%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG216+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 04:58:44 AM UTC 2025
% Result : Theorem 0.67s 0.85s
% Output : Proof 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG216+1 : TPTP v9.0.0. Released v3.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.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 10:48:54 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.67/0.85 % SZS status Theorem
% 0.67/0.85 % SZS output start Proof
% 0.67/0.85 tff(m1_subset_1_type, type, (
% 0.67/0.85 m1_subset_1: ( $i * $i ) > $o)).
% 0.67/0.85 tff(u1_struct_0_type, type, (
% 0.67/0.85 u1_struct_0: $i > $i)).
% 0.67/0.85 tff(tptp_fun_B_1_type, type, (
% 0.67/0.85 tptp_fun_B_1: $i)).
% 0.67/0.85 tff(v1_rmod_5_type, type, (
% 0.67/0.85 v1_rmod_5: ( $i * $i * $i ) > $o)).
% 0.67/0.85 tff(tptp_fun_A_0_type, type, (
% 0.67/0.85 tptp_fun_A_0: $i)).
% 0.67/0.85 tff(k8_rlvect_2_type, type, (
% 0.67/0.85 k8_rlvect_2: ( $i * $i * $i ) > $i)).
% 0.67/0.85 tff(k1_rlvect_1_type, type, (
% 0.67/0.85 k1_rlvect_1: $i > $i)).
% 0.67/0.85 tff(k2_group_1_type, type, (
% 0.67/0.85 k2_group_1: $i > $i)).
% 0.67/0.85 tff(l1_vectsp_2_type, type, (
% 0.67/0.85 l1_vectsp_2: ( $i * $i ) > $o)).
% 0.67/0.85 tff(v5_vectsp_2_type, type, (
% 0.67/0.85 v5_vectsp_2: ( $i * $i ) > $o)).
% 0.67/0.85 tff(v6_rlvect_1_type, type, (
% 0.67/0.85 v6_rlvect_1: $i > $o)).
% 0.67/0.85 tff(v5_rlvect_1_type, type, (
% 0.67/0.85 v5_rlvect_1: $i > $o)).
% 0.67/0.85 tff(v4_rlvect_1_type, type, (
% 0.67/0.85 v4_rlvect_1: $i > $o)).
% 0.67/0.85 tff(v3_rlvect_1_type, type, (
% 0.67/0.85 v3_rlvect_1: $i > $o)).
% 0.67/0.85 tff(v3_struct_0_type, type, (
% 0.67/0.85 v3_struct_0: $i > $o)).
% 0.67/0.85 tff(v8_vectsp_1_type, type, (
% 0.67/0.85 v8_vectsp_1: $i > $o)).
% 0.67/0.85 tff(v7_vectsp_1_type, type, (
% 0.67/0.85 v7_vectsp_1: $i > $o)).
% 0.67/0.85 tff(v6_vectsp_1_type, type, (
% 0.67/0.85 v6_vectsp_1: $i > $o)).
% 0.67/0.85 tff(v4_group_1_type, type, (
% 0.67/0.85 v4_group_1: $i > $o)).
% 0.67/0.85 tff(l3_vectsp_1_type, type, (
% 0.67/0.85 l3_vectsp_1: $i > $o)).
% 0.67/0.85 tff(tptp_fun_C_2_type, type, (
% 0.67/0.85 tptp_fun_C_2: $i)).
% 0.67/0.85 tff(l2_struct_0_type, type, (
% 0.67/0.85 l2_struct_0: $i > $o)).
% 0.67/0.85 tff(l1_rlvect_1_type, type, (
% 0.67/0.85 l1_rlvect_1: $i > $o)).
% 0.67/0.85 tff(l1_struct_0_type, type, (
% 0.67/0.85 l1_struct_0: $i > $o)).
% 0.67/0.85 tff(l2_vectsp_1_type, type, (
% 0.67/0.85 l2_vectsp_1: $i > $o)).
% 0.67/0.85 tff(1,plain,
% 0.67/0.85 (^[A: $i] : refl((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(2,plain,
% 0.67/0.85 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[1])).
% 0.67/0.85 tff(3,plain,
% 0.67/0.85 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(4,plain,
% 0.67/0.85 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[3])).
% 0.67/0.85 tff(5,plain,
% 0.67/0.85 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.67/0.85 inference(transitivity,[status(thm)],[4, 2])).
% 0.67/0.85 tff(6,plain,
% 0.67/0.85 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) <=> (~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) <=> (~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))) <=> ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))), (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_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) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))) <=> ((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))), rewrite(((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_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) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_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))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_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, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))) <=> ((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))))), rewrite(((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_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))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_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, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(7,plain,
% 0.67/0.85 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[6])).
% 0.67/0.85 tff(8,plain,
% 0.67/0.85 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(9,plain,
% 0.67/0.85 (^[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(rewrite((v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))))) <=> ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)))), ((m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))) <=> (m1_subset_1(D, u1_struct_0(B)) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)))))), rewrite((m1_subset_1(D, u1_struct_0(B)) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)))) <=> ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))), ((m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))) <=> ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))), (![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))) <=> ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))), ((m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))))))) <=> (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))), rewrite((m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))) <=> ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))), ((m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))))))) <=> ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_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) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_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) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))))), (![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_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, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_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)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_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, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_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, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_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, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_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, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_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))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_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, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(10,plain,
% 0.67/0.86 (![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(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_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[9])).
% 0.67/0.86 tff(11,axiom,(![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_rmod_5')).
% 0.67/0.86 tff(12,plain,
% 0.67/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.67/0.86 tff(13,plain,
% 0.67/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.67/0.86 tff(14,plain,(
% 0.67/0.86 ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.67/0.86 inference(skolemize,[status(sab)],[13])).
% 0.67/0.86 tff(15,plain,
% 0.67/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.67/0.86 tff(16,plain,
% 0.67/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.67/0.86 tff(17,plain,
% 0.67/0.86 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)) & ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(18,plain,
% 0.67/0.86 ((((~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)) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))) <=> ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(19,plain,
% 0.67/0.86 ((~(((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))) <=> (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(20,plain,
% 0.67/0.86 ((((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (~(((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))) <=> (((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[19])).
% 0.67/0.86 tff(21,plain,
% 0.67/0.86 ((((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (~(((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))) <=> ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))),
% 0.67/0.86 inference(transitivity,[status(thm)],[20, 18])).
% 0.67/0.86 tff(22,plain,
% 0.67/0.86 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)) & (((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (~(((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))) <=> (((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)) & ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[21])).
% 0.67/0.86 tff(23,plain,
% 0.67/0.86 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)) & (((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (~(((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))),
% 0.67/0.86 inference(transitivity,[status(thm)],[22, 17])).
% 0.67/0.86 tff(24,plain,
% 0.67/0.86 ((~![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] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B)))))))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(25,plain,
% 0.67/0.86 ((~![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ((~(k1_rlvect_1(A) = k2_group_1(A))) => ((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), 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] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B)))))))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(26,axiom,(~![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ((~(k1_rlvect_1(A) = k2_group_1(A))) => ((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t6_rmod_5')).
% 0.67/0.86 tff(27,plain,
% 0.67/0.86 (~![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] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.67/0.86 tff(28,plain,
% 0.67/0.86 (~![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] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.67/0.86 tff(29,plain,
% 0.67/0.86 (~![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] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.67/0.86 tff(30,plain,
% 0.67/0.86 (~![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] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.67/0.86 tff(31,plain,
% 0.67/0.86 ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.67/0.86 tff(32,plain,
% 0.67/0.86 (l3_vectsp_1(A!0)),
% 0.67/0.86 inference(and_elim,[status(thm)],[31])).
% 0.67/0.86 tff(33,plain,
% 0.67/0.86 (v8_vectsp_1(A!0)),
% 0.67/0.86 inference(and_elim,[status(thm)],[31])).
% 0.67/0.86 tff(34,plain,
% 0.67/0.86 (v7_vectsp_1(A!0)),
% 0.67/0.86 inference(and_elim,[status(thm)],[31])).
% 0.67/0.86 tff(35,plain,
% 0.67/0.86 (v6_vectsp_1(A!0)),
% 0.67/0.86 inference(and_elim,[status(thm)],[31])).
% 0.67/0.86 tff(36,plain,
% 0.67/0.86 (v4_group_1(A!0)),
% 0.67/0.86 inference(and_elim,[status(thm)],[31])).
% 0.67/0.86 tff(37,plain,
% 0.67/0.86 (v6_rlvect_1(A!0)),
% 0.67/0.86 inference(and_elim,[status(thm)],[31])).
% 0.67/0.86 tff(38,plain,
% 0.67/0.86 (v5_rlvect_1(A!0)),
% 0.67/0.86 inference(and_elim,[status(thm)],[31])).
% 0.67/0.86 tff(39,plain,
% 0.67/0.86 (v4_rlvect_1(A!0)),
% 0.67/0.86 inference(and_elim,[status(thm)],[31])).
% 0.67/0.86 tff(40,plain,
% 0.67/0.86 (v3_rlvect_1(A!0)),
% 0.67/0.87 inference(and_elim,[status(thm)],[31])).
% 0.67/0.87 tff(41,plain,
% 0.67/0.87 (~v3_struct_0(A!0)),
% 0.67/0.87 inference(and_elim,[status(thm)],[31])).
% 0.67/0.87 tff(42,plain,
% 0.67/0.87 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | (v3_struct_0(A!0) | (~v8_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v4_group_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v3_rlvect_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_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | v3_struct_0(A!0) | (~v8_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v4_group_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v3_rlvect_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_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(43,plain,
% 0.67/0.87 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) <=> (v3_struct_0(A!0) | (~v8_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v4_group_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v3_rlvect_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_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(44,plain,
% 0.67/0.87 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))) <=> ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))), (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))), rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_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!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(45,plain,
% 0.67/0.87 (![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, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))) <=> ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[44])).
% 0.67/0.87 tff(46,plain,
% 0.67/0.87 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[45])).
% 0.67/0.87 tff(47,plain,
% 0.67/0.87 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> (v3_struct_0(A!0) | (~v8_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v4_group_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v3_rlvect_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_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))),
% 0.67/0.87 inference(transitivity,[status(thm)],[46, 43])).
% 0.67/0.87 tff(48,plain,
% 0.67/0.87 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | (v3_struct_0(A!0) | (~v8_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v4_group_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v3_rlvect_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_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[47])).
% 0.67/0.87 tff(49,plain,
% 0.67/0.87 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | v3_struct_0(A!0) | (~v8_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v4_group_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v3_rlvect_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_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))),
% 0.67/0.87 inference(transitivity,[status(thm)],[48, 42])).
% 0.67/0.87 tff(50,plain,
% 0.67/0.87 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(51,plain,
% 0.67/0.87 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | v3_struct_0(A!0) | (~v8_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v4_group_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v3_rlvect_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_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.67/0.87 tff(52,plain,
% 0.67/0.87 (![B: $i] : (v3_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, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[51, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 16])).
% 0.67/0.87 tff(53,plain,
% 0.67/0.87 (l1_vectsp_2(B!1, A!0)),
% 0.67/0.87 inference(and_elim,[status(thm)],[31])).
% 0.67/0.87 tff(54,plain,
% 0.67/0.87 (v5_vectsp_2(B!1, A!0)),
% 0.67/0.87 inference(and_elim,[status(thm)],[31])).
% 0.67/0.87 tff(55,plain,
% 0.67/0.87 (v6_rlvect_1(B!1)),
% 0.67/0.87 inference(and_elim,[status(thm)],[31])).
% 0.67/0.87 tff(56,plain,
% 0.67/0.87 (v5_rlvect_1(B!1)),
% 0.67/0.87 inference(and_elim,[status(thm)],[31])).
% 0.67/0.87 tff(57,plain,
% 0.67/0.87 (v4_rlvect_1(B!1)),
% 0.67/0.87 inference(and_elim,[status(thm)],[31])).
% 0.67/0.87 tff(58,plain,
% 0.67/0.87 (v3_rlvect_1(B!1)),
% 0.67/0.87 inference(and_elim,[status(thm)],[31])).
% 0.67/0.87 tff(59,plain,
% 0.67/0.87 (~v3_struct_0(B!1)),
% 0.67/0.87 inference(and_elim,[status(thm)],[31])).
% 0.67/0.87 tff(60,plain,
% 0.67/0.87 (((~![B: $i] : (v3_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, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | (v3_struct_0(B!1) | (~v6_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v3_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | v3_struct_0(B!1) | (~v6_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v3_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(61,plain,
% 0.67/0.87 ((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, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) <=> (v3_struct_0(B!1) | (~v6_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v3_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(62,plain,
% 0.67/0.87 (^[C: $i] : rewrite(((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))) <=> ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(63,plain,
% 0.67/0.87 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[62])).
% 0.67/0.87 tff(64,plain,
% 0.67/0.87 ((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, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) <=> (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[63])).
% 0.67/0.87 tff(65,plain,
% 0.67/0.87 ((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, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) <=> (v3_struct_0(B!1) | (~v6_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v3_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))),
% 0.67/0.87 inference(transitivity,[status(thm)],[64, 61])).
% 0.67/0.87 tff(66,plain,
% 0.67/0.87 (((~![B: $i] : (v3_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, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | (v3_struct_0(B!1) | (~v6_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v3_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[65])).
% 0.67/0.87 tff(67,plain,
% 0.67/0.87 (((~![B: $i] : (v3_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, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | v3_struct_0(B!1) | (~v6_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v3_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))),
% 0.67/0.87 inference(transitivity,[status(thm)],[66, 60])).
% 0.67/0.87 tff(68,plain,
% 0.67/0.87 ((~![B: $i] : (v3_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, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(69,plain,
% 0.67/0.87 ((~![B: $i] : (v3_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, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | v3_struct_0(B!1) | (~v6_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v3_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.67/0.87 tff(70,plain,
% 0.67/0.87 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[69, 59, 58, 57, 56, 55, 54, 53, 52])).
% 0.67/0.87 tff(71,plain,
% 0.67/0.87 (^[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))))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(72,plain,
% 0.67/0.87 (![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)))))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[71])).
% 0.67/0.87 tff(73,plain,
% 0.67/0.87 (^[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))))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(74,plain,
% 0.67/0.87 (![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)))))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[73])).
% 0.67/0.87 tff(75,plain,
% 0.67/0.87 (![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)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(76,plain,
% 0.67/0.87 (^[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))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(77,plain,
% 0.67/0.87 (![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)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[76])).
% 0.67/0.87 tff(78,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')).
% 0.67/0.87 tff(79,plain,
% 0.67/0.87 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.67/0.87 tff(80,plain,
% 0.67/0.87 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.67/0.87 tff(81,plain,(
% 0.67/0.87 ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.67/0.87 inference(skolemize,[status(sab)],[80])).
% 0.67/0.87 tff(82,plain,
% 0.67/0.87 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.67/0.87 tff(83,plain,
% 0.67/0.87 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.67/0.87 tff(84,plain,
% 0.67/0.87 (((~![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)))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(85,plain,
% 0.67/0.87 ((~![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)))))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(86,plain,
% 0.67/0.87 ((~![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))))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.67/0.87 tff(87,plain,
% 0.67/0.87 (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[86, 32, 83])).
% 0.67/0.87 tff(88,plain,
% 0.67/0.87 (((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0))) | l1_rlvect_1(A!0)),
% 0.67/0.87 inference(tautology,[status(thm)],[])).
% 0.67/0.87 tff(89,plain,
% 0.67/0.87 (l1_rlvect_1(A!0)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.67/0.87 tff(90,plain,
% 0.67/0.87 (^[A: $i] : refl((l2_struct_0(A) | (~l1_rlvect_1(A))) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(91,plain,
% 0.67/0.87 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[90])).
% 0.67/0.87 tff(92,plain,
% 0.67/0.87 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(93,plain,
% 0.67/0.87 (^[A: $i] : rewrite((l1_rlvect_1(A) => l2_struct_0(A)) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(94,plain,
% 0.67/0.87 (![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A)) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[93])).
% 0.67/0.87 tff(95,axiom,(![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_rlvect_1')).
% 0.67/0.87 tff(96,plain,
% 0.67/0.87 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.67/0.87 tff(97,plain,
% 0.67/0.87 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.67/0.87 tff(98,plain,(
% 0.67/0.87 ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.67/0.87 inference(skolemize,[status(sab)],[97])).
% 0.67/0.87 tff(99,plain,
% 0.67/0.87 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.67/0.87 tff(100,plain,
% 0.67/0.87 (((~![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)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(101,plain,
% 0.67/0.87 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(102,plain,
% 0.67/0.87 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(A!0) | (~l1_rlvect_1(A!0))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.67/0.87 tff(103,plain,
% 0.67/0.87 (l2_struct_0(A!0)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[102, 99, 89])).
% 0.67/0.87 tff(104,plain,
% 0.67/0.87 (^[A: $i] : refl((l1_struct_0(A) | (~l2_struct_0(A))) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(105,plain,
% 0.67/0.87 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[104])).
% 0.67/0.87 tff(106,plain,
% 0.67/0.87 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(107,plain,
% 0.67/0.87 (^[A: $i] : rewrite((l2_struct_0(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(108,plain,
% 0.67/0.87 (![A: $i] : (l2_struct_0(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[107])).
% 0.67/0.87 tff(109,axiom,(![A: $i] : (l2_struct_0(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_struct_0')).
% 0.67/0.87 tff(110,plain,
% 0.67/0.87 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.67/0.87 tff(111,plain,
% 0.67/0.87 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.67/0.87 tff(112,plain,(
% 0.67/0.87 ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.67/0.87 inference(skolemize,[status(sab)],[111])).
% 0.67/0.87 tff(113,plain,
% 0.67/0.87 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.67/0.87 tff(114,plain,
% 0.67/0.87 (((~![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)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(115,plain,
% 0.67/0.87 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | (l1_struct_0(A!0) | (~l2_struct_0(A!0)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(116,plain,
% 0.67/0.87 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | l1_struct_0(A!0) | (~l2_struct_0(A!0))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.67/0.87 tff(117,plain,
% 0.67/0.87 (l1_struct_0(A!0)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[116, 113, 103])).
% 0.67/0.87 tff(118,plain,
% 0.67/0.87 (^[A: $i] : refl(((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(119,plain,
% 0.67/0.87 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[118])).
% 0.67/0.87 tff(120,plain,
% 0.67/0.87 (^[A: $i] : rewrite(((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(121,plain,
% 0.67/0.87 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[120])).
% 0.67/0.87 tff(122,plain,
% 0.67/0.87 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.67/0.87 inference(transitivity,[status(thm)],[121, 119])).
% 0.67/0.87 tff(123,plain,
% 0.67/0.87 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(124,plain,
% 0.67/0.87 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((l1_vectsp_2(B, A) => l1_rlvect_1(B)) <=> (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))), (![B: $i] : (l1_vectsp_2(B, A) => l1_rlvect_1(B)) <=> ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))), ((l1_struct_0(A) => ![B: $i] : (l1_vectsp_2(B, A) => l1_rlvect_1(B))) <=> (l1_struct_0(A) => ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))))), rewrite((l1_struct_0(A) => ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))), ((l1_struct_0(A) => ![B: $i] : (l1_vectsp_2(B, A) => l1_rlvect_1(B))) <=> ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(125,plain,
% 0.67/0.87 (![A: $i] : (l1_struct_0(A) => ![B: $i] : (l1_vectsp_2(B, A) => l1_rlvect_1(B))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[124])).
% 0.67/0.87 tff(126,axiom,(![A: $i] : (l1_struct_0(A) => ![B: $i] : (l1_vectsp_2(B, A) => l1_rlvect_1(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_vectsp_2')).
% 0.67/0.87 tff(127,plain,
% 0.67/0.87 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.67/0.87 tff(128,plain,
% 0.67/0.87 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.67/0.87 tff(129,plain,(
% 0.67/0.87 ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.67/0.88 inference(skolemize,[status(sab)],[128])).
% 0.67/0.88 tff(130,plain,
% 0.67/0.88 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.67/0.88 tff(131,plain,
% 0.67/0.88 (((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))) | ((~l1_struct_0(A!0)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0))))) <=> ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))) | (~l1_struct_0(A!0)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0))))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(132,plain,
% 0.67/0.88 ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))) | ((~l1_struct_0(A!0)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0))))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(133,plain,
% 0.67/0.88 ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))) | (~l1_struct_0(A!0)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.67/0.88 tff(134,plain,
% 0.67/0.88 (![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[133, 130, 117])).
% 0.67/0.88 tff(135,plain,
% 0.67/0.88 (((~![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))) | (l1_rlvect_1(B!1) | (~l1_vectsp_2(B!1, A!0)))) <=> ((~![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))) | l1_rlvect_1(B!1) | (~l1_vectsp_2(B!1, A!0)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(136,plain,
% 0.67/0.88 ((~![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))) | (l1_rlvect_1(B!1) | (~l1_vectsp_2(B!1, A!0)))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(137,plain,
% 0.67/0.88 ((~![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))) | l1_rlvect_1(B!1) | (~l1_vectsp_2(B!1, A!0))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.67/0.88 tff(138,plain,
% 0.67/0.88 (l1_rlvect_1(B!1)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[137, 53, 134])).
% 0.67/0.88 tff(139,plain,
% 0.67/0.88 (((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(B!1) | (~l1_rlvect_1(B!1)))) <=> ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(B!1) | (~l1_rlvect_1(B!1)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(140,plain,
% 0.67/0.88 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(B!1) | (~l1_rlvect_1(B!1)))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(141,plain,
% 0.67/0.88 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(B!1) | (~l1_rlvect_1(B!1))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.67/0.88 tff(142,plain,
% 0.67/0.88 (l2_struct_0(B!1)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[141, 99, 138])).
% 0.67/0.88 tff(143,plain,
% 0.67/0.88 (^[A: $i] : refl(((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))) <=> ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))))),
% 0.67/0.88 inference(bind,[status(th)],[])).
% 0.67/0.88 tff(144,plain,
% 0.67/0.88 (![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.67/0.88 inference(quant_intro,[status(thm)],[143])).
% 0.67/0.88 tff(145,plain,
% 0.67/0.88 (![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(146,plain,
% 0.67/0.88 (^[A: $i] : rewrite((l2_struct_0(A) => m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))) <=> ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))))),
% 0.67/0.88 inference(bind,[status(th)],[])).
% 0.67/0.88 tff(147,plain,
% 0.67/0.88 (![A: $i] : (l2_struct_0(A) => m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.67/0.88 inference(quant_intro,[status(thm)],[146])).
% 0.67/0.88 tff(148,axiom,(![A: $i] : (l2_struct_0(A) => m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_rlvect_1')).
% 0.67/0.88 tff(149,plain,
% 0.67/0.88 (![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.67/0.88 tff(150,plain,
% 0.67/0.88 (![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.67/0.88 tff(151,plain,(
% 0.67/0.88 ![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.67/0.88 inference(skolemize,[status(sab)],[150])).
% 0.67/0.88 tff(152,plain,
% 0.67/0.88 (![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.67/0.88 tff(153,plain,
% 0.67/0.88 (((~![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))) | ((~l2_struct_0(B!1)) | m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1)))) <=> ((~![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))) | (~l2_struct_0(B!1)) | m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(154,plain,
% 0.67/0.88 ((~![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))) | ((~l2_struct_0(B!1)) | m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1)))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(155,plain,
% 0.67/0.88 ((~![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))) | (~l2_struct_0(B!1)) | m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.67/0.88 tff(156,plain,
% 0.67/0.88 ((~l2_struct_0(B!1)) | m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[155, 152])).
% 0.67/0.88 tff(157,plain,
% 0.67/0.88 (m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[156, 142])).
% 0.67/0.88 tff(158,plain,
% 0.67/0.88 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1)))))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(159,plain,
% 0.67/0.88 (((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (k1_rlvect_1(B!1) = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)))) <=> ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1)))))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(160,plain,
% 0.67/0.88 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (k1_rlvect_1(B!1) = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[159])).
% 0.67/0.88 tff(161,plain,
% 0.67/0.88 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (k1_rlvect_1(B!1) = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1)))))),
% 0.67/0.88 inference(transitivity,[status(thm)],[160, 158])).
% 0.67/0.88 tff(162,plain,
% 0.67/0.88 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (k1_rlvect_1(B!1) = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1))))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(163,plain,
% 0.67/0.88 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.67/0.88 tff(164,plain,
% 0.67/0.88 (![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[163, 157, 70])).
% 0.67/0.88 tff(165,plain,
% 0.67/0.88 (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))),
% 0.67/0.88 inference(and_elim,[status(thm)],[31])).
% 0.67/0.88 tff(166,plain,
% 0.67/0.88 (m1_subset_1(C!2, u1_struct_0(B!1))),
% 0.67/0.88 inference(or_elim,[status(thm)],[165])).
% 0.67/0.88 tff(167,plain,
% 0.67/0.88 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(C!2, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1))))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(168,plain,
% 0.67/0.88 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(C!2, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1))))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(169,plain,
% 0.67/0.88 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.67/0.88 tff(170,plain,
% 0.67/0.88 (![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[169, 166, 70])).
% 0.67/0.88 tff(171,plain,
% 0.67/0.88 (~(k1_rlvect_1(A!0) = k2_group_1(A!0))),
% 0.67/0.88 inference(or_elim,[status(thm)],[165])).
% 0.67/0.88 tff(172,plain,
% 0.67/0.88 (((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))))) <=> ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(173,plain,
% 0.67/0.88 (((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | $false | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1))) <=> ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(174,plain,
% 0.67/0.88 ((~$true) <=> $false),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(175,plain,
% 0.67/0.88 (($true | (C!2 = k1_rlvect_1(B!1))) <=> $true),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(176,plain,
% 0.67/0.88 ((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) <=> $true),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(177,plain,
% 0.67/0.88 (((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1))) <=> ($true | (C!2 = k1_rlvect_1(B!1)))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[176])).
% 0.67/0.88 tff(178,plain,
% 0.67/0.88 (((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1))) <=> $true),
% 0.67/0.88 inference(transitivity,[status(thm)],[177, 175])).
% 0.67/0.88 tff(179,plain,
% 0.67/0.88 ((~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) <=> (~$true)),
% 0.67/0.88 inference(monotonicity,[status(thm)],[178])).
% 0.67/0.88 tff(180,plain,
% 0.67/0.88 ((~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) <=> $false),
% 0.67/0.88 inference(transitivity,[status(thm)],[179, 174])).
% 0.67/0.88 tff(181,plain,
% 0.67/0.88 (((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | (~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1))) <=> ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | $false | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[180])).
% 0.67/0.88 tff(182,plain,
% 0.67/0.88 (((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | (~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1))) <=> ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))))),
% 0.67/0.88 inference(transitivity,[status(thm)],[181, 173])).
% 0.67/0.88 tff(183,plain,
% 0.67/0.88 (((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | (~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)))) <=> ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1)))))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[182])).
% 0.67/0.88 tff(184,plain,
% 0.67/0.88 (((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | (~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)))) <=> ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))))),
% 0.67/0.88 inference(transitivity,[status(thm)],[183, 172])).
% 0.67/0.88 tff(185,plain,
% 0.67/0.88 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | (~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(186,plain,
% 0.67/0.88 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1)))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.67/0.88 tff(187,plain,
% 0.67/0.88 (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[186, 171, 157, 170])).
% 0.67/0.88 tff(188,plain,
% 0.67/0.88 ((~(~(v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)))) <=> (v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(189,plain,
% 0.67/0.88 (((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) <=> (~(v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(190,plain,
% 0.67/0.88 ((~((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)))) <=> (~(~(v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[189])).
% 0.67/0.89 tff(191,plain,
% 0.67/0.89 ((~((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)))) <=> (v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))),
% 0.67/0.89 inference(transitivity,[status(thm)],[190, 188])).
% 0.67/0.89 tff(192,plain,
% 0.67/0.89 (~((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)))),
% 0.67/0.89 inference(or_elim,[status(thm)],[165])).
% 0.67/0.89 tff(193,plain,
% 0.67/0.89 (v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.67/0.89 tff(194,plain,
% 0.67/0.89 (v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[193, 187])).
% 0.67/0.89 tff(195,plain,
% 0.67/0.89 (((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))) <=> ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(196,plain,
% 0.67/0.89 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))),
% 0.67/0.89 inference(quant_inst,[status(thm)],[])).
% 0.67/0.89 tff(197,plain,
% 0.67/0.89 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)) | (~m1_subset_1(C!2, u1_struct_0(B!1)))),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.67/0.89 tff(198,plain,
% 0.67/0.89 ($false),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[197, 171, 194, 166, 164])).
% 0.67/0.89 % SZS output end Proof
% 0.67/0.89 % E exiting
%------------------------------------------------------------------------------