%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG214+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 04:58:43 AM UTC 2025
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : ALG214+1 : TPTP v9.0.0. Released v3.4.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 10:48:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(r1_tarski_type, type, (
% 0.20/0.47 r1_tarski: ( $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_D_3_type, type, (
% 0.20/0.47 tptp_fun_D_3: $i)).
% 0.20/0.47 tff(tptp_fun_C_2_type, type, (
% 0.20/0.47 tptp_fun_C_2: $i)).
% 0.20/0.47 tff(m2_rmod_4_type, type, (
% 0.20/0.47 m2_rmod_4: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_B_1_type, type, (
% 0.20/0.47 tptp_fun_B_1: $i)).
% 0.20/0.47 tff(tptp_fun_A_0_type, type, (
% 0.20/0.47 tptp_fun_A_0: $i)).
% 0.20/0.47 tff(m1_subset_1_type, type, (
% 0.20/0.47 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.47 tff(k1_zfmisc_1_type, type, (
% 0.20/0.47 k1_zfmisc_1: $i > $i)).
% 0.20/0.47 tff(u1_struct_0_type, type, (
% 0.20/0.47 u1_struct_0: $i > $i)).
% 0.20/0.47 tff(l1_vectsp_2_type, type, (
% 0.20/0.47 l1_vectsp_2: ( $i * $i ) > $o)).
% 0.20/0.47 tff(v5_vectsp_2_type, type, (
% 0.20/0.47 v5_vectsp_2: ( $i * $i ) > $o)).
% 0.20/0.47 tff(v6_rlvect_1_type, type, (
% 0.20/0.47 v6_rlvect_1: $i > $o)).
% 0.20/0.47 tff(v5_rlvect_1_type, type, (
% 0.20/0.47 v5_rlvect_1: $i > $o)).
% 0.20/0.47 tff(v4_rlvect_1_type, type, (
% 0.20/0.47 v4_rlvect_1: $i > $o)).
% 0.20/0.47 tff(v3_rlvect_1_type, type, (
% 0.20/0.47 v3_rlvect_1: $i > $o)).
% 0.20/0.47 tff(v3_struct_0_type, type, (
% 0.20/0.47 v3_struct_0: $i > $o)).
% 0.20/0.47 tff(v8_vectsp_1_type, type, (
% 0.20/0.47 v8_vectsp_1: $i > $o)).
% 0.20/0.47 tff(v7_vectsp_1_type, type, (
% 0.20/0.47 v7_vectsp_1: $i > $o)).
% 0.20/0.47 tff(v6_vectsp_1_type, type, (
% 0.20/0.47 v6_vectsp_1: $i > $o)).
% 0.20/0.47 tff(v4_group_1_type, type, (
% 0.20/0.47 v4_group_1: $i > $o)).
% 0.20/0.47 tff(l3_vectsp_1_type, type, (
% 0.20/0.47 l3_vectsp_1: $i > $o)).
% 0.20/0.47 tff(v1_rmod_5_type, type, (
% 0.20/0.47 v1_rmod_5: ( $i * $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_D_4_type, type, (
% 0.20/0.47 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(k1_rlvect_1_type, type, (
% 0.20/0.47 k1_rlvect_1: $i > $i)).
% 0.20/0.47 tff(k5_rmod_4_type, type, (
% 0.20/0.47 k5_rmod_4: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(k1_xboole_0_type, type, (
% 0.20/0.47 k1_xboole_0: $i)).
% 0.20/0.47 tff(k2_rmod_4_type, type, (
% 0.20/0.47 k2_rmod_4: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))), (![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))), ((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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))))), 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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))) <=> (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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))), ((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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (^[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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(4,plain,
% 0.20/0.47 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (^[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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (^[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))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))) <=> ((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))), rewrite(((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))) <=> ((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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))), rewrite(((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))) <=> (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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 (![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))) <=> ![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 (![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))) <=> ![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((r1_tarski(C, D) => m2_rmod_4(E, A, B, D)) <=> ((~r1_tarski(C, D)) | m2_rmod_4(E, A, B, D))), ((m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D))) <=> (m2_rmod_4(E, A, B, C) => ((~r1_tarski(C, D)) | m2_rmod_4(E, A, B, D))))), rewrite((m2_rmod_4(E, A, B, C) => ((~r1_tarski(C, D)) | m2_rmod_4(E, A, B, D))) <=> (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))), ((m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D))) <=> (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))), (![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D))) <=> ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D)))) <=> (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))), rewrite((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))) <=> ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D)))) <=> ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D)))) <=> ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D))))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D)))))) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D)))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))))), (![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D)))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & 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, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D))))))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))))), 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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & 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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & 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, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (![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, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.48 tff(13,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, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ![E: $i] : (m2_rmod_4(E, A, B, C) => (r1_tarski(C, D) => m2_rmod_4(E, A, B, D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t25_rmod_4')).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.48 tff(16,plain,(
% 0.20/0.48 ![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[15])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C))))) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 ((((~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) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & 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) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 ((((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 ((~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))) <=> (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 ((m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))) <=> (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 ((((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))) <=> (((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 ((((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[24, 21])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 ((((~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)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))))) <=> (((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & 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) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 ((((~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)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & 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) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[26, 20])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 ((~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (v1_rmod_5(C, A, B) | (~(r1_tarski(C, D) & v1_rmod_5(D, A, B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & 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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (v1_rmod_5(C, A, B) | (~(r1_tarski(C, D) & v1_rmod_5(D, A, B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 ((~![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, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((r1_tarski(C, D) & v1_rmod_5(D, A, B)) => v1_rmod_5(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] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (v1_rmod_5(C, A, B) | (~(r1_tarski(C, D) & v1_rmod_5(D, A, B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(30,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, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((r1_tarski(C, D) & v1_rmod_5(D, A, B)) => v1_rmod_5(C, A, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_rmod_5')).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (v1_rmod_5(C, A, B) | (~(r1_tarski(C, D) & v1_rmod_5(D, A, B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (v1_rmod_5(C, A, B) | (~(r1_tarski(C, D) & v1_rmod_5(D, A, B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (v1_rmod_5(C, A, B) | (~(r1_tarski(C, D) & v1_rmod_5(D, A, B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : (v1_rmod_5(C, A, B) | (~(r1_tarski(C, D) & v1_rmod_5(D, A, B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 ((~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) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) & (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (l3_vectsp_1(A!0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[35])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (v8_vectsp_1(A!0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[35])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (v7_vectsp_1(A!0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[35])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (v6_vectsp_1(A!0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[35])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (v4_group_1(A!0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[35])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (v6_rlvect_1(A!0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[35])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (v5_rlvect_1(A!0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[35])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (v4_rlvect_1(A!0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[35])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (v3_rlvect_1(A!0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[35])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (~v3_struct_0(A!0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[35])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (((~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))) | (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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C)))))))) <=> ((~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))) | 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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 ((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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))) <=> (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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A!0, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A!0, B, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))), (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A!0, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A!0, B, C))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A!0, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A!0, B, C)))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C)))))))), rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C)))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A!0, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A!0, B, C)))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A!0, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A!0, B, C)))))) <=> ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 ((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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A!0, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A!0, B, C))))))) <=> (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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 ((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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A!0, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A!0, B, C))))))) <=> (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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C)))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[50, 47])).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 (((~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))) | (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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A!0, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A!0, B, C)))))))) <=> ((~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))) | (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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (((~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))) | (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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A!0, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A!0, B, C)))))))) <=> ((~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))) | 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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C)))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[52, 46])).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 ((~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))) | (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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A!0, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A!0, B, C)))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 ((~![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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : (m2_rmod_4(E, A, B, D) | (~r1_tarski(C, D)) | (~m2_rmod_4(E, A, B, C)))))))) | 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, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 (![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[55, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 19])).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (l1_vectsp_2(B!1, A!0)),
% 0.20/0.49 inference(and_elim,[status(thm)],[35])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (v5_vectsp_2(B!1, A!0)),
% 0.20/0.49 inference(and_elim,[status(thm)],[35])).
% 0.20/0.49 tff(59,plain,
% 0.20/0.49 (v6_rlvect_1(B!1)),
% 0.20/0.49 inference(and_elim,[status(thm)],[35])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 (v5_rlvect_1(B!1)),
% 0.20/0.49 inference(and_elim,[status(thm)],[35])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 (v4_rlvect_1(B!1)),
% 0.20/0.49 inference(and_elim,[status(thm)],[35])).
% 0.20/0.49 tff(62,plain,
% 0.20/0.49 (v3_rlvect_1(B!1)),
% 0.20/0.49 inference(and_elim,[status(thm)],[35])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (~v3_struct_0(B!1)),
% 0.20/0.49 inference(and_elim,[status(thm)],[35])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))) | (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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))) | 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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))) <=> (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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))) | (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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))) | 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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[66, 64])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B, D) | (~m2_rmod_4(E, A!0, B, C))))))) | 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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[69, 63, 62, 61, 60, 59, 58, 57, 56])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.20/0.49 inference(and_elim,[status(thm)],[35])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D) | (~r1_tarski(C!2, D)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D) | (~r1_tarski(C!2, D)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C!2, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C!2))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D) | (~r1_tarski(C!2, D)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C!2, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C!2)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D) | (~r1_tarski(C!2, D))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[73])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C!2, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C!2)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D) | (~r1_tarski(C!2, D)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[74, 72])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C!2, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C!2)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~r1_tarski(C, D)) | m2_rmod_4(E, A!0, B!1, D) | (~m2_rmod_4(E, A!0, B!1, C)))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D) | (~r1_tarski(C!2, D))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D) | (~r1_tarski(C!2, D))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[77, 71, 70])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (~(v1_rmod_5(C!2, A!0, B!1) | (~(r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.20/0.49 inference(and_elim,[status(thm)],[35])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.20/0.49 inference(or_elim,[status(thm)],[79])).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D) | (~r1_tarski(C!2, D))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D) | (~r1_tarski(C!2, D))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D) | (~r1_tarski(C!2, D))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D) | (~r1_tarski(C!2, D))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | ![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[83, 80, 78])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 (^[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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))) <=> (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))) <=> ![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (^[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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))) <=> (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 (![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))) <=> ![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))) <=> ![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[88, 86])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (^[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, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))), (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))) <=> ((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))), rewrite(((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & 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, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))) <=> ((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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))))), 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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))))) <=> (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & 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, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))) <=> (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 (![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, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C))))))))) <=> ![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.50 tff(92,plain,
% 0.20/0.50 (![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, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))) <=> ![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, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 (^[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(rewrite((v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0)))) <=> (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0)))))) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0)))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))))), (![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_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) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & 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, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & 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, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))))), 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, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & 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, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & 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, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & 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, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(94,plain,
% 0.20/0.50 (![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, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0))))))) <=> ![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, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.50 tff(95,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, k1_zfmisc_1(u1_struct_0(B))) => (v1_rmod_5(C, A, B) <=> ![D: $i] : (m2_rmod_4(D, A, B, C) => ((k5_rmod_4(A, B, D) = k1_rlvect_1(B)) => (k2_rmod_4(A, B, D) = k1_xboole_0)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_rmod_5')).
% 0.20/0.50 tff(96,plain,
% 0.20/0.50 (![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, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.50 tff(97,plain,
% 0.20/0.50 (![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, k1_zfmisc_1(u1_struct_0(B)))) | (v1_rmod_5(C, A, B) <=> ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.50 tff(98,plain,(
% 0.20/0.50 ![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, k1_zfmisc_1(u1_struct_0(B)))) | (((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C)))) & (v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[97])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 (![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 (![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 (((~![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))) | (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0))))))))))) <=> ((~![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))) | 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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 ((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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))) <=> (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C))))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))), (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C))))))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)))))))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0))))))))))), rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0))))))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)))))))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(104,plain,
% 0.20/0.50 (![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)))))))))) <=> ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.50 tff(105,plain,
% 0.20/0.50 ((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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C))))))))))) <=> (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0))))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.50 tff(106,plain,
% 0.20/0.50 ((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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C))))))))))) <=> (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0))))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[105, 102])).
% 0.20/0.50 tff(107,plain,
% 0.20/0.50 (((~![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))) | (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)))))))))))) <=> ((~![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))) | (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.50 tff(108,plain,
% 0.20/0.50 (((~![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))) | (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)))))))))))) <=> ((~![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))) | 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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0))))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[107, 101])).
% 0.20/0.50 tff(109,plain,
% 0.20/0.50 ((~![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))) | (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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)))))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 ((~![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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A, B)) | ![D: $i] : ((k2_rmod_4(A, B, D) = k1_xboole_0) | (~(k5_rmod_4(A, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A, B, C))))) | (~(v1_rmod_5(C, A, B) | (~((k2_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_xboole_0) | (~(k5_rmod_4(A, B, tptp_fun_D_4(C, B, A)) = k1_rlvect_1(B))) | (~m2_rmod_4(tptp_fun_D_4(C, B, A), A, B, C)))))))))))) | 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, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 (![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[110, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 100])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))) | (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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0)))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))) | 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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0)))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) <=> (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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0)))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0)))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))) | (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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[113])).
% 0.20/0.51 tff(115,plain,
% 0.20/0.51 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0)))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))) | 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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0)))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[114, 112])).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_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)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0)))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(117,plain,
% 0.20/0.51 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v1_rmod_5(C, A!0, B)) | ![D: $i] : ((k2_rmod_4(A!0, B, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B, D) = k1_rlvect_1(B))) | (~m2_rmod_4(D, A!0, B, C))))) | (~(v1_rmod_5(C, A!0, B) | (~((~m2_rmod_4(tptp_fun_D_4(C, B, A!0), A!0, B, C)) | (~(k5_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_rlvect_1(B))) | (k2_rmod_4(A!0, B, tptp_fun_D_4(C, B, A!0)) = k1_xboole_0)))))))))) | 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)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.51 tff(118,plain,
% 0.20/0.51 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[117, 63, 62, 61, 60, 59, 58, 57, 111])).
% 0.20/0.51 tff(119,plain,
% 0.20/0.51 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(120,plain,
% 0.20/0.51 (((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, D!3))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0)))))))) <=> ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(121,plain,
% 0.20/0.51 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, D!3))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.51 tff(122,plain,
% 0.20/0.51 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, D!3))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[121, 119])).
% 0.20/0.51 tff(123,plain,
% 0.20/0.51 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, D!3))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(124,plain,
% 0.20/0.51 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.51 tff(125,plain,
% 0.20/0.51 (~((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[124, 80, 118])).
% 0.20/0.52 tff(126,plain,
% 0.20/0.52 (((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(D!3, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(D!3, B!1, A!0), A!0, B!1, D!3)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(D!3, B!1, A!0)) = k1_xboole_0)))))) | ((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(127,plain,
% 0.20/0.52 ((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.20/0.52 tff(128,plain,
% 0.20/0.52 (r1_tarski(C!2, D!3) & v1_rmod_5(D!3, A!0, B!1)),
% 0.20/0.52 inference(or_elim,[status(thm)],[79])).
% 0.20/0.52 tff(129,plain,
% 0.20/0.52 (v1_rmod_5(D!3, A!0, B!1)),
% 0.20/0.52 inference(and_elim,[status(thm)],[128])).
% 0.20/0.52 tff(130,plain,
% 0.20/0.52 ((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(131,plain,
% 0.20/0.52 ((~((~v1_rmod_5(D!3, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.20/0.52 tff(132,plain,
% 0.20/0.52 (![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[131, 127])).
% 0.20/0.52 tff(133,plain,
% 0.20/0.52 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, C!2)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, C!2)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(134,plain,
% 0.20/0.52 (((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C!2))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0)))))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, C!2)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(135,plain,
% 0.20/0.52 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C!2))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, C!2)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0)))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.52 tff(136,plain,
% 0.20/0.52 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C!2))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, C!2)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[135, 133])).
% 0.20/0.52 tff(137,plain,
% 0.20/0.52 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C!2))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(138,plain,
% 0.20/0.52 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C, A!0, B!1)) | ![D: $i] : ((k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))) | (~m2_rmod_4(D, A!0, B!1, C))))) | (~(v1_rmod_5(C, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C, B!1, A!0), A!0, B!1, C)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C, B!1, A!0)) = k1_xboole_0))))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, C!2)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0)))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.52 tff(139,plain,
% 0.20/0.52 (~((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, C!2)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[138, 71, 118])).
% 0.20/0.52 tff(140,plain,
% 0.20/0.52 (((~((~v1_rmod_5(C!2, A!0, B!1)) | ![D: $i] : ((~m2_rmod_4(D, A!0, B!1, C!2)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1)))))) | (~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0)))))) | (v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(141,plain,
% 0.20/0.52 (v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.20/0.52 tff(142,plain,
% 0.20/0.52 (~v1_rmod_5(C!2, A!0, B!1)),
% 0.20/0.52 inference(or_elim,[status(thm)],[79])).
% 0.20/0.52 tff(143,plain,
% 0.20/0.52 ((~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))))) | v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(144,plain,
% 0.20/0.52 ((~(v1_rmod_5(C!2, A!0, B!1) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))))) | (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 (~((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[144, 141])).
% 0.20/0.52 tff(146,plain,
% 0.20/0.52 (((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0)) | (~(k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(147,plain,
% 0.20/0.52 (~(k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.52 tff(148,plain,
% 0.20/0.52 (((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0)) | (k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(149,plain,
% 0.20/0.52 (k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[148, 145])).
% 0.20/0.52 tff(150,plain,
% 0.20/0.52 (((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))) | ((k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3)))) <=> ((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(151,plain,
% 0.20/0.52 (((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1)))) <=> ((k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(152,plain,
% 0.20/0.52 (((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))) | ((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))))) <=> ((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))) | ((k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.52 tff(153,plain,
% 0.20/0.52 (((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))) | ((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))))) <=> ((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[152, 150])).
% 0.20/0.52 tff(154,plain,
% 0.20/0.52 ((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))) | ((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(155,plain,
% 0.20/0.52 ((~![D: $i] : ((~m2_rmod_4(D, A!0, B!1, D!3)) | (k2_rmod_4(A!0, B!1, D) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, D) = k1_rlvect_1(B!1))))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.52 tff(156,plain,
% 0.20/0.52 (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[155, 149, 147, 132])).
% 0.20/0.52 tff(157,plain,
% 0.20/0.52 (((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | (~(k5_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_rlvect_1(B!1))) | (k2_rmod_4(A!0, B!1, tptp_fun_D_4(C!2, B!1, A!0)) = k1_xboole_0)) | m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(158,plain,
% 0.20/0.52 (m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[157, 145])).
% 0.20/0.52 tff(159,plain,
% 0.20/0.52 (r1_tarski(C!2, D!3)),
% 0.20/0.52 inference(and_elim,[status(thm)],[128])).
% 0.20/0.52 tff(160,plain,
% 0.20/0.52 (((~![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))) | ((~r1_tarski(C!2, D!3)) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3))) <=> ((~![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))) | (~r1_tarski(C!2, D!3)) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(161,plain,
% 0.20/0.52 (((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3) | (~r1_tarski(C!2, D!3))) <=> ((~r1_tarski(C!2, D!3)) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(162,plain,
% 0.20/0.52 (((~![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))) | ((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))) <=> ((~![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))) | ((~r1_tarski(C!2, D!3)) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.53 tff(163,plain,
% 0.20/0.53 (((~![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))) | ((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))) <=> ((~![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))) | (~r1_tarski(C!2, D!3)) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3))),
% 0.20/0.53 inference(transitivity,[status(thm)],[162, 160])).
% 0.20/0.53 tff(164,plain,
% 0.20/0.53 ((~![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))) | ((~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(165,plain,
% 0.20/0.53 ((~![E: $i] : ((~m2_rmod_4(E, A!0, B!1, C!2)) | m2_rmod_4(E, A!0, B!1, D!3) | (~r1_tarski(C!2, D!3)))) | (~r1_tarski(C!2, D!3)) | (~m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, C!2)) | m2_rmod_4(tptp_fun_D_4(C!2, B!1, A!0), A!0, B!1, D!3)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.53 tff(166,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[165, 159, 158, 156, 84])).
% 0.20/0.53 % SZS output end Proof
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------