_vectsp_2(A!0)) | (~v7_group_1(A!0)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(370,plain,
% 0.63/0.84 ((v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1))))) <=> (v10_vectsp_1(A!0) | v3_struct_0(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)) | (~v2_vectsp_2(A!0)) | (~v7_group_1(A!0)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(371,plain,
% 0.63/0.84 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v10_vectsp_1(A!0) | v3_struct_0(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)) | (~v2_vectsp_2(A!0)) | (~v7_group_1(A!0)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[370])).
% 0.63/0.84 tff(372,plain,
% 0.63/0.84 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | v10_vectsp_1(A!0) | v3_struct_0(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)) | (~v2_vectsp_2(A!0)) | (~v7_group_1(A!0)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[371, 369])).
% 0.63/0.84 tff(373,plain,
% 0.63/0.84 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v10_vectsp_1(A) | v3_struct_0(A) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v2_vectsp_2(A)) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~((~v3_vectsp_2(k1_rmod_5(A, B, C), A)) | (~m1_rmod_2(k1_rmod_5(A, B, C), A, B)))))) | (v3_struct_0(B!1) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(374,plain,
% 0.63/0.84 ((~![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) | (~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)) | (~m1_subset_1(k5_subset_1(u1_struct_0(B!1), C!2, D!3), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.63/0.84 tff(375,plain,
% 0.63/0.84 (~((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[374, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 13, 304])).
% 0.63/0.84 tff(376,plain,
% 0.63/0.84 (((~v3_vectsp_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)),
% 0.63/0.84 inference(tautology,[status(thm)],[])).
% 0.63/0.84 tff(377,plain,
% 0.63/0.84 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[376, 375])).
% 0.63/0.84 tff(378,plain,
% 0.63/0.84 (((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E)))))) <=> ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E)))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(379,plain,
% 0.63/0.85 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E)))))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(380,plain,
% 0.63/0.85 ((~![C: $i] : ((~m1_rmod_2(C, A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(C, A!0, D)) | (~m1_rmod_2(C, A!0, E)) | m1_rmod_2(C, A!0, k2_rmod_3(A!0, B!1, D, E)))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, B!1)) | ![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.63/0.85 tff(381,plain,
% 0.63/0.85 (![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[380, 377, 368])).
% 0.63/0.85 tff(382,plain,
% 0.63/0.85 (((~![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))) | ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E))))) <=> ((~![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(383,plain,
% 0.63/0.85 ((~![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))) | ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E))))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(384,plain,
% 0.63/0.85 ((~![D: $i] : ((~m1_rmod_2(D, A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, D)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, D, E))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.63/0.85 tff(385,plain,
% 0.63/0.85 ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), A!0, B!1)) | ![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[384, 381])).
% 0.63/0.85 tff(386,plain,
% 0.63/0.85 (![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[385, 330])).
% 0.63/0.85 tff(387,plain,
% 0.63/0.85 (((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))) <=> ((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(388,plain,
% 0.63/0.85 (((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))) <=> ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(389,plain,
% 0.63/0.85 (((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))) <=> ((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | ((~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[388])).
% 0.63/0.86 tff(390,plain,
% 0.63/0.86 (((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))) <=> ((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))),
% 0.63/0.86 inference(transitivity,[status(thm)],[389, 387])).
% 0.63/0.86 tff(391,plain,
% 0.63/0.86 ((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(392,plain,
% 0.70/0.86 ((~![E: $i] : ((~m1_rmod_2(E, A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, E)) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), E)))) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))))) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))), A!0, B!1)) | (~m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3))))) | m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.70/0.86 tff(393,plain,
% 0.70/0.86 (m1_rmod_2(k1_rmod_5(A!0, B!1, k5_subset_1(u1_struct_0(B!1), C!2, D!3)), A!0, k2_rmod_3(A!0, B!1, g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_rlvect_1(k1_rmod_5(A!0, B!1, C!2)), u2_struct_0(k1_rmod_5(A!0, B!1, C!2)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, C!2))), g1_vectsp_2(A!0, u1_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_rlvect_1(k1_rmod_5(A!0, B!1, D!3)), u2_struct_0(k1_rmod_5(A!0, B!1, D!3)), u1_vectsp_2(A!0, k1_rmod_5(A!0, B!1, D!3)))))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[392, 386, 327, 324, 315])).
% 0.70/0.86 tff(394,plain,
% 0.70/0.86 ($false),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[393, 195])).
% 0.70/0.86 % SZS output end Proof
% 0.70/0.87 % E exiting
%------------------------------------------------------------------------------