%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP639+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:08:16 AM UTC 2025
% Result : Theorem 2.37s 2.54s
% Output : Proof 2.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP639+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 16:35:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 2.37/2.54 % SZS status Theorem
% 2.37/2.54 % SZS output start Proof
% 2.37/2.54 tff(m1_group_2_type, type, (
% 2.37/2.54 m1_group_2: ( $i * $i ) > $o)).
% 2.37/2.54 tff(g1_group_1_type, type, (
% 2.37/2.54 g1_group_1: ( $i * $i ) > $i)).
% 2.37/2.54 tff(u1_group_1_type, type, (
% 2.37/2.54 u1_group_1: $i > $i)).
% 2.37/2.54 tff(k5_group_4_type, type, (
% 2.37/2.54 k5_group_4: ( $i * $i ) > $i)).
% 2.37/2.54 tff(tptp_fun_D_3_type, type, (
% 2.37/2.54 tptp_fun_D_3: $i)).
% 2.37/2.54 tff(tptp_fun_A_0_type, type, (
% 2.37/2.54 tptp_fun_A_0: $i)).
% 2.37/2.54 tff(u1_struct_0_type, type, (
% 2.37/2.54 u1_struct_0: $i > $i)).
% 2.37/2.54 tff(r1_tarski_type, type, (
% 2.37/2.54 r1_tarski: ( $i * $i ) > $o)).
% 2.37/2.54 tff(v1_group_1_type, type, (
% 2.37/2.54 v1_group_1: $i > $o)).
% 2.37/2.54 tff(l1_group_1_type, type, (
% 2.37/2.54 l1_group_1: $i > $o)).
% 2.37/2.54 tff(v4_group_1_type, type, (
% 2.37/2.54 v4_group_1: $i > $o)).
% 2.37/2.54 tff(v3_group_1_type, type, (
% 2.37/2.54 v3_group_1: $i > $o)).
% 2.37/2.54 tff(m1_subset_1_type, type, (
% 2.37/2.54 m1_subset_1: ( $i * $i ) > $o)).
% 2.37/2.54 tff(k1_zfmisc_1_type, type, (
% 2.37/2.54 k1_zfmisc_1: $i > $i)).
% 2.37/2.54 tff(v3_struct_0_type, type, (
% 2.37/2.54 v3_struct_0: $i > $o)).
% 2.37/2.54 tff(k2_funct_2_type, type, (
% 2.37/2.54 k2_funct_2: ( $i * $i * $i * $i ) > $i)).
% 2.37/2.54 tff(tptp_fun_C_2_type, type, (
% 2.37/2.54 tptp_fun_C_2: $i)).
% 2.37/2.54 tff(tptp_fun_B_1_type, type, (
% 2.37/2.54 tptp_fun_B_1: $i)).
% 2.37/2.54 tff(m2_relset_1_type, type, (
% 2.37/2.54 m2_relset_1: ( $i * $i * $i ) > $o)).
% 2.37/2.54 tff(v1_funct_2_type, type, (
% 2.37/2.54 v1_funct_2: ( $i * $i * $i ) > $o)).
% 2.37/2.54 tff(v1_funct_1_type, type, (
% 2.37/2.54 v1_funct_1: $i > $o)).
% 2.37/2.54 tff(k9_relat_1_type, type, (
% 2.37/2.54 k9_relat_1: ( $i * $i ) > $i)).
% 2.37/2.54 tff(m1_relset_1_type, type, (
% 2.37/2.54 m1_relset_1: ( $i * $i * $i ) > $o)).
% 2.37/2.54 tff(v1_relat_1_type, type, (
% 2.37/2.54 v1_relat_1: $i > $o)).
% 2.37/2.54 tff(k2_zfmisc_1_type, type, (
% 2.37/2.54 k2_zfmisc_1: ( $i * $i ) > $i)).
% 2.37/2.54 tff(tptp_fun_D_4_type, type, (
% 2.37/2.54 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 2.37/2.54 tff(1,plain,
% 2.37/2.54 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A))))))),
% 2.37/2.54 inference(bind,[status(th)],[])).
% 2.37/2.54 tff(2,plain,
% 2.37/2.54 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A))))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))),
% 2.37/2.54 inference(quant_intro,[status(thm)],[1])).
% 2.37/2.54 tff(3,plain,
% 2.37/2.54 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), rewrite((v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)) <=> (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A))))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))))),
% 2.37/2.54 inference(bind,[status(th)],[])).
% 2.37/2.54 tff(4,plain,
% 2.37/2.54 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))),
% 2.37/2.54 inference(quant_intro,[status(thm)],[3])).
% 2.37/2.54 tff(5,plain,
% 2.37/2.54 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))),
% 2.37/2.54 inference(rewrite,[status(thm)],[])).
% 2.37/2.54 tff(6,plain,
% 2.37/2.54 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))))),
% 2.37/2.55 inference(bind,[status(th)],[])).
% 2.37/2.55 tff(7,plain,
% 2.37/2.55 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))),
% 2.37/2.55 inference(quant_intro,[status(thm)],[6])).
% 2.37/2.55 tff(8,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_group_4')).
% 2.37/2.55 tff(9,plain,
% 2.37/2.55 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[8, 7])).
% 2.37/2.55 tff(10,plain,
% 2.37/2.55 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[9, 5])).
% 2.37/2.55 tff(11,plain,(
% 2.37/2.55 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))),
% 2.37/2.55 inference(skolemize,[status(sab)],[10])).
% 2.37/2.55 tff(12,plain,
% 2.37/2.55 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[11, 4])).
% 2.37/2.55 tff(13,plain,
% 2.37/2.55 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[12, 2])).
% 2.37/2.55 tff(14,plain,
% 2.37/2.55 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(15,plain,
% 2.37/2.55 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))))))) <=> ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(16,plain,
% 2.37/2.55 (((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))))))) <=> (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(17,plain,
% 2.37/2.55 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))))))) <=> (((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))))))))),
% 2.37/2.55 inference(monotonicity,[status(thm)],[16])).
% 2.37/2.55 tff(18,plain,
% 2.37/2.55 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))))))) <=> ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))))))),
% 2.37/2.55 inference(transitivity,[status(thm)],[17, 15])).
% 2.37/2.55 tff(19,plain,
% 2.37/2.55 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))))))))) <=> (((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))))))))),
% 2.37/2.55 inference(monotonicity,[status(thm)],[18])).
% 2.37/2.55 tff(20,plain,
% 2.37/2.55 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))))))),
% 2.37/2.55 inference(transitivity,[status(thm)],[19, 14])).
% 2.37/2.55 tff(21,plain,
% 2.37/2.55 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | r1_tarski(k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(k5_group_4(A, D))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | r1_tarski(k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(k5_group_4(A, D)))))))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(22,plain,
% 2.37/2.55 ((~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(k5_group_4(A, D))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | r1_tarski(k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(k5_group_4(A, D)))))))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(23,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(k5_group_4(A, D))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_latsubgr')).
% 2.37/2.55 tff(24,plain,
% 2.37/2.55 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | r1_tarski(k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(k5_group_4(A, D))))))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[23, 22])).
% 2.37/2.55 tff(25,plain,
% 2.37/2.55 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | r1_tarski(k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(k5_group_4(A, D))))))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[24, 21])).
% 2.37/2.55 tff(26,plain,
% 2.37/2.55 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | r1_tarski(k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(k5_group_4(A, D))))))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[25, 21])).
% 2.37/2.55 tff(27,plain,
% 2.37/2.55 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | r1_tarski(k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(k5_group_4(A, D))))))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[26, 21])).
% 2.37/2.55 tff(28,plain,
% 2.37/2.55 ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[27, 20])).
% 2.37/2.55 tff(29,plain,
% 2.37/2.55 (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))))),
% 2.37/2.55 inference(and_elim,[status(thm)],[28])).
% 2.37/2.55 tff(30,plain,
% 2.37/2.55 (m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))),
% 2.37/2.55 inference(or_elim,[status(thm)],[29])).
% 2.37/2.55 tff(31,plain,
% 2.37/2.55 (l1_group_1(A!0)),
% 2.37/2.55 inference(and_elim,[status(thm)],[28])).
% 2.37/2.55 tff(32,plain,
% 2.37/2.55 (v4_group_1(A!0)),
% 2.37/2.55 inference(and_elim,[status(thm)],[28])).
% 2.37/2.55 tff(33,plain,
% 2.37/2.55 (v3_group_1(A!0)),
% 2.37/2.55 inference(and_elim,[status(thm)],[28])).
% 2.37/2.55 tff(34,plain,
% 2.37/2.55 (~v3_struct_0(A!0)),
% 2.37/2.55 inference(and_elim,[status(thm)],[28])).
% 2.37/2.55 tff(35,plain,
% 2.37/2.55 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_group_1(A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_group_1(A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0)))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(36,plain,
% 2.37/2.55 ((v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_group_1(A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0)))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(37,plain,
% 2.37/2.55 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_group_1(A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0))))))),
% 2.37/2.55 inference(monotonicity,[status(thm)],[36])).
% 2.37/2.55 tff(38,plain,
% 2.37/2.55 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_group_1(A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0)))))),
% 2.37/2.55 inference(transitivity,[status(thm)],[37, 35])).
% 2.37/2.55 tff(39,plain,
% 2.37/2.55 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0)))))),
% 2.37/2.55 inference(quant_inst,[status(thm)],[])).
% 2.37/2.55 tff(40,plain,
% 2.37/2.55 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_group_1(A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[39, 38])).
% 2.37/2.55 tff(41,plain,
% 2.37/2.55 (~((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0)))),
% 2.37/2.55 inference(unit_resolution,[status(thm)],[40, 34, 33, 32, 31, 30, 13])).
% 2.37/2.55 tff(42,plain,
% 2.37/2.55 (((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0))) | v1_group_1(k5_group_4(A!0, D!3))),
% 2.37/2.55 inference(tautology,[status(thm)],[])).
% 2.37/2.55 tff(43,plain,
% 2.37/2.55 (v1_group_1(k5_group_4(A!0, D!3))),
% 2.37/2.55 inference(unit_resolution,[status(thm)],[42, 41])).
% 2.37/2.55 tff(44,plain,
% 2.37/2.55 (((~v1_group_1(k5_group_4(A!0, D!3))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0))) | m1_group_2(k5_group_4(A!0, D!3), A!0)),
% 2.37/2.55 inference(tautology,[status(thm)],[])).
% 2.37/2.55 tff(45,plain,
% 2.37/2.55 (m1_group_2(k5_group_4(A!0, D!3), A!0)),
% 2.37/2.55 inference(unit_resolution,[status(thm)],[44, 41])).
% 2.37/2.55 tff(46,plain,
% 2.37/2.55 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 2.37/2.55 inference(bind,[status(th)],[])).
% 2.37/2.55 tff(47,plain,
% 2.37/2.55 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 2.37/2.55 inference(quant_intro,[status(thm)],[46])).
% 2.37/2.55 tff(48,plain,
% 2.37/2.55 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 2.37/2.55 inference(bind,[status(th)],[])).
% 2.37/2.55 tff(49,plain,
% 2.37/2.55 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 2.37/2.55 inference(quant_intro,[status(thm)],[48])).
% 2.37/2.55 tff(50,plain,
% 2.37/2.55 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 2.37/2.55 inference(transitivity,[status(thm)],[49, 47])).
% 2.37/2.55 tff(51,plain,
% 2.37/2.55 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))))),
% 2.37/2.55 inference(bind,[status(th)],[])).
% 2.37/2.55 tff(52,plain,
% 2.37/2.55 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 2.37/2.55 inference(quant_intro,[status(thm)],[51])).
% 2.37/2.55 tff(53,plain,
% 2.37/2.55 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(54,plain,
% 2.37/2.55 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> (m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), rewrite((m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), (![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))))),
% 2.37/2.55 inference(bind,[status(th)],[])).
% 2.37/2.55 tff(55,plain,
% 2.37/2.55 (![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 2.37/2.55 inference(quant_intro,[status(thm)],[54])).
% 2.37/2.55 tff(56,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_group_2')).
% 2.37/2.55 tff(57,plain,
% 2.37/2.55 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[56, 55])).
% 2.37/2.55 tff(58,plain,
% 2.37/2.55 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[57, 53])).
% 2.37/2.55 tff(59,plain,(
% 2.37/2.55 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 2.37/2.55 inference(skolemize,[status(sab)],[58])).
% 2.37/2.55 tff(60,plain,
% 2.37/2.55 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[59, 52])).
% 2.37/2.55 tff(61,plain,
% 2.37/2.55 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[60, 50])).
% 2.37/2.55 tff(62,plain,
% 2.37/2.55 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(63,plain,
% 2.37/2.55 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 2.37/2.55 inference(quant_inst,[status(thm)],[])).
% 2.37/2.55 tff(64,plain,
% 2.37/2.55 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[63, 62])).
% 2.37/2.55 tff(65,plain,
% 2.37/2.55 (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 2.37/2.55 inference(unit_resolution,[status(thm)],[64, 34, 33, 31, 61])).
% 2.37/2.55 tff(66,plain,
% 2.37/2.55 (((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(k5_group_4(A!0, D!3), A!0)) | (~(v3_struct_0(k5_group_4(A!0, D!3)) | (~l1_group_1(k5_group_4(A!0, D!3))) | (~v3_group_1(k5_group_4(A!0, D!3))))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0)) | (~(v3_struct_0(k5_group_4(A!0, D!3)) | (~l1_group_1(k5_group_4(A!0, D!3))) | (~v3_group_1(k5_group_4(A!0, D!3))))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(67,plain,
% 2.37/2.55 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(k5_group_4(A!0, D!3), A!0)) | (~(v3_struct_0(k5_group_4(A!0, D!3)) | (~l1_group_1(k5_group_4(A!0, D!3))) | (~v3_group_1(k5_group_4(A!0, D!3))))))),
% 2.37/2.55 inference(quant_inst,[status(thm)],[])).
% 2.37/2.55 tff(68,plain,
% 2.37/2.55 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(k5_group_4(A!0, D!3), A!0)) | (~(v3_struct_0(k5_group_4(A!0, D!3)) | (~l1_group_1(k5_group_4(A!0, D!3))) | (~v3_group_1(k5_group_4(A!0, D!3)))))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[67, 66])).
% 2.37/2.55 tff(69,plain,
% 2.37/2.55 (~(v3_struct_0(k5_group_4(A!0, D!3)) | (~l1_group_1(k5_group_4(A!0, D!3))) | (~v3_group_1(k5_group_4(A!0, D!3))))),
% 2.37/2.55 inference(unit_resolution,[status(thm)],[68, 65, 45])).
% 2.37/2.55 tff(70,plain,
% 2.37/2.55 ((v3_struct_0(k5_group_4(A!0, D!3)) | (~l1_group_1(k5_group_4(A!0, D!3))) | (~v3_group_1(k5_group_4(A!0, D!3)))) | l1_group_1(k5_group_4(A!0, D!3))),
% 2.37/2.55 inference(tautology,[status(thm)],[])).
% 2.37/2.55 tff(71,plain,
% 2.37/2.55 (l1_group_1(k5_group_4(A!0, D!3))),
% 2.37/2.55 inference(unit_resolution,[status(thm)],[70, 69])).
% 2.37/2.55 tff(72,plain,
% 2.37/2.55 (^[A: $i] : refl(((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))))),
% 2.37/2.55 inference(bind,[status(th)],[])).
% 2.37/2.55 tff(73,plain,
% 2.37/2.55 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.37/2.55 inference(quant_intro,[status(thm)],[72])).
% 2.37/2.55 tff(74,plain,
% 2.37/2.55 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(75,plain,
% 2.37/2.55 (^[A: $i] : trans(monotonicity(rewrite((v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))) <=> ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> (l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))))), rewrite((l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))))),
% 2.37/2.55 inference(bind,[status(th)],[])).
% 2.37/2.55 tff(76,plain,
% 2.37/2.55 (![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.37/2.55 inference(quant_intro,[status(thm)],[75])).
% 2.37/2.55 tff(77,axiom,(![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v1_group_1')).
% 2.37/2.55 tff(78,plain,
% 2.37/2.55 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[77, 76])).
% 2.37/2.55 tff(79,plain,
% 2.37/2.55 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[78, 74])).
% 2.37/2.55 tff(80,plain,(
% 2.37/2.55 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.37/2.55 inference(skolemize,[status(sab)],[79])).
% 2.37/2.55 tff(81,plain,
% 2.37/2.55 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.37/2.55 inference(modus_ponens,[status(thm)],[80, 73])).
% 2.37/2.55 tff(82,plain,
% 2.37/2.55 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~l1_group_1(k5_group_4(A!0, D!3))) | (~v1_group_1(k5_group_4(A!0, D!3))) | (k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~l1_group_1(k5_group_4(A!0, D!3))) | (~v1_group_1(k5_group_4(A!0, D!3))) | (k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(83,plain,
% 2.37/2.55 (((k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))) | (~v1_group_1(k5_group_4(A!0, D!3))) | (~l1_group_1(k5_group_4(A!0, D!3)))) <=> ((~l1_group_1(k5_group_4(A!0, D!3))) | (~v1_group_1(k5_group_4(A!0, D!3))) | (k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))),
% 2.37/2.55 inference(rewrite,[status(thm)],[])).
% 2.37/2.55 tff(84,plain,
% 2.37/2.55 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))) | (~v1_group_1(k5_group_4(A!0, D!3))) | (~l1_group_1(k5_group_4(A!0, D!3))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~l1_group_1(k5_group_4(A!0, D!3))) | (~v1_group_1(k5_group_4(A!0, D!3))) | (k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))))),
% 2.37/2.56 inference(monotonicity,[status(thm)],[83])).
% 2.37/2.56 tff(85,plain,
% 2.37/2.56 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))) | (~v1_group_1(k5_group_4(A!0, D!3))) | (~l1_group_1(k5_group_4(A!0, D!3))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~l1_group_1(k5_group_4(A!0, D!3))) | (~v1_group_1(k5_group_4(A!0, D!3))) | (k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))),
% 2.37/2.56 inference(transitivity,[status(thm)],[84, 82])).
% 2.37/2.56 tff(86,plain,
% 2.37/2.56 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))) | (~v1_group_1(k5_group_4(A!0, D!3))) | (~l1_group_1(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(quant_inst,[status(thm)],[])).
% 2.37/2.56 tff(87,plain,
% 2.37/2.56 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~l1_group_1(k5_group_4(A!0, D!3))) | (~v1_group_1(k5_group_4(A!0, D!3))) | (k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[86, 85])).
% 2.37/2.56 tff(88,plain,
% 2.37/2.56 ((~l1_group_1(k5_group_4(A!0, D!3))) | (~v1_group_1(k5_group_4(A!0, D!3))) | (k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[87, 81])).
% 2.37/2.56 tff(89,plain,
% 2.37/2.56 (k5_group_4(A!0, D!3) = g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[88, 71, 43])).
% 2.37/2.56 tff(90,plain,
% 2.37/2.56 (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)),
% 2.37/2.56 inference(symmetry,[status(thm)],[89])).
% 2.37/2.56 tff(91,plain,
% 2.37/2.56 (u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))) = u1_struct_0(k5_group_4(A!0, D!3))),
% 2.37/2.56 inference(monotonicity,[status(thm)],[90])).
% 2.37/2.56 tff(92,plain,
% 2.37/2.56 (r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) <=> r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3)))),
% 2.37/2.56 inference(monotonicity,[status(thm)],[91])).
% 2.37/2.56 tff(93,plain,
% 2.37/2.56 (r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3))) <=> r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))),
% 2.37/2.56 inference(symmetry,[status(thm)],[92])).
% 2.37/2.56 tff(94,plain,
% 2.37/2.56 ((~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3)))) <=> (~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))))),
% 2.37/2.56 inference(monotonicity,[status(thm)],[93])).
% 2.37/2.56 tff(95,plain,
% 2.37/2.56 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 2.37/2.56 inference(bind,[status(th)],[])).
% 2.37/2.56 tff(96,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.37/2.56 inference(quant_intro,[status(thm)],[95])).
% 2.37/2.56 tff(97,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(98,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 2.37/2.56 tff(99,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[98, 97])).
% 2.37/2.56 tff(100,plain,(
% 2.37/2.56 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.37/2.56 inference(skolemize,[status(sab)],[99])).
% 2.37/2.56 tff(101,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[100, 96])).
% 2.37/2.56 tff(102,plain,
% 2.37/2.56 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 2.37/2.56 inference(quant_inst,[status(thm)],[])).
% 2.37/2.56 tff(103,plain,
% 2.37/2.56 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[102, 101])).
% 2.37/2.56 tff(104,plain,
% 2.37/2.56 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.37/2.56 inference(and_elim,[status(thm)],[28])).
% 2.37/2.56 tff(105,plain,
% 2.37/2.56 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.37/2.56 inference(tautology,[status(thm)],[])).
% 2.37/2.56 tff(106,plain,
% 2.37/2.56 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[105, 104])).
% 2.37/2.56 tff(107,plain,
% 2.37/2.56 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[106, 103])).
% 2.37/2.56 tff(108,plain,
% 2.37/2.56 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) <=> ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))),
% 2.37/2.56 inference(bind,[status(th)],[])).
% 2.37/2.56 tff(109,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 2.37/2.56 inference(quant_intro,[status(thm)],[108])).
% 2.37/2.56 tff(110,plain,
% 2.37/2.56 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))))),
% 2.37/2.56 inference(bind,[status(th)],[])).
% 2.37/2.56 tff(111,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 2.37/2.56 inference(quant_intro,[status(thm)],[110])).
% 2.37/2.56 tff(112,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(113,plain,
% 2.37/2.56 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))))),
% 2.37/2.56 inference(bind,[status(th)],[])).
% 2.37/2.56 tff(114,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i, D: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 2.37/2.56 inference(quant_intro,[status(thm)],[113])).
% 2.37/2.56 tff(115,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k2_funct_2')).
% 2.37/2.56 tff(116,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[115, 114])).
% 2.37/2.56 tff(117,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[116, 112])).
% 2.37/2.56 tff(118,plain,(
% 2.37/2.56 ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 2.37/2.56 inference(skolemize,[status(sab)],[117])).
% 2.37/2.56 tff(119,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[118, 111])).
% 2.37/2.56 tff(120,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[119, 109])).
% 2.37/2.56 tff(121,plain,
% 2.37/2.56 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.37/2.56 inference(and_elim,[status(thm)],[28])).
% 2.37/2.56 tff(122,plain,
% 2.37/2.56 (v1_funct_1(C!2)),
% 2.37/2.56 inference(and_elim,[status(thm)],[28])).
% 2.37/2.56 tff(123,plain,
% 2.37/2.56 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(124,plain,
% 2.37/2.56 (((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(125,plain,
% 2.37/2.56 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3))))))),
% 2.37/2.56 inference(monotonicity,[status(thm)],[124])).
% 2.37/2.56 tff(126,plain,
% 2.37/2.56 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))))),
% 2.37/2.56 inference(transitivity,[status(thm)],[125, 123])).
% 2.37/2.56 tff(127,plain,
% 2.37/2.56 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.37/2.56 inference(quant_inst,[status(thm)],[])).
% 2.37/2.56 tff(128,plain,
% 2.37/2.56 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[127, 126])).
% 2.37/2.56 tff(129,plain,
% 2.37/2.56 ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[128, 122, 121, 120])).
% 2.37/2.56 tff(130,plain,
% 2.37/2.56 (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[129, 107])).
% 2.37/2.56 tff(131,plain,
% 2.37/2.56 (k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))),
% 2.37/2.56 inference(symmetry,[status(thm)],[130])).
% 2.37/2.56 tff(132,plain,
% 2.37/2.56 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3)))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(133,plain,
% 2.37/2.56 (((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3)))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(134,plain,
% 2.37/2.56 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3))))),
% 2.37/2.56 inference(monotonicity,[status(thm)],[133])).
% 2.37/2.56 tff(135,plain,
% 2.37/2.56 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3)))),
% 2.37/2.56 inference(transitivity,[status(thm)],[134, 132])).
% 2.37/2.56 tff(136,plain,
% 2.37/2.56 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.37/2.56 inference(quant_inst,[status(thm)],[])).
% 2.37/2.56 tff(137,plain,
% 2.37/2.56 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[136, 135])).
% 2.37/2.56 tff(138,plain,
% 2.37/2.56 ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[137, 122, 121, 120])).
% 2.37/2.56 tff(139,plain,
% 2.37/2.56 (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3) = k9_relat_1(C!2, D!3)),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[138, 107])).
% 2.37/2.56 tff(140,plain,
% 2.37/2.56 (k9_relat_1(C!2, D!3) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3)),
% 2.37/2.56 inference(symmetry,[status(thm)],[139])).
% 2.37/2.56 tff(141,plain,
% 2.37/2.56 (r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) <=> r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(monotonicity,[status(thm)],[140, 131])).
% 2.37/2.56 tff(142,plain,
% 2.37/2.56 (r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3)))) <=> r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(symmetry,[status(thm)],[141])).
% 2.37/2.56 tff(143,plain,
% 2.37/2.56 ((~r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))))) <=> (~r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))))),
% 2.37/2.56 inference(monotonicity,[status(thm)],[142])).
% 2.37/2.56 tff(144,plain,
% 2.37/2.56 (~r1_tarski(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D!3), k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(or_elim,[status(thm)],[29])).
% 2.37/2.56 tff(145,plain,
% 2.37/2.56 (~r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[144, 143])).
% 2.37/2.56 tff(146,plain,
% 2.37/2.56 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.37/2.56 inference(bind,[status(th)],[])).
% 2.37/2.56 tff(147,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.37/2.56 inference(quant_intro,[status(thm)],[146])).
% 2.37/2.56 tff(148,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(149,plain,
% 2.37/2.56 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.37/2.56 inference(bind,[status(th)],[])).
% 2.37/2.56 tff(150,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.37/2.56 inference(quant_intro,[status(thm)],[149])).
% 2.37/2.56 tff(151,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 2.37/2.56 tff(152,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[151, 150])).
% 2.37/2.56 tff(153,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[152, 148])).
% 2.37/2.56 tff(154,plain,(
% 2.37/2.56 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.37/2.56 inference(skolemize,[status(sab)],[153])).
% 2.37/2.56 tff(155,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[154, 147])).
% 2.37/2.56 tff(156,plain,
% 2.37/2.56 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(157,plain,
% 2.37/2.56 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.37/2.56 inference(quant_inst,[status(thm)],[])).
% 2.37/2.56 tff(158,plain,
% 2.37/2.56 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[157, 156])).
% 2.37/2.56 tff(159,plain,
% 2.37/2.56 (m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[158, 104, 155])).
% 2.37/2.56 tff(160,plain,
% 2.37/2.56 (^[A: $i, B: $i, C: $i] : refl((v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 2.37/2.56 inference(bind,[status(th)],[])).
% 2.37/2.56 tff(161,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.37/2.56 inference(quant_intro,[status(thm)],[160])).
% 2.37/2.56 tff(162,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(163,plain,
% 2.37/2.56 (^[A: $i, B: $i, C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 2.37/2.56 inference(bind,[status(th)],[])).
% 2.37/2.56 tff(164,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.37/2.56 inference(quant_intro,[status(thm)],[163])).
% 2.37/2.56 tff(165,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_relset_1')).
% 2.37/2.56 tff(166,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[165, 164])).
% 2.37/2.56 tff(167,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[166, 162])).
% 2.37/2.56 tff(168,plain,(
% 2.37/2.56 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.37/2.56 inference(skolemize,[status(sab)],[167])).
% 2.37/2.56 tff(169,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[168, 161])).
% 2.37/2.56 tff(170,plain,
% 2.37/2.56 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(171,plain,
% 2.37/2.56 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.37/2.56 inference(quant_inst,[status(thm)],[])).
% 2.37/2.56 tff(172,plain,
% 2.37/2.56 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[171, 170])).
% 2.37/2.56 tff(173,plain,
% 2.37/2.56 (v1_relat_1(C!2)),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[172, 169, 159])).
% 2.37/2.56 tff(174,plain,
% 2.37/2.56 (^[A: $i, B: $i, C: $i] : refl((r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))))),
% 2.37/2.56 inference(bind,[status(th)],[])).
% 2.37/2.56 tff(175,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 2.37/2.56 inference(quant_intro,[status(thm)],[174])).
% 2.37/2.56 tff(176,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(177,plain,
% 2.37/2.56 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B))) <=> ((~r1_tarski(A, B)) | r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))), ((v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> (v1_relat_1(C) => ((~r1_tarski(A, B)) | r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))))), rewrite((v1_relat_1(C) => ((~r1_tarski(A, B)) | r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))), ((v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))))),
% 2.37/2.56 inference(bind,[status(th)],[])).
% 2.37/2.56 tff(178,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 2.37/2.56 inference(quant_intro,[status(thm)],[177])).
% 2.37/2.56 tff(179,axiom,(![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t156_relat_1')).
% 2.37/2.56 tff(180,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[179, 178])).
% 2.37/2.56 tff(181,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[180, 176])).
% 2.37/2.56 tff(182,plain,(
% 2.37/2.56 ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 2.37/2.56 inference(skolemize,[status(sab)],[181])).
% 2.37/2.56 tff(183,plain,
% 2.37/2.56 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[182, 175])).
% 2.37/2.56 tff(184,plain,
% 2.37/2.56 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | ((~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3)))))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3)))))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(185,plain,
% 2.37/2.56 ((r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3)))) | (~v1_relat_1(C!2))) <=> ((~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3)))))),
% 2.37/2.56 inference(rewrite,[status(thm)],[])).
% 2.37/2.56 tff(186,plain,
% 2.37/2.56 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3)))) | (~v1_relat_1(C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | ((~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3))))))),
% 2.37/2.56 inference(monotonicity,[status(thm)],[185])).
% 2.37/2.56 tff(187,plain,
% 2.37/2.56 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3)))) | (~v1_relat_1(C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3)))))),
% 2.37/2.56 inference(transitivity,[status(thm)],[186, 184])).
% 2.37/2.56 tff(188,plain,
% 2.37/2.56 ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3)))) | (~v1_relat_1(C!2)))),
% 2.37/2.56 inference(quant_inst,[status(thm)],[])).
% 2.37/2.56 tff(189,plain,
% 2.37/2.56 ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[188, 187])).
% 2.37/2.56 tff(190,plain,
% 2.37/2.56 (r1_tarski(k9_relat_1(C!2, D!3), k9_relat_1(C!2, u1_struct_0(k5_group_4(A!0, D!3)))) | (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[189, 183, 173])).
% 2.37/2.56 tff(191,plain,
% 2.37/2.56 (~r1_tarski(D!3, u1_struct_0(k5_group_4(A!0, D!3)))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[190, 145])).
% 2.37/2.56 tff(192,plain,
% 2.37/2.56 (~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))),
% 2.37/2.56 inference(modus_ponens,[status(thm)],[191, 94])).
% 2.37/2.56 tff(193,plain,
% 2.37/2.56 (((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D)))) | r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))),
% 2.37/2.56 inference(tautology,[status(thm)],[])).
% 2.37/2.56 tff(194,plain,
% 2.37/2.56 ((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D)))),
% 2.37/2.56 inference(unit_resolution,[status(thm)],[193, 192])).
% 2.37/2.56 tff(195,plain,
% 2.37/2.56 (v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))) <=> v1_group_1(k5_group_4(A!0, D!3))),
% 2.37/2.56 inference(monotonicity,[status(thm)],[90])).
% 2.37/2.56 tff(196,plain,
% 2.37/2.56 (v1_group_1(k5_group_4(A!0, D!3)) <=> v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))),
% 2.37/2.56 inference(symmetry,[status(thm)],[195])).
% 2.37/2.57 tff(197,plain,
% 2.37/2.57 (v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))),
% 2.37/2.57 inference(modus_ponens,[status(thm)],[43, 196])).
% 2.37/2.57 tff(198,plain,
% 2.37/2.57 (m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0) <=> m1_group_2(k5_group_4(A!0, D!3), A!0)),
% 2.37/2.57 inference(monotonicity,[status(thm)],[90])).
% 2.37/2.57 tff(199,plain,
% 2.37/2.57 (m1_group_2(k5_group_4(A!0, D!3), A!0) <=> m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)),
% 2.37/2.57 inference(symmetry,[status(thm)],[198])).
% 2.37/2.57 tff(200,plain,
% 2.37/2.57 (m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)),
% 2.37/2.57 inference(modus_ponens,[status(thm)],[45, 199])).
% 2.37/2.57 tff(201,plain,
% 2.37/2.57 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A))))))))))))))),
% 2.37/2.57 inference(bind,[status(th)],[])).
% 2.37/2.57 tff(202,plain,
% 2.37/2.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))))))))),
% 2.37/2.57 inference(quant_intro,[status(thm)],[201])).
% 2.37/2.57 tff(203,plain,
% 2.37/2.57 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))))),
% 2.37/2.57 inference(bind,[status(th)],[])).
% 2.37/2.57 tff(204,plain,
% 2.37/2.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 2.37/2.57 inference(quant_intro,[status(thm)],[203])).
% 2.37/2.57 tff(205,plain,
% 2.37/2.57 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))))),
% 2.37/2.57 inference(bind,[status(th)],[])).
% 2.37/2.57 tff(206,plain,
% 2.37/2.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 2.37/2.57 inference(quant_intro,[status(thm)],[205])).
% 2.37/2.57 tff(207,plain,
% 2.37/2.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 2.37/2.57 inference(transitivity,[status(thm)],[206, 204])).
% 2.37/2.57 tff(208,plain,
% 2.37/2.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (((~(C = k5_group_4(A, B))) | (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))) & ((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~(v1_group_1(tptp_fun_D_4(C, B, A)) & m1_group_2(tptp_fun_D_4(C, B, A), A))))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))), (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (((~(C = k5_group_4(A, B))) | (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))) & ((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~(v1_group_1(tptp_fun_D_4(C, B, A)) & m1_group_2(tptp_fun_D_4(C, B, A), A))))))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (((~(C = k5_group_4(A, B))) | (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))) & ((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~(v1_group_1(tptp_fun_D_4(C, B, A)) & m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (((~(C = k5_group_4(A, B))) | (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))) & ((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~(v1_group_1(tptp_fun_D_4(C, B, A)) & m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))))),
% 2.37/2.57 inference(bind,[status(th)],[])).
% 2.37/2.57 tff(209,plain,
% 2.37/2.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (((~(C = k5_group_4(A, B))) | (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))) & ((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~(v1_group_1(tptp_fun_D_4(C, B, A)) & m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 2.37/2.57 inference(quant_intro,[status(thm)],[208])).
% 2.37/2.57 tff(210,plain,
% 2.37/2.57 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (((~(C = k5_group_4(A, B))) | (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))) & ((C = k5_group_4(A, B)) | ((~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~(v1_group_1(tptp_fun_D_4(C, B, A)) & m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (((~(C = k5_group_4(A, B))) | (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))) & ((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~(v1_group_1(tptp_fun_D_4(C, B, A)) & m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 2.37/2.57 inference(bind,[status(th)],[])).
% 2.37/2.57 tff(211,plain,
% 2.37/2.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (((~(C = k5_group_4(A, B))) | (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))) & ((C = k5_group_4(A, B)) | ((~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~(v1_group_1(tptp_fun_D_4(C, B, A)) & m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (((~(C = k5_group_4(A, B))) | (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))) & ((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~(v1_group_1(tptp_fun_D_4(C, B, A)) & m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))),
% 2.37/2.57 inference(quant_intro,[status(thm)],[210])).
% 2.37/2.57 tff(212,plain,
% 2.37/2.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))))))),
% 2.37/2.57 inference(rewrite,[status(thm)],[])).
% 2.37/2.57 tff(213,plain,
% 2.37/2.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : ((v1_group_1(D) & m1_group_2(D, A)) => (r1_tarski(B, u1_struct_0(D)) => m1_group_2(C, D))))) <=> ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A))))))), (((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : ((v1_group_1(D) & m1_group_2(D, A)) => (r1_tarski(B, u1_struct_0(D)) => m1_group_2(C, D)))))) <=> ((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A))))))))), rewrite(((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A))))))) <=> ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))))), (((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : ((v1_group_1(D) & m1_group_2(D, A)) => (r1_tarski(B, u1_struct_0(D)) => m1_group_2(C, D)))))) <=> ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))))))), (![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : ((v1_group_1(D) & m1_group_2(D, A)) => (r1_tarski(B, u1_struct_0(D)) => m1_group_2(C, D)))))) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A))))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : ((v1_group_1(D) & m1_group_2(D, A)) => (r1_tarski(B, u1_struct_0(D)) => m1_group_2(C, D))))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A))))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : ((v1_group_1(D) & m1_group_2(D, A)) => (r1_tarski(B, u1_struct_0(D)) => m1_group_2(C, D))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A))))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : ((v1_group_1(D) & m1_group_2(D, A)) => (r1_tarski(B, u1_struct_0(D)) => m1_group_2(C, D))))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : ((v1_group_1(D) & m1_group_2(D, A)) => (r1_tarski(B, u1_struct_0(D)) => m1_group_2(C, D)))))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A))))))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A))))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : ((v1_group_1(D) & m1_group_2(D, A)) => (r1_tarski(B, u1_struct_0(D)) => m1_group_2(C, D)))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))))))))),
% 2.37/2.57 inference(bind,[status(th)],[])).
% 2.37/2.57 tff(214,plain,
% 2.37/2.57 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : ((v1_group_1(D) & m1_group_2(D, A)) => (r1_tarski(B, u1_struct_0(D)) => m1_group_2(C, D)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))))))),
% 2.37/2.57 inference(quant_intro,[status(thm)],[213])).
% 2.37/2.57 tff(215,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : ((v1_group_1(D) & m1_group_2(D, A)) => (r1_tarski(B, u1_struct_0(D)) => m1_group_2(C, D))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_group_4')).
% 2.37/2.57 tff(216,plain,
% 2.37/2.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))))))),
% 2.37/2.57 inference(modus_ponens,[status(thm)],[215, 214])).
% 2.37/2.57 tff(217,plain,
% 2.37/2.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | ((C = k5_group_4(A, B)) <=> (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))))))),
% 2.37/2.57 inference(modus_ponens,[status(thm)],[216, 212])).
% 2.37/2.57 tff(218,plain,(
% 2.37/2.57 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (((~(C = k5_group_4(A, B))) | (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))) & ((C = k5_group_4(A, B)) | ((~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~(v1_group_1(tptp_fun_D_4(C, B, A)) & m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 2.37/2.57 inference(skolemize,[status(sab)],[217])).
% 2.37/2.57 tff(219,plain,
% 2.37/2.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (((~(C = k5_group_4(A, B))) | (r1_tarski(B, u1_struct_0(C)) & ![D: $i] : (m1_group_2(C, D) | (~r1_tarski(B, u1_struct_0(D))) | (~(v1_group_1(D) & m1_group_2(D, A)))))) & ((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~(v1_group_1(tptp_fun_D_4(C, B, A)) & m1_group_2(tptp_fun_D_4(C, B, A), A))))))))))),
% 2.37/2.57 inference(modus_ponens,[status(thm)],[218, 211])).
% 2.37/2.57 tff(220,plain,
% 2.37/2.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 2.37/2.57 inference(modus_ponens,[status(thm)],[219, 209])).
% 2.37/2.57 tff(221,plain,
% 2.37/2.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))) | (~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 2.37/2.57 inference(modus_ponens,[status(thm)],[220, 207])).
% 2.37/2.57 tff(222,plain,
% 2.37/2.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))))))))),
% 2.37/2.57 inference(modus_ponens,[status(thm)],[221, 202])).
% 2.37/2.57 tff(223,plain,
% 2.37/2.57 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0)))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0)))))))))))))),
% 2.37/2.57 inference(rewrite,[status(thm)],[])).
% 2.37/2.57 tff(224,plain,
% 2.37/2.57 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((C = k5_group_4(A!0, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0)))))))))))))),
% 2.37/2.57 inference(rewrite,[status(thm)],[])).
% 2.37/2.57 tff(225,plain,
% 2.37/2.57 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((C = k5_group_4(A!0, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0)))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))))),
% 2.37/2.57 inference(monotonicity,[status(thm)],[224])).
% 2.37/2.57 tff(226,plain,
% 2.37/2.57 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((C = k5_group_4(A!0, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0)))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0)))))))))))))),
% 2.37/2.57 inference(transitivity,[status(thm)],[225, 223])).
% 2.37/2.57 tff(227,plain,
% 2.37/2.57 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((C = k5_group_4(A!0, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0)))))))))))))),
% 2.37/2.57 inference(quant_inst,[status(thm)],[])).
% 2.37/2.57 tff(228,plain,
% 2.37/2.57 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A)) | (~((~((C = k5_group_4(A, B)) | (~r1_tarski(B, u1_struct_0(C))) | (~(m1_group_2(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A)))) | (~v1_group_1(tptp_fun_D_4(C, B, A))) | (~m1_group_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k5_group_4(A, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A)))))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))),
% 2.37/2.57 inference(modus_ponens,[status(thm)],[227, 226])).
% 2.37/2.57 tff(229,plain,
% 2.37/2.57 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))),
% 2.37/2.57 inference(unit_resolution,[status(thm)],[228, 34, 33, 32, 31, 222])).
% 2.37/2.57 tff(230,plain,
% 2.37/2.57 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D)))))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D)))))))))))))),
% 2.37/2.58 inference(rewrite,[status(thm)],[])).
% 2.37/2.58 tff(231,plain,
% 2.37/2.58 (((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(D!3, u1_struct_0(D))) | (~m1_group_2(D, A!0)))))))))))) <=> ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D)))))))))))))),
% 2.37/2.58 inference(rewrite,[status(thm)],[])).
% 2.37/2.58 tff(232,plain,
% 2.37/2.58 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(D!3, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))))),
% 2.37/2.58 inference(monotonicity,[status(thm)],[231])).
% 2.37/2.58 tff(233,plain,
% 2.37/2.58 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(D!3, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D)))))))))))))),
% 2.37/2.58 inference(transitivity,[status(thm)],[232, 230])).
% 2.37/2.58 tff(234,plain,
% 2.37/2.58 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(D!3, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))),
% 2.37/2.58 inference(quant_inst,[status(thm)],[])).
% 2.37/2.58 tff(235,plain,
% 2.37/2.58 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(B, u1_struct_0(C))) | (C = k5_group_4(A!0, B)) | (~((~m1_group_2(tptp_fun_D_4(C, B, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(C, B, A!0))) | (~r1_tarski(B, u1_struct_0(tptp_fun_D_4(C, B, A!0)))) | m1_group_2(C, tptp_fun_D_4(C, B, A!0)))))) | (~((~(C = k5_group_4(A!0, B))) | (~((~r1_tarski(B, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~r1_tarski(B, u1_struct_0(D))) | (~m1_group_2(D, A!0))))))))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))),
% 2.37/2.58 inference(modus_ponens,[status(thm)],[234, 233])).
% 2.37/2.58 tff(236,plain,
% 2.37/2.58 (![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))),
% 2.37/2.58 inference(unit_resolution,[status(thm)],[235, 30, 229])).
% 2.37/2.58 tff(237,plain,
% 2.37/2.58 (((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))) | ((~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D))))))))))) <=> ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D))))))))))),
% 2.37/2.58 inference(rewrite,[status(thm)],[])).
% 2.37/2.58 tff(238,plain,
% 2.37/2.58 (((~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~(m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : (m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D)))))))))))) <=> ((~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D))))))))))),
% 2.37/2.58 inference(rewrite,[status(thm)],[])).
% 2.37/2.58 tff(239,plain,
% 2.37/2.58 (((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))) | ((~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~(m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : (m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))) <=> ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))) | ((~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D)))))))))))),
% 2.37/2.58 inference(monotonicity,[status(thm)],[238])).
% 2.37/2.58 tff(240,plain,
% 2.37/2.58 (((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))) | ((~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~(m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : (m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))) <=> ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D))))))))))),
% 2.37/2.58 inference(transitivity,[status(thm)],[239, 237])).
% 2.37/2.58 tff(241,plain,
% 2.37/2.58 ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))) | ((~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~(m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : (m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))),
% 2.37/2.59 inference(quant_inst,[status(thm)],[])).
% 2.37/2.59 tff(242,plain,
% 2.37/2.59 ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(C))) | (C = k5_group_4(A!0, D!3)) | (~(m1_group_2(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(C, D!3, A!0)))) | (~v1_group_1(tptp_fun_D_4(C, D!3, A!0))) | (~m1_group_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(C))) | (~![D: $i] : (m1_group_2(C, D) | (~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))))))))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D)))))))))),
% 2.37/2.59 inference(modus_ponens,[status(thm)],[241, 240])).
% 2.37/2.59 tff(243,plain,
% 2.37/2.59 ((~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), A!0)) | (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D)))))))))),
% 2.37/2.59 inference(unit_resolution,[status(thm)],[242, 236])).
% 2.37/2.59 tff(244,plain,
% 2.37/2.59 (~((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D))))))))),
% 2.37/2.59 inference(unit_resolution,[status(thm)],[243, 200, 197])).
% 2.37/2.59 tff(245,plain,
% 2.37/2.59 (((~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3)) | (~((~m1_group_2(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0), A!0)) | (~v1_group_1(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0))) | (~r1_tarski(D!3, u1_struct_0(tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), tptp_fun_D_4(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D!3, A!0)))))) | (~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D)))))))) | ((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D))))))),
% 2.37/2.59 inference(tautology,[status(thm)],[])).
% 2.45/2.61 tff(246,plain,
% 2.45/2.61 ((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D)))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[245, 244])).
% 2.45/2.61 tff(247,plain,
% 2.45/2.61 ((~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D))))))) | (~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D)))))),
% 2.45/2.61 inference(tautology,[status(thm)],[])).
% 2.45/2.61 tff(248,plain,
% 2.45/2.61 ((~((~(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))) = k5_group_4(A!0, D!3))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D))))))) | (~((~r1_tarski(D!3, u1_struct_0(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3)))))) | (~![D: $i] : ((~v1_group_1(D)) | (~m1_group_2(D, A!0)) | (~r1_tarski(D!3, u1_struct_0(D))) | m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, D!3)), u1_group_1(k5_group_4(A!0, D!3))), D)))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[247, 90])).
% 2.45/2.61 tff(249,plain,
% 2.45/2.61 ($false),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[248, 246, 194])).
% 2.45/2.61 % SZS output end Proof
% 2.45/2.61 % E exiting
%------------------------------------------------------------------------------